Aristotle (384 B.C.E.—322 B.C.E.)

Aristotle is a towering figure in ancient Greek philosophy, who made important contributions to logic, criticism, rhetoric, physics, biology, psychology, mathematics, metaphysics, ethics, and politics. He was a student of Plato for twenty years but is famous for rejecting Plato’s theory of forms. He was more empirically minded than both Plato and Plato’s teacher, Socrates.

A prolific writer, lecturer, and polymath, Aristotle radically transformed most of the topics he investigated. In his lifetime, he wrote dialogues and as many as 200 treatises, of which only 31 survive. These works are in the form of lecture notes and draft manuscripts never intended for general readership. Nevertheless, they are the earliest complete philosophical treatises we still possess.

As the father of western logic, Aristotle was the first to develop a formal system for reasoning. He observed that the deductive validity of any argument can be determined by its structure rather than its content, for example, in the syllogism: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Even if the content of the argument were changed from being about Socrates to being about someone else, because of its structure, as long as the premises are true, then the conclusion must also be true. Aristotelian logic dominated until the rise of modern propositional logic and predicate logic 2000 years later.

The emphasis on good reasoning serves as the backdrop for Aristotle’s other investigations. In his natural philosophy, Aristotle combines logic with observation to make general, causal claims. For example, in his biology, Aristotle uses the concept of species to make empirical claims about the functions and behavior of individual animals. However, as revealed in his psychological works, Aristotle is no reductive materialist. Instead, he thinks of the body as the matter, and the psyche as the form of each living animal.

Though his natural scientific work is firmly based on observation, Aristotle also recognizes the possibility of knowledge that is not empirical. In his metaphysics, he claims that there must be a separate and unchanging being that is the source of all other beings. In his ethics, he holds that it is only by becoming excellent that one could achieve eudaimonia, a sort of happiness or blessedness that constitutes the best kind of human life.

Aristotle was the founder of the Lyceum, a school based in Athens, Greece; and he was the first of the Peripatetics, his followers from the Lyceum. Aristotle’s works, exerted tremendous influence on ancient and medieval thought and continue to inspire philosophers to this day.

Table of Contents

  1. Life and Lost Works
  2. Analytics or “Logic”
    1. The Meaning and Purpose of Logic
    2. Demonstrative Syllogistic
    3. Induction, Experience, and Principles
    4. Rhetoric and Poetics
  3. Theoretical Philosophy
    1. Natural Philosophy
      1. Cosmology and Geology
      2. Biology
      3. Psychology
    2. Mathematics
    3. First Philosophy
  4. Practical Philosophy
    1. Habituation and Excellence
    2. Ethical Deliberation
    3. Self and Others
    4. The Household and the State
  5. Aristotle’s Influence
  6. Abbreviations
    1. Abbreviations of Aristotle’s Works
    2. Other Abbreviations
  7. References and Further Reading
    1. Aristotle’s Complete Works
    2. Secondary Sources
      1. Life and Early Works
      2. Logic
      3. Theoretical Philosophy
      4. Practical Philosophy
      5. Aristotle’s Influence

1. Life and Lost Works

Though our main ancient source on Aristotle’s life, Diogenes Laertius, is of questionable reliability, the outlines of his biography are credible. Diogenes reports that Aristotle’s Greek father, Nicomachus, served as private physician to the Macedonian king Amyntas (DL 5.1.1). At the age of seventeen, Aristotle migrated to Athens where he joined the Academy, studying under Plato for twenty years (DL 5.1.9). During this period Aristotle acquired his encyclopedic knowledge of the philosophical tradition, which he draws on extensively in his works.

Aristotle left Athens around the time Plato died, in 348 or 347 B.C.E. One explanation is that as a resident alien, Aristotle was excluded from leadership of the Academy in favor of Plato’s nephew, the Athenian citizen Speusippus. Another possibility is that Aristotle was forced to flee as Philip of Macedon’s expanding power led to the spread of anti-Macedonian sentiment in Athens (Chroust 1967). Whatever the cause, Aristotle subsequently moved to Atarneus, which was ruled by another former student at the Academy, Hermias. During his three years there, Aristotle married Pythias, the niece or adopted daughter of Hermias, and perhaps engaged in negotiations or espionage on behalf of the Macedonians (Chroust 1972). Whatever the case, the couple relocated to Macedonia, where Aristotle was employed by Philip, serving as tutor to his son, Alexander the Great (DL 5.1.3–4). Aristotle’s philosophical career was thus directly entangled with the rise of a major power.

After some time in Macedonia, Aristotle returned to Athens, where he founded his own school in rented buildings in the Lyceum. It was presumably during this period that he authored most of his surviving texts, which have the appearance of lecture transcripts edited so they could be read aloud in Aristotle’s absence. Indeed, this must have been necessary, since after his school had been in operation for thirteen years, he again departed from Athens, possibly because a charge of impiety was brought against him (DL 5.1.5). He died at age 63 in Chalcis (DL 5.1.10).

Diogenes tells us that Aristotle was a thin man who dressed flashily, wearing a fashionable hairstyle and a number of rings. If the will quoted by Diogenes (5.1.11–16) is authentic, Aristotle must have possessed significant personal wealth, since it promises a furnished house in Stagira, three female slaves, and a talent of silver to his concubine, Herpyllis. Aristotle fathered a daughter with Pythias and, with Herpyllis, a son, Nicomachus (named after his grandfather), who may have edited Aristotle’s Nicomachean Ethics. Unfortunately, since there are few extant sources on Aristotle’s life, one’s judgment about the accuracy and completeness of these details depends largely on how much one trusts Diogenes’ testimony.

Since commentaries on Aristotle’s work have been produced for around two thousand years, it is not immediately obvious which sources are reliable guides to his thought. Aristotle’s works have a condensed style and make use of a peculiar vocabulary. Though he wrote an introduction to philosophy, a critique of Plato’s theory of forms, and several philosophical dialogues, these works survive only in fragments. The extant Corpus Aristotelicum consists of Aristotle’s recorded lectures, which cover almost all the major areas of philosophy. Before the invention of the printing press, handwritten copies of these works circulated in the Near East, northern Africa, and southern Europe for centuries. The surviving manuscripts were collected and edited in August Immanuel Bekker’s authoritative 1831–1836 Berlin edition of the Corpus (“Bekker” 1910). All references to Aristotle’s works in this article follow the standard Bekker numbering.

The extant fragments of Aristotle’s lost works, which modern commentators sometimes use as the basis for conjectures about his philosophical development, are noteworthy. A fragment of his Protrepticus preserves a striking analogy according to which the psyche or soul’s attachment to the body is a form of punishment:

The ancients blessedly say that the psyche pays penalty and that our life is for the atonement of great sins. And the yoking of the psyche to the body seems very much like this. For they say that, as Etruscans torture captives by chaining the dead face to face with the living, fitting each to each part, so the psyche seems to be stretched throughout, and constrained to all the sensitive members of the body. (Pistelli 1888, 47.24–48.1)

According to this allegedly inspired theory, the fetters that bind the psyche to the body are similar to those by which the Etruscans torture their prisoners. Just as the Etruscans chain prisoners face to face with a dead body so that each part of the living body touches a part of the corpse, the psyche is said to be aligned with the parts of one’s living body. On this view, the psyche is embodied as a painful but corrective atonement for its badness. (See Bos 2003 and Hutchinson and Johnson’s webpage).

The incompatibility of this passage with Aristotle’s view that the psyche is inseparable from the body (discussed below) has been explained in various ways. Neo-Platonic commentators distinguish between Aristotle’s esoteric and exoteric writings, that is, writings intended for circulation within his school, and writings like the Protrepticus intended for a broader reading public (Gerson 2005, 47–75). Some modern scholars have argued to the contrary that the imprisonment of the psyche in the body indicates that Aristotle was still a Platonist at the time he composed the Protrepticus, which must have been written earlier than his mature works (Jaeger 1948, 100). Aristotle’s dialogue Eudemus, which contains arguments for the immortality of the psyche, and his Politicus, which is about the ideal statesman, seem to corroborate the view that Aristotle’s exoteric works hold much that is Platonic in spirit (Chroust 1965; 1966). The latter contains the seemingly Platonic assertion that “the good is the most exact of measures” (Kroll 1902, 168: 927b4–5).

But not all agree. Owen (1968, 162–163) argues that Aristotle’s fundamental logical distinction between individual and species depends on an antecedent break with Plato. According to this view, Aristotle’s On Ideas (Fine 1993), a collection of arguments against Platonic forms, shows that Aristotle rejected Platonism early in his career, though he later became more sympathetic to the master’s views. However, as Lachterman (1980) points out, such historical theses depend on substantive hermeneutical assumptions about how to read Aristotle and on theoretical assumptions about what constitutes a philosophical system. This article focuses not on this historical debate but on the theories propounded in Aristotle’s extant works.

2. Analytics or “Logic”

Aristotle is usually identified as the founder of logic in the West (although autonomous logical traditions also developed in India and China), where his “Organon,” consisting of his works the Categories, On Interpretation, Prior Analytics, Posterior Analytics, Sophistical Refutations, and Topics, long served as the traditional manuals of logic. Two other works—Rhetoric and Poetics—are not about logic, but also concern how to communicate to an audience. Curiously, Aristotle never used the words “logic” or “organon” to refer to his own work but calls this discipline “analytics.” Though Aristotelian logic is sometimes referred to as an “art” (Ross 1940, iii), it is clearly not an art in Aristotle’s sense, which would require it to be productive of some end outside itself. Nevertheless, this article follows the convention of referring to the content of Aristotle’s analytics as “logic.”

a. The Meaning and Purpose of Logic

What is logic for Aristotle? On Interpretation begins with a discussion of meaning, according to which written words are symbols of spoken words, while spoken words are symbols of thoughts (Int.16a3–8). This theory of signification can be understood as a semantics that explains how different alphabets can signify the same spoken language, while different languages can signify the same thoughts. Moreover, this theory connects the meaning of symbols to logical consequence, since commitment to some set of utterances rationally requires commitment to the thoughts signified by those utterances and to what is entailed by them. Hence, though Cook Wilson (1926, 30–33) correctly notes that Aristotle nowhere defines logic, it may be called the science of thinking, where the role of the science is not to describe ordinary human reasoning but rather to demonstrate what one ought to think given one’s other commitments. Though the elements of Aristotelian logic are implicit in our conscious reasoning, Aristotelian “analysis” makes explicit what was formerly implicit (Cook Wilson 1926, 49).

Aristotle shows how logic can demonstrate what one should think, given one’s commitments, by developing the syntactical concepts of truth, predication, and definition. In order for a written sentence, utterance, or thought to be true or false, Aristotle says, it must include at least two terms: a subject and a predicate. Thus, a simple thought or utterance such as “horse” is neither true nor false but must be combined with another term, say, “fast” in order to form a compound—“the horse is fast”—that describes reality truly or falsely. The written sentence “the horse is fast” has meaning insofar as it signifies the spoken sentence, which in turn has meaning in virtue of its signifying the thought that the horse is fast (Int.16a10–18, Cat.13b10–12, DA 430a26–b1). Aristotle holds that there are two kinds of constituents of meaningful sentences: nouns and their derivatives, which are conventional symbols without tense or aspect; and verbs, which have a tense and aspect. Though all meaningful speech consists of combinations of these constituents, Aristotle limits logic to the consideration of statements, which assert or deny the presence of something in the past, present, or future (Int.17a20–24).

Aristotle analyzes statements as cases of predication, in which a predicate P is attributed to a subject S as in a sentence of the form “S is P.” Since he holds that every statement expresses something about being, statements of this form are to be read as “S is (exists) as a P” (Bäck 2000, 11). In every true predication, either the subject and predicate are of the same category, or the subject term refers to a substance while the predicate term refers to one of the other categories. The primary substances are individuals, while secondary substances are species and genera composed of individuals (Cat.2a11–18). This distinction between primary and secondary reflects a dependence relation: if all the individuals of a species or genus were annihilated, the species and genus could not, in the present tense, be truly predicated of any subject.

Every individual is of a species and that species is predicated of the individual. Every species is the member of a genus, which is predicated of the species and of each individual of that species (Cat.2b13–22). For example, if Callias is of the species “man,” and the species is a member of the genus “animal,” then “man” is predicated of Callias, and “animal” is predicated both of “man” and of Callias. The individual, Callias, inherits the predicate “animal” in virtue of being of the species “man.” But inheritance stops at the individual and does not apply to its proper parts. For example, “man” is not truly predicated of Callias’ hand. A genus can be divided with reference to the specific differences among its members; for example, “biped” differentiates “man” from “horse.”

While no definition can be given of an individual or primary substance such as Callias, when one gives the genus and all the specific differences possessed by a kind of thing, one can define a thing’s species. A specific difference is a predicate that falls under one of the categories. Thus, Aristotelian categories can be seen as a taxonomical scheme, a way of organizing predicates for discovery, or as a metaphysical doctrine about the kinds of beings there are. But any reading must accommodate Aristotle’s views that primary substances are never predicated of a subject (Cat.3a6), that a predicate may fall under multiple categories (Cat.11a20–39), and that some terms, such as “good,” are predicated in all the categories (NE 1096a23–29). Moreover, definitions are reached not by demonstration but by other kinds of inquiry, such as dialectic, the art by which one makes divisions in a genus; and induction, which can reveal specific differences from the observation of individual examples.

b. Demonstrative Syllogistic

Syllogistic reasoning builds on Aristotle’s theory of predication, showing how to reason from premises to conclusions. A syllogism is a discourse in which when taking some statements as premises a different statement can be shown to follow as a conclusion (AnPr.24b18–22). The basic form of the Aristotelian syllogism involves a major premise, a minor premise, and a conclusion, so that it has the form

If A is predicated of all B,

And B is predicated of all C,

Then A is predicated of all C.

This is an assertion of formal logic, since by removing the values of the variables A, B, and C, one treats the inference formally, such that the values of the subject A and predicates B and C are not given as part of the syllogistic form (Łukasiewicz, 10–14).

Though this form can be utilized in dialectic, in which the major term A is related to C through the middle term B credibly rather than necessarily (AnPo.81b10–23), Aristotle is mainly concerned with how to use syllogistic in what he calls demonstrative reasoning, that is, in inference from certain premises to a certain conclusion. A demonstrative syllogism is not concerned with a mere opinion but proves a cause, that is, answers a “why” question (AnPo.85b 23–26).

The validity of a syllogism can be tested through comparison of four basic types of assertions: All S are P (A), No S are P (E), Some S are P (I), and Some S are not P (O). The truth conditions of these assertions are determined relationally: through contradiction, in which if one of the assertions is true, the other must be false; contrariety, in which both assertions cannot be true; and subalternation, in which the universal assertion’s being true requires that the particular assertion must be true, as well. These relationships are summed up in the traditional square of opposition used by medieval Aristotelian logicians. (see Groarke, Aristotle: Logic).figure 1

Figure 1: The Traditional Square of Opposition illustrates the relations between the fundamental judgment-forms in Aristotelian syllogistic: (A) All S are P, (E) No S are P, (I) Some S are P, and (O) Some S are not P.

Syllogistic may be employed dialectically when the premises are accepted on the authority of common opinion, from tradition, or from the wise. In any dialectical syllogism, the premises can be generally accepted opinions rather than necessary principles (Top.100a25–b21). At least some premises in rhetorical proofs must be not necessary but only probable, happening only for the most part.

When the premises are known, and conclusions are shown to follow from those premises, one gains knowledge by demonstration. Demonstration is necessary (AnPo.73a21–27) because the conclusion of a demonstrative syllogism predicates something that is either necessarily true or necessarily false of the subject of the premise. One has demonstrative knowledge when one knows the premises and has derived a necessary conclusion from them, since the cause given in the premises explains why the conclusion is so (AnPo.75a12–17, 35–37). Consequently, valid demonstration depends on the known premises containing terms for the genus of which the species in the conclusion is a member (AnPo.76a29–30).

One interesting problem that arises within Aristotle’s theory of demonstration concerns the connection between temporality and necessity. By the principle of excluded middle, necessarily, either there will be a sea-battle tomorrow or there will not be a sea-battle tomorrow. But since the sea-battle itself has yet neither come about nor failed to come about, it seems that one must say, paradoxically, that one alternative is necessary but that either alternative might come about (Int.19a22–34). The question of how to account for unrealized possibilities and necessities is part of Aristotle’s modal syllogistic, which is discussed at length in his Prior Analytics. For a discussion, see Malink (2013).

c. Induction, Experience, and Principles

Whenever a speaker reasons from premises, an auditor can ask for their demonstration. The speaker then needs to adduce additional premises for that demonstration. But if this line of questioning went on interminably, no demonstration could be made, since every premise would require a further demonstration, ad infinitum. In order to stop an infinite regress of premises, Aristotle postulates that for an inference to count as demonstrative, one must know its indemonstrable premises (AnPo.73a16–20). Thus, demonstrative science depends on the view that all teaching and learning proceed from already present knowledge (AnPo.72b5–20). In other words, the possibility of making a complete argument, whether inductive or deductive, depends on the reasoner possessing the concept in question.

The acquisition of concepts must in some way be perceptual, since Aristotle says that universals come to rest in the soul through experience, which comes about from many memories of the same thing, which in turn comes about by perception (AnPo.99b32–100a9). However, Aristotle holds that some concepts are already manifested in one’s perceptual experience: children initially call all men father and all women mother, only later developing the capacity to apply the relevant concepts to particular individuals (Phys.184b3–5). As Cook Wilson (1926, 45) puts it, perception is in a way already of a universal. Upon learning to speak, the child already possesses the concept “mother” but does not grasp the conditions of its correct application. The role of perception, and hence of memory and experience, is then not to supply the child with universal concepts but to fix the conditions under which they are correctly predicated of an individual or species. Hence the ability to arrive at definitions, which serve as starting points of a science, rests on the human being’s natural capacity to use language and on the culturally specific social and political conditions in which that capacity is manifested (Winslow 2013, 45–49).

While deduction proceeds by a form of syllogistic reasoning in which the major and minor premise both predicate what is necessarily true of a subject, inductive reasoning moves from particulars to universals, so it is impossible to gain knowledge of universals except by induction (AnPo.81a38–b9). This movement, from the observation of the same occurrence, to an experience that emerges from many memories, to a universal judgment, is a cognitive process by which human beings understand reality (see AnPo.88a2–5, Met.980b28–981a1, EN 1098b2–4, 1142a12).

But what makes such an inference a good one? Aristotle seems to say an inductive inference is sound when what is true in each case is also true of the class under which the cases fall (AnPr.68b15–29). For example, it is inferred from the observation that each kind of bileless animal (men, horses, mules, and so on) is long-lived just when the following syllogism is sound: (1) All men, horses, mules, and so on are long-lived; (2) All long-lived animals are bileless; therefore (3) all men, horses, mules, and so on are bileless (see Groarke sections 10 and 11). However, Aristotle does not think that knowledge of universals is pieced together from knowledge of particulars but rather he thinks that induction is what allows one to actualize knowledge by grasping how the particular case falls under the universal (AnPr.67a31–b5).

A true definition reveals the essential nature of something, what it is to be that thing (AnPo.90b30–31). A sound demonstration shows what is necessary of an observed subject (AnPo.90b38–91a5). It is essential, however, that the observation on which a definition is based be inductively true, that is, that it be based on causes rather than on chance. Regardless of whether one is asking what something is in a definition or why something is the way it is by giving its cause, it is only when the principles or starting points of a science are given that demonstration becomes possible. Since experience is what gives the principles of each science (AnPr.46a17–27), logic can only be employed at a later stage to demonstrate conclusions from these starting points. This is why logic, though it is employed in all branches of philosophy, is not a part of philosophy. Rather, in the Aristotelian tradition, logic is an instrument for the philosopher, just as a hammer and anvil are instruments for the blacksmith (Ierodiakonou 1998).

d. Rhetoric and Poetics

Just as dialectic searches for truth, Aristotelian rhetoric serves as its counterpart (Rhet.1354a1), searching for the means by which truth can be grasped through language. Thus, rhetorical demonstration, or enthymeme, is a kind of syllogism that strictly speaking belongs to dialectic (Rhet.1355a8–10). Because rhetoric uses the particularly human capacity of reason to formulate verbal arguments, it is the art that can cause the most harm when it is used wrongly. It is thus not a technique for persuasion at any cost, as some Sophists have taught, but a fundamentally second-personal way of using language that allows the auditor to reach a judgment (Grimaldi 1972, 3–5). More fundamentally, rhetoric is defined as the detection of persuasive features of each subject matter (Rhet.1355b12–22).

Proofs given in speech depend on three things: the character (ethos) of the speaker, the disposition (pathos) of the audience, and the meaning (logos) of the sounds and gestures used (Rhet.1356a2–6). Rhetorical proofs show that the speaker is worthy of credence, producing an emotional state (pathos) in the audience, or demonstrating a consequence using the words alone. Aristotle holds that ethos is the most important of these elements, since trust in the speaker is required if one is to believe the speech. However, the best speech balances ethos, pathos, and logos. In rhetoric, enthymemes play a deductive role, while examples play an inductive role (Rhet.1356b11–18).

The deductive form of rhetoric, enthymeme, is a dialectical syllogism in which the probable premise is suppressed so that one reasons directly from the necessary premise to the conclusion. For example, one may reason that an animal has given birth because she has milk (Rhet.1357b14–16) without providing the intermediate premise. Aristotle also calls this deductive form of inference “reasoning by signs” or “reasoning from evidence,” since the animal’s having milk is a sign of, or evidence for, her having given birth. Though the audience seemingly “immediately” grasps the fact of birth without it being given in perception, the passage from the perception to the fact is inferential and depends on the background assumption of the suppressed premise.

The inductive form of rhetoric, reasoning from example, can be illustrated as follows. Peisistratus in Athens and Theagenes in Megara both petitioned for guards shortly before establishing themselves as tyrants. Thus, someone plotting a tyranny requests a guard (Rhet.1357b30–37). This proof by example does not have the force of necessity or universality and does not count as a case of scientific induction, since it is possible someone could petition for a guard without plotting a tyranny. But when it is necessary to base some decision, for example, whether to grant a request for a bodyguard, on its likely outcome, one must look to prior examples. It is the work of the rhetorician to know these examples and to formulate them in such a way as to suggest definite policies on the basis of that knowledge.

Rhetoric is divided into deliberative, forensic, and display rhetoric. Deliberative rhetoric is concerned with the future, namely with what to do, and the deliberative rhetorician is to discuss the advantages and harms associated with a specific course of action. Forensic rhetoric, typical of the courtroom, concerns the past, especially what was done and whether it was just or unjust. Display rhetoric concerns the present and is about what is noble or base, that is, what should be praised or denigrated (Rhet.1358b6–16). In all these domains, the rhetorician practices a kind of reasoning that draws on similarities and differences to produce a likely prediction that is of value to the political community.

A common characteristic of insightful philosophers, rhetoricians, and poets is the capacity to observe similarities in things that are unlike, as Archytas did when he said that a judge and an alter are kindred, since someone who has been wronged has recourse to both (Rhet.1412a10–14). This noticing of similarities and differences is part of what separates those who are living the good life from those who are merely living (Sens.437a2–3). Likewise, the highest achievement of poetry is to use good metaphors, since to make metaphors well is to contemplate what is like (Poet.1459a6–9). Poetry is thus closely related to both philosophy and rhetoric, though it differs from them in being fundamentally mimetic, imitating reality through an artistic form.

Imitation in poetry is achieved by means of rhythm, language, and harmony (Poet.1447a13–16, 21–22). While other arts share some or all these elements—painting imitates visually by the same means, while dance imitates only through rhythm—poetry is a kind of vocalized music, in which voice and discursive meaning are combined. Aristotle is interested primarily in the kinds of poetry that imitate human actions, which fall into the broad categories of comedy and tragedy. Comedy is an imitation of worse types of people and actions, which reflect our lower natures. These imitations are not despicable or painful, but simply ridiculous or distorted, and observing them gives us pleasure (Poet.1449a31–38). Aristotle wrote a book of his Poetics on comedy, but the book did not survive. Hence, through a historical accident, the traditions of aesthetics and criticism that proceed from Aristotle are concerned almost completely with tragedy.

Tragedy imitates actions that are excellent and complete. As opposed to comedy, which is episodic, tragedy should have a single plot that ends in a presentation of pity and fear and thus a catharsis—a cleansing or purgation—of the passions (Poet.1449b24–28). (As discussed below, the passions or emotions also play an important role in Aristotle’s practical philosophy.) The most important aspect of a tragedy is how it uses a story or myth to lead the psyches of its audience to this catharsis (Poet.1450a32–34). Since the beauty or fineness of a thing—say, of an animal—consists in the orderly arrangement of parts of a definite magnitude (Poet.1450b35–38), the parts of a tragedy should also be proportionate.

A tragedy’s ability to lead the psyche depends on its myth turning at a moment of recognition at which the central character moves from a state of ignorance to a state of knowledge. In the best case, this recognition coincides with a reversal of intention, such as in Sophocles’ Oedipus, in which Oedipus recognizes himself as the man who was prophesied to murder his father and marry his mother. This moment produces pity and fear in the audience, fulfilling the purpose of tragic imitation (Poet.1452a23–b1). The pity and fear produced by imitative poetry are the source of a peculiar form of pleasure (Poet.1453b11–14). Though the imitation itself is a kind of technique or art, this pleasure is natural to human beings. Because of this potential to produce emotions and lead the psyche, poetics borders both on what is well natured and on madness (Poet.1455a30–34).

Why do people write plays, read stories, and watch movies? Aristotle thinks that because a series of sounds with minute differences can be strung together to form conventional symbols that name particular things, hearing has the accidental property of supporting meaningful speech, which is the cause of learning (Sens.437a10–18). Consequently, though sound is not intrinsically meaningful, voice can carry meaning when it “ensouled,” transmitting an appearance about how absent things might be (DA 420b5-10, 27–33). Poetry picks up on this natural capacity, artfully imitating reality in language without requiring that things are actually the way they are presented as being (Poet.1447a13–16).

The poet’s consequent power to lead the psyche through true or false imitations, like the rhetorician’s power to lead it through persuasive speech, leads to a parallel question: how should the poet use his power? Should the poet imitate things as they are, or as they should be? Though it is clear that the standard of correctness in poetry and politics is not the same (Poet.1460b13–1461a1), the question of how and to what extent the state should constrain poetic production remains unresolved.

3. Theoretical Philosophy

Aristotle’s classification of the sciences makes a distinction between theoretical philosophy, which aims at contemplation, and practical philosophy, which aims at action or production. Within theoretical philosophy, first philosophy studies objects that are motionless and separate from material things, mathematics studies objects that are motionless but not separate, and natural philosophy studies objects that are in motion and not separate (Met.1026a6–22).

This threefold distinction among the beings that can be contemplated corresponds to the level of precision that can be attained by each branch of theoretical philosophy. First philosophy can be perfectly exact because there is no variation among its objects and thus it has the potential to give one knowledge in the most profound sense. Mathematics is also absolutely certain because its objects are unchanging, but since there are many mathematical objects of a given kind (for example, one could draw a potentially infinite number of different triangles), mathematical proofs require a peculiar method that Aristotle calls “abstraction.” Natural philosophy gives less exact knowledge because of the diversity and variability of natural things and thus requires attention to particular, empirical facts. Studies of nature—including treatises on special sciences like cosmology, biology, and psychology—account for a large part of Aristotle’s surviving writings.

a. Natural Philosophy

Aristotle’s natural philosophy aims for theoretical knowledge about things that are subject to change. Whereas all generated things, including artifacts and products of chance, have a source that generates them, natural change is caused by a thing’s inner principle and cause, which may accordingly be called the thing’s “nature” (Phys.192b8–20). To grasp the nature of a thing is to be able to explain why it was generated essentially: the nature of a thing does not merely contribute to a change but is the primary determinant of the change as such (Waterlow 1982, p.28).

Though some hold that Aristotle’s principles are epistemic, explanatory concepts, principles are best understood ontologically as unique, continuous natures that govern the generation and self-preservation of natural beings. To understand a thing’s nature is primarily to grasp “how a being displays itself by its nature.” Such a grasp counts as a correct explanation only insofar as it constitutes a form of understanding of beings in themselves as they give themselves (Winslow 2007, 3–7).

Aristotle’s description of principles as the start and end of change (Phys.235b6) distinguishes between two kinds of natural change. Substantial change occurs when a substance is generated (Phys.225a1–5), for example, when the seed of a plant gives rise to another plant of the same kind. Non-substantial change occurs when a substance’s accidental qualities are affected, for example, the change of color in a ripening pomegranate. Aristotelians describe this as the activity of contraries of blackness and whiteness in the plant’s material in which the fruit of the pomegranate, as its juices become colored by ripening, itself becomes shaded, changing to a purple color (de Coloribus 796a20–26). Ripening occurs when heat burns up the air in the part of the plant near the ground, causing convection that alters the originally light color of the fruit to its dark contrary (de Plantis 820b19–23). Both kinds of change are caused by the plant’s containing in itself a principle of change. In substantial change, a new primary substance is generated; in non-substantial change, some property of preexisting substance changes to a contrary state.

A process of change is completely described when its four causes are given. This can be illustrated with Aristotle’s favorite example of the production of a bronze sculpture. The (1) material cause of the change is given when the underlying matter of the thing has been described, such as the bronze matter of which a statue is composed. The (2) formal cause is given when one says what kind of thing the thing is, for example, “sphere” for a bronze sphere or “Callias” for a bronze statue of Callias. The (3) efficient cause is given when one says what brought the change about, for example, when one names the sculptor. The (4) final cause is given when one says the purpose of the change, for example, when one says why the sculptor chose to make the bronze sphere (Phys.194b16–195a2).

In natural change the principle of change is internal, so the formal, efficient, and final causes typically coincide. Moreover, in such cases, the metaphysical and epistemological sides of causal explanation are normally unified: a formal cause counts both as a thing’s essence—what it is to be that thing—and as its rational account or reason for being (Bianchi 2014, 35). Thus, when speaking of natural changes rather than the making of an artifact, Aristotle will usually offer “hylomorphic” descriptions of the natural being as a compound of matter and form.

Because Aristotle holds that a thing’s underlying nature is analogous to the bronze in a statue (Phys.191a7–12), some have argued that the underlying thing refers to “prime matter,” that is, to an absolutely indeterminate matter that has no form. But Cook (1989) has shown that the underlying thing normally means matter that already has some form. Indeed, Aristotle claims that the matter of perceptible things has no separate existence but is always already informed by a contrary (Gen et Corr.329a25–27). The matter that traditional natural philosophy calls the “elements”—fire, water, air, and earth—already has the form of the basic contraries, hot and cold, and moist and dry, so that, for example, fire is matter with a hot and dry form (Gen et Corr.330a25–b4). Thus, even in the most basic cases, matter is always actually informed, even though the form is potentially subject to change. For example, throwing water on a fire cools and moistens it, and bringing about a new quality in the underlying material. Thus, Aristotle sometimes describes natural powers as being latent or active “in the material” (Meteor.370b14–18).

Aristotle’s general works in natural philosophy offer analyses of concepts necessarily assumed in accounts of natural processes, including time, change, and place. In general, Aristotle will describe changes that occur in time as arising from a potential, which is actualized when the change is complete. However, what is actual is logically prior to what is potential, since a potentiality aims at its own actualization and thus must be defined in terms of what is actual. Indeed, generically the actual is also temporally prior to potentiality, since there must invariably be a preexisting actuality that brings the potentiality to its own actualization (Met.1049b4–19). Perhaps because of the priority of the actual to the potential, whenever Aristotle speaks of natural change, he is concerned with a field of naturalistic inquiry that is continuous rather than atomistic and purposeful or teleological rather than mechanical. In his more specific naturalistic works, Aristotle lays out a program of specialized studies about the heavens and Earth, living things, and the psyche.

i. Cosmology and Geology

Aristotle’s cosmology depends on the basic observation that while bodies on Earth either rise to a limit or fall to Earth, heavenly bodies keep moving, without any apparent external force being exerted on them (DC 284a10–15). On the basis of this observation, he distinguishes between circular motion, which is operative in the “superlunary” heavens, and rectilinear motion on “sublunary” Earth below the Moon. Since all sublunary bodies move in a rectilinear pattern, the heavenly bodies must be composed of a different body that naturally moves in a circle (DC 269a2–10, Meteor.340b6–15). This body cannot have an opposite, because there is no opposite to circular motion (DC 270a20, compare 269a19–22). Indeed, since there is nothing to oppose its motion, Aristotle supposes that this fifth element, which he calls “aether,” as well as the heavenly bodies composed of it, move eternally (DC 275b1–5, 21–25).

In Aristotle’s view the heavens are ungenerated, neither coming to be nor passing away (DC 279b18–21, 282a24–30). Aristotle defines time as the number of motion, since motion is necessarily measured by time (Phys.224a24). Thus, the motion of the eternal bodies is what makes time, so the life and being of sublunary things depends on them. Indeed, Aristotle says that their own time is eternal or “aeon.”

Noticing that water naturally forms spherical droplets and that it flows towards the lowest point on a plane, Aristotle concludes that both the heavens and the earth are spherical (DC 287b1–14). This is further confirmed by observations of eclipses (DC 297b23–31) and that different stars are visible at different latitudes (DC 297b14–298a22).

The gathering of such observations is an important part of Aristotle’s scientific procedure (AnPr.46a17–22) and sets his theories above those of the ancients that lacked such “experience” (Phys.191a24–27). Just as in his biology, where Aristotle draws on animal anatomy observed at sacrifices (HA 496b25) and records reports from India (HA 501a25), so in his astronomy he cites Egyptian and Babylonian observations of the planets (DC 292a4–9). By gathering evidence from many sources, Aristotle is able to conclude that the stars and the Moon are spherical (DC 291b11–20) and that the Milky Way is an appearance produced by the sight of many stars moving in the outermost sphere (Meteor.346a16–24).

Assuming the hypothesis that the Earth does not move (DC 289b6–7), Aristotle argues that there are in the heavens both stars, which are large and distant from earth, and planets, which are smaller and closer. The two can be distinguished since stars appear to twinkle while planets do not (Aristotle somewhat mysteriously attributes the twinkling stars to their distance from the eye of the observer) (DC 290b14–24). Unlike earthly creatures, which move because of their distinct organs or parts, both the moving stars and the unmoving heaven that contains them are spherical (DC 289a30–b11). As opposed to superlunary (eternal) substances, sublunary beings, like clouds and human beings, participate in the eternal through coming to be and passing away. In doing so, the individual or primary substance is not preserved, but rather the species or secondary substance is preserved (as we shall see below, the same thought is utilized in Aristotle’s explanation of biological reproduction) (Gen et Corr.338b6–20).

Aristotle holds that the Earth is composed of four spheres, each of which is dominated by one of the four elements. The innermost and heaviest sphere is predominantly earth, on which rests upper spheres of water, air, and fire. The sun acts to burn up or vaporize the water, which rises to the upper spheres when heated, but when cooled later condenses into rain (Meteor.354b24–34). If unqualified necessity is restricted to the superlunary sphere, teleology—the seeking of ends that may or may not be brought about—seems to be limited to the sublunary sphere.

Due to his belief that the Earth is eternal, being neither created nor destroyed, Aristotle holds that the epochs move cyclically in patterns of increase and decrease (Meteor.351b5–19). Aristotle’s cyclical understanding of both natural and human history is implicit in his comment that while Egypt used to be a fertile land, it has over the centuries grown arid (Meteor.351b28–35). Indeed, parts of the world that are ocean periodically become land, while those that are land are covered over by ocean (Meteor.253a15–24). Because of periodic catastrophes, all human wisdom that is now sought concerning both the arts and divine things was previously possessed by forgotten ancestors. However, some of this wisdom is preserved in myths, which pass on knowledge of the divine by allegorically portraying the gods in human or animal form so that the masses can be persuaded to follow laws (Met.1074a38-b14, compare Meteor.339b28–30, Pol.1329b25).

Aristotle’s geology or earth science, given in the latter books of his Meteorology, offers theories of the formation of oceans, of wind and rainfall, and of other natural events such as earthquakes, lightning, and thunder. His theory of the rainbow suggests that drops of water suspended in the air form mirrors which reflect the multiply-colored visual ray that proceeds from the eye without its proper magnitude (Meteor.373a32–373b34). Though the explanations given by Aristotle of these phenomena contradict those of modern physics, his careful observations often give interest to his account.

Aristotle’s material science offers the first description of what are now called non-Newtonian fluids—honey and must—which he characterizes as liquids in which earth and heat predominate (Meteor.385b1–5). Although the Ancient Greeks did not distill alcohol, he reports on the accidental distillation of some ethanol from wine (“sweet wine”), which he observes is more combustible than ordinary wine (Meteor.387b10–14). Finally, Aristotle’s material science makes an informative distinction between compounds, in which the constituents maintain their identity, and mixtures, in which one constituent comes to dominate or in which a new kind of material is generated (see Sharvy 1983 for discussion). Though it would be inaccurate to describe him as a methodological empiricist, Aristotle’s collection and careful recording of observations shows that in all of his scientific endeavors, his explanations were designed to accord with publicly observable natural phenomena.

ii. Biology

The phenomenon of life, as opposed to inanimate nature, involves distinctive types of change (Phys.244b10–245a5) and thus requires distinctive types of explanation. Biological explanations should give all four causes of an organism or species—the material of which it is composed, the processes that bring it about, the particular form it has, and its purpose. For Aristotle, the investigation of individual organisms gives one causal knowledge since the individuals belong to a natural kind. Men and horses both have eyes, which serve similar functions in each of them, but because their species are different, a man’s eye is similar to the eyes of other men, while a horse’s eyes are similar to the eyes of other horses (HA 486a15–20). Biology should explain both why homologous forms exist in different species and the ways in which they differ, and therefore the causes for the persistence of each natural kind of living thing.

Although all four causes are relevant in biology, Aristotle tends to group final causes with formal causes in teleological explanations, and material causes with efficient causes in mechanical explanations. Boylan (section 4) shows, for example, that Aristotle’s teleological explanation of respiration is that it exists in order to bring air into the body to produce pneuma, which is the means by which an animal moves itself. Aristotle’s mechanical explanation is that air that has been heated in the lungs is pushed out by colder air outside the body (On Breath 481b10–16, PA 642a31–b4).

Teleological explanations are necessary conditionally; that is, they depend on the assumption that the biologist has correctly identified the end for the sake of which the organism behaves as it does. Mechanical explanations, in distinction, have absolute necessity in the sense that they require no assumptions about the purpose of the organism or behavior. In general, however, teleological explanations are more important in biology (PA 639b24–26), because making a distinction between living and inanimate things depends on the assumption that “nature does nothing in vain” (GA 741b5).

The final cause of each kind corresponds to the reason that it continues to persist. As opposed to superlunary, eternal substances, sublunary living things cannot preserve themselves individually or, as Aristotle puts it, “in number.” Nevertheless, because living is better than not living (EN 1170b2–5), each individual has a natural drive to preserve itself “in kind.” Such a drive for self-preservation is the primary way in which living creatures participate in the divine (DA 415a25–b7). Nutrition and reproduction therefore are, in Aristotle’s philosophy, value-laden and goal-directed activities. They are activated, whether consciously or not, for the good of the species, namely for its continuation, in which it imitates the eternal things (Gen et Corr.338b12–17). In this way, life can be considered to be directed toward and imitative of the divine (DC 292b18–22).

This basic teleological or goal-directed orientation of Aristotle’s biology allows him to explain the various functions of living creatures in terms of their growth and preservation of form. Perhaps foremost among these is reproduction, which establishes the continuity of a species through a generation. As Aristotle puts it, the seed is temporally prior to the fully developed organism, since each organism develops from a seed. But the fully developed organism is logically prior to the seed, since it is the end or final cause, for the sake of which the seed is produced (PA 641b29–642a2).

In asexual reproduction in plants and animals, the seed is produced by an individual organism and implanted in soil, which activates it and thus actualizes its potentiality to become an organism of the kind from which it was produced. Aristotle thus utilizes a conception of “type” as an endogenous teleonomic principle, which explains why an individual animal can produce other animals of its own type (Mayr 1982, 88). Hence, the natural kind to which an individual belongs makes it what it is. Animals of the same natural kind have the same form of life and can reproduce with one another but not with animals of other kinds.

In animal sexual reproduction, Aristotle understands the seed possessed by the male as the source or principle of generation, which contains the form of the animal and must be implanted in the female, who provides the matter (GA 716a14–25). In providing the form, the male sets up the formation of the embryo in the matter provided by the female, as rennet causes milk to coagulate into cheese (GA 729a10–14). Just as rennet causes milk to separate into a solid, earthy part (or cheese), and a fluid, watery part (or whey), so the semen causes the menstrual fluid to set. In this process, the principle of growth potentially contained in the seed is activated, which, like a seed planted in soil, produces an animal’s body as the embryo (GA 739b21–740a9).

The form of the animal, its psyche, may thus be said to be potentially in the matter, since the matter contains all the necessary nutrients for the production of the complete organism. However, it is invariably the male that brings about the reproduction by providing the principle of the perceptual soul, a process Aristotle compares with the movement of automatic puppets by a mover that is not in the puppet (GA 741b6–15). (Whether the female produces the nutritive psyche is an open question.) Thus, form or psyche is provided by the male, while the matter is provided by the female: when the two come together, they form a hylomorphic product—the living animal.

While the form of an animal is preserved in kind by reproduction, organisms are also preserved individually over their natural lifespans through feeding. In species that have blood, feeding is a kind of concoction, in which food is chewed and broken down in the stomach, then enters the blood, and is finally cooked up to form the external parts of the body. In plants, feeding occurs by the nutritive psyche alone. But in animals, the senses exist for the sake of detecting food, since it is by the senses that animals pursue what is beneficial and avoid what is harmful. In human beings, a similar explanation can be given of the intellectual powers: understanding and practical wisdom exist so that human beings might not only live but also enjoy the good life achievable by action (Sens.436b19–437a3).

Although Aristotle’s teleology has been criticized by some modern biologists, others have argued that his biological work is still of interest to naturalists. For example, Haldane (1955) shows that Aristotle gave the earliest report of the bee waggle dance, which received a comprehensive explanation only in the 20th century work of Von Frisch. Aristotle also observed lordosis behavior in cattle (HA 572b1–2) and notes that some plants and animals are divisible (Youth and Old Age 468b2–15), a fact that has been vividly illustrated in modern studies of planaria. Even when Aristotle’s biological explanations are incorrect, his observations may be of enduring value.

iii. Psychology

Psychology is the study of the psyche, which is often translated as “soul.” While prior philosophers were interested in the psyche as a part of political inquiry, for Aristotle, the study of the psyche is part of natural science (Ibn Bajjah 1961, 24), continuous with biology. This is because Aristotle conceives of the psyche as the form of a living being, the body being its material. Although the psyche and body are never really separated, they can be given different descriptions. For example, the passion of anger can be described physiologically as a boiling of the blood around the heart, while it can be described dialectically as the desire to pay back with pain someone who has insulted one (DA 403a25–b2). While the physiologist examines the material and efficient causes, the dialectician considers only the form and definition of the object of investigation (DA 403a30–b3). Since the psyche is “the first principle of the living thing” (DA 402a6–7), neither the dialectical method nor the physiological method nor a combination of the two is sufficient for a systematic account of the psyche (DA 403a2, b8). Rather than relying on dialectical or materialist speculation, Aristotle holds that demonstration is the proper method of psychology, since the starting point is a definition (DA 402b25–26), and the psyche is the form and definition of a living thing.

Aristotle conceives of psychology as an exact science, with greater precision than the lesser sciences (DA 402a1–5), and accordingly offers a complete sequence of the kinds or “parts” of psyche. The nutritive psyche—possessed by both plants and animals—is responsible for the basic functions of nourishment and reproduction. Perception is possible only in an animal that also has the nutritive power that allows it to grow and reproduce, while desire depends on perceiving the object desired, and locomotion depends on desiring objects in different locations (DA 415a1–8). More intellectual powers like imagination, judgment, and understanding itself exist only in humans, who also have the lower powers.

The succession of psychological powers ensures the completeness, order, and necessity of the relations of psychological parts. Like rectilinear figures, which proceed from triangles to quadrilaterals, to pentagons, and so forth, without there being any intermediate forms, there are no other psyches than those in this succession (DA 414b20–32). This demonstrative approach ensures that although the methods of psychology and physiology are distinct, psychological divisions map onto biological distinctions. For Aristotle, the parts of the psyche are not separable or “modular” but related genetically: each posterior part of the psyche “contains” the parts before it, and each lower part is the necessary but not sufficient condition for possession of the part that comes after it.

The psyche is defined by Aristotle as the first actuality of a living animal, which is the form of a natural body potentially having life (DA 412a19–22). This form is possessed even when it is not being used; for example, a sleeping person has the power to hear a melody, though while he is sleeping, he is not exercising the power. In distinction, though a corpse looks just like a sleeping body, it has no psyche, since it lacks the power to respond to such stimuli. The second actuality of an animal comes when the power is actually exercised such as when one actually hears the melody (DA 417b9–16).

Perception is the reception of the form of an object of perception without its matter, just as wax receives the seal of a ring without its iron or gold (DA 424a17–28). When one sees wine, for example, one perceives something dark and liquid without becoming dark and liquid. Some hold that Aristotle thinks the reception of the form happens in matter so that part of the body becomes like the object perceived (for example, one’s eye might be dark while one is looking at wine). Others hold that Aristotelian perception is a spiritual change so that no bodily change is required. But presumably one is changing both bodily and spiritually all the time, even when one is not perceiving. Consequently, the formulation that perception is of “form without matter” is probably not intended to describe physiological or spiritual change but rather to indicate the conceptual nature of perception. For, as discussed in the section on first philosophy below, Aristotle considers forms to be definitions or concepts; for example, one defines “horse” by articulating its form. If he is using “form” in the same way in his discussion of perception, he means that in perceiving something, such as in seeing a horse, one gains an awareness of it as it is; that is, one grasps the concept of the horse. In that case, all the doctrine means is that perception is conceptual, giving one a grasp not just of parts of perceptible objects, say, the color and shape of a horse, but of the objects themselves, that is, of the horse as horse. Indeed, Aristotle describes perception as conferring knowledge of particulars and in that sense being like contemplation (DA 417b19–24).

This theory of perception distinguishes three kinds of perceptible objects: proper sensibles, which are perceived only by one sense modality; common sensibles, which are perceived by all the senses; and accidental sensibles, which are facts about the sensible object that are not directly given (DA 418a8–23). For example, in seeing wine, its color is a proper sensible, its volume a common sensible, and the fact that it belongs to Callias an accidental sensible. While one normally could not be wrong about the wine’s color, one might overestimate or underestimate its volume under nonstandard conditions, and one is apt to be completely wrong about the accidental sensible (for example, Callias might have sold the wine).

The five senses are distinguished by their proper sensibles: though the wine’s color might accidentally make one aware that it is sweet, color is proper to sight and sweetness to taste. But this raises a question: how do the different senses work together to give one a coherent experience of reality? If they were not coordinated, then one would perceive each quality of an object separately, for example, darkness and sweetness without putting them together. However, actual perceptual experience is coordinated: one perceives wine as both dark and sweet. In order to explain this, Aristotle says that they must be coordinated by the central sense, which is probably located in the body’s central organ, the heart. When one is awake, and the external sense organs are functioning normally, they are coordinated in the heart to discern reality as being the way it is (Sens.448b31–449a22).

Aristotle claims that one hears that one hears and sees that one sees (DA 425b12–17). Though there is a puzzle as to whether such higher-order seeing is due to sight itself or to the central perceptual power (compare On Sleep 455a3–26), the higher-order perception counts as an awareness of how the perceptual power grasps an object in the world. Though later philosophers named this higher-order perception “consciousness” and argued that it could be separated from an actualized perception of a real object, for Aristotle it is intrinsically dependent on the first-order grasp of an object (Nakahata 2014, 109–110). Indeed, Aristotle describes perceptual powers as being potentially like the perceptual object in actuality (DA 418a3–5) and goes so far as to say that the activity of the external object and that of the perceptual power are one, though what it is to be each one is different (DA 425b26–27). Thus, consciousness seems to be a property that arises automatically when perception is activated.

In at least some animals, the perceptual powers give rise to other psychological powers that are not themselves perceptual in a strict sense. In one simple case, the perception of a color is altered by its surroundings, that is, by how it is illuminated and by the other colors in one’s field of vision. Far from assuming the constancy of perception, Aristotle notes that under such circumstances, one color can take the place of another and appear differently than it does under standard conditions, for example, of full illumination (Meteor.375a22–28).

Memory is another power that arises through the collection of many perceptions. Memory is an affection of perception (though when the content of the memory is intellectual, it is an affection of the judgmental power of the psyche, see Mem.449b24–25), produced when the motion of perception acts like a signet ring in sealing wax, impressing itself on an animal and leaving an image in the psyche (Mem.450a25–b1). The resultant image has a depictive function so that it can be present even when the object it portrays is absent: when one remembers a person, for example, the memory-image is fully present in one’s psyche, though the person might be absent (Mem.450b20–25).

Closely related to memory, the imagination is a power to present absent things to oneself. Identical neither to perception nor judgment (DA 427b27–8, 433a10), imagining has an “as if” quality. For example, imagining a terror is like looking at a picture without feeling the corresponding emotion of fear (DA 427b21–24). Imagination may be defined as a kind of change or motion that comes about by means of activated perception (DA 429a1–2). This does not entail that imagination is merely reproductive but simply that activated perceptions trigger the imagination, which in turn produces an image or appearance “before our eyes” (DA 427b19–20). The resultant appearances that “comes to be for us” (DA 428a1–2, 11–12) could be true or false, since unlike the object of perception, what is imagined is not present (Humphreys 2019).

Human beings are distinct from other animals, Aristotle says, in their possession of rational psyche. Foremost among the rational powers is intellect or understanding (this article uses the terms interchangeably), which grasps universals in a way that is analogous to the perceptual grasp of particulars. However, unlike material particulars grasped by perception, universals are not mixed with body and are thus in a sense contained in the psyche itself (DA 417b22–24, 432a1–3). This has sometimes been called the intentional inexistence of an object, or intentionality, the property of being directed to or about something. Since one can think or understand any universal, the understanding is potentially about anything, like an empty writing tablet (DA 429b29–430a1).

The doctrine of the intentionality of intellect leads Aristotle to make a distinction between two kinds of intellect. Receptive or passive intellect is characterized by the ability to become like all things and is analogous to the writing tablet. Productive or active intellect is characterized by the ability to bring about all things and is analogous to the act of writing. The active intellect is thus akin to the light that illuminates objects, making them perceptible by sight. Aristotle holds that the soul never thinks without an image produced by imagination to serve as its material. Thus, in understanding something, the productive intellect actuates the receptive intellect, which stimulates the imagination to produce a particular image corresponding to the universal content of the understanding. Hence, while Aristotle describes the active intellect as unaffected, separate, and immaterial, it serves to bring to completion the passive intellect, the latter of which is inseparable from imagination and hence from perception and nutrition.

Aristotle’s insistence that intellect is not a subject of natural science (PA 641a33–b9) motivates the view that thinking requires a contribution from the supernatural or divine. Indeed, in Metaphysics (1072b19–30) Aristotle argues that intellect actively understanding the intelligible is the everlasting God. For readers like the medieval Arabic commentator Ibn Rushd, passive intellect is spread like matter among thinking beings. This “material intellect” is activated by God, the agent intellect, so that when one is thinking, one participates in the activity of the divine intellect. According to this view, every act of thinking is also an act of divine illumination in which God actuates one’s thinking power as the writer actuates a blank writing tablet.

However, in other passages Aristotle says that when the body is destroyed, the soul is destroyed too (Length and Shortness of Life, 465b23–32). Thus, it seems that Aristotle’s psychological explanations assume embodiment and require that thinking be something done by the individual human being. Indeed, Aristotle argues that if thinking is either a kind of imaginative representation or impossible without imagination, then it will be impossible without body (DA 403a8–10). But the psyche never thinks without imagination (DA 431a16–17). It seems to follow that far from being a part of the everlasting thinking of God, human thinking is something that happens in a living body and ends when that body is no longer alive. Thus, Jiminez (2014, 95–99) argues that thinking is embodied in three ways: it is proceeded by bodily processes, simultaneous with embodied processes, and anticipates bodily processes, namely intentional actions. For further discussion see Jiminez (2017).

The whole psyche governs the characteristic functions and changes of a living thing. The nutritive psyche is the formal cause of growth and metabolism and is shared by plants, while the perceptual psyche gives rise to desire, which causes self-moving animals to act. When one becomes aware of an apparent good by perception or imagination, one forms either an appetite, the desire for pleasure, or thumos, the spirited desire for revenge or honor. A third form of desire, wish, is the product of the rational psyche (DA 433a20–30).

Boeri has pointed out that Aristotle’s psychology cuts a middle path between physicalism, which identifies the psyche with body, and dualism, which posits the independent existence of the soul and body. By characterizing the psyche as he does, Aristotle can at once deny that the psyche is a body but also insist that it does not exist without a body. The living body of an animal can thus be thought of as a form that has been “materialized” (Boeri 2018, 166–169).

b. Mathematics

Aristotle was educated in Plato’s Academy, in which it was commonly argued that mathematical objects like lines and numbers exist independently of physical beings and are thus ”separable” from matter. Aristotle’s conception of the hierarchy of beings led him to reject Platonism since the category of quantity is posterior to that of substance. But he also rejects nominalism, the view that mathematical things are not real. Against both positions, Aristotle argues that mathematical things are real but do not exist separately from sensible bodies (Met.1090a29–30, 1093b27–28). Mathematical objects thus depend on the things in which they inhere and have no separate or independent being (Met.1059b12–14).

Although mathematical beings are not separate from the material cosmos, when the mathematician defines what it is to be a sphere or circle, he does not include a material like gold or bronze in the definition, because it is not the gold ball or bronze ring that the mathematician wants to define. The mathematician is justified in proceeding in this way, because although there are no separate entities beyond the concrete thing, it is just the mathematical aspects of real things that are relevant to mathematics (DC 278a2–6). This process by which the material features of a substance are systematically ignored by the mathematician, who focuses only on the quantitative features, Aristotle describes as “abstraction.” Because it always involves final ends, no abstraction is possible in natural science (PA 641b11–13, Phys.193b31–35). A consequence of this abstraction is that “why” questions in mathematics are invariably answered not by providing a final cause but by giving the correct definition (Phys.198a14–21, 200a30–34).

One reason that Aristotle believes that mathematics must proceed by abstraction is that he wants to prevent a multiplication of entities. For example, he does not want to say that, in addition to there being a sphere of bronze, there is another separate, mathematical sphere, and that in addition to that sphere, there is a separate mathematical plane cutting it, and that in addition to that plane, there is an additional line limiting the plane (see Katz 2014). It is enough for a mathematical ontology simply to acknowledge that natural objects have real mathematical properties not separate in being, which can nevertheless be studied independently from natural investigation. Aristotle also favors this view due to his belief that mathematics is a demonstrative science. Aristotle was aware that geometry uses diagrammatic representations of abstracted properties, which allow one to grasp how a demonstration is true not just of a particular object but of any class of objects that share its quantitative features (Humphreys 2017). Through the concept of abstraction, Aristotle could explain why a particular diagram may be used to prove a universal geometrical result.

Why study mathematics? Although Aristotle rejected the Platonic doctrine that mathematical beings are separate, intermediate entities between perceptible things and forms, he agreed with the Platonists that mathematics is about things that are beautiful and good, since it offers insight into the nature of arrangement, symmetry, and definiteness (Met.1078a31–b6). Thus, the study of mathematics reveals that beauty is not so much in the eye of the beholder as it is in the nature of things (Hoinski and Polansky 2016, 51–60). Moreover, Aristotle holds that mathematical beings are all potential objects of the intellect, which exist only potentially when they are not understood. The activity of understanding is the actuation of their being, but also actuates the intellect (Met.1051a26–33). Mathematics, then, not only gives insight into beauty but is also a source of intellectual pleasure, since gaining mathematical knowledge exercises the human being’s best power.

c. First Philosophy

In addition to natural and mathematical sciences, there is a science of independent beings that Aristotle calls “first philosophy” or “wisdom.” What is the proper aim of this science? In some instances, Aristotle seems to say that it concerns being insofar as it is (Met.1003a21–22), whereas in others, he seems to consider it to be equivalent to “theology,” restricting contemplation to the highest kind of being (Met.1026a19–22), which is unchanging and separable from matter. However, Menn (2013, 10–11) shows that Aristotle is primarily concerned with describing first philosophy as a science that seeks the causes and sources of being qua being. Hence, when Aristotle holds that wisdom is a kind of rational knowledge concerning causes and principles (Met.982a1–3), he probably means that the investigation of these causes of being as being seeks to discover the divine things as the cause of ordinary beings. First philosophy is consequently quite unlike natural philosophy and mathematics, since rather than proceeding from systematic observation or from hypotheses, it begins with an attitude of wonder towards ordinary things and aims to contemplate them not under a particular description but simply as beings (Sachs 2018).

The fundamental premise of this science is the law of noncontradiction, which states that something cannot both be and not be (Met.1006a1). Aristotle holds that this law is indemonstrable and necessary to assume in any meaningful discussion about being. Consequently, a person who demands a demonstration of this principle is no better than a plant. As Anscombe (1961, 40) puts it, “Aristotle evidently had some very irritating people to argue with.” But as Anscombe also points out, this principle is what allows Aristotle to make a distinction between substances as the primary kind of being and accidents that fall in the other categories. While it is possible for a substance to take on contrary accidents, for example, coffee first being hot and later cold, substances have no contraries. The law requires that a substance either is or is not, independently of its further, accidental properties.

Aristotle insists that in order for the word “being” to have any meaning at all, there must be some primary beings, whereas other beings modify these primary beings (Met.1003b6–10). As we saw in the section on Aristotle’s logic, primary substances are individual substances while their accidents are what is predicated of them in the categories. This takes on metaphysical significance when one thinks of this distinction in terms of a dependence relation in which substances can exist independently of their accidents, but accidents are dependent in being on a substance. For example, a shaggy dog is substantially a dog, but only accidentally shaggy. If it lost all its hair, it would cease to be shaggy but would be no less a dog: it would then be a non-shaggy dog. But if it ceased to be a dog—for example, if it were turned into fertilizer—then it would cease to be shaggy at the same moment. Unlike the “shagginess,” “dogness” cannot be separated from a shaggy dog: the “what it is to be” a dog is the dog’s dogness in the category of substance, while its accidents are in other categories, in this case shagginess being in the category of quality (Met.1031a1–5).

Given that substances can be characterized as forms, as matter, or as compounds of form and matter, it seems that Aristotle gives the cause and source of a being by listing its material and formal cause. Indeed, Aristotle sometimes describes primary being as the “immanent form” from which the concrete primary being is derived (Met.1037a29). This probably means that a primary substance is always a compound, its formal component serving as the substance’s final cause. However, primary beings are not composed of other primary beings (Met.1041a3–5). Thus, despite some controversy on the question, there seems to be no form of an individual, form being what is shared by all the individuals of a kind.

A substance is defined by a universal, and thus when one defines the form, one defines the substance (Met.1035b31–1036a1). However, when one grasps a substance directly in perception or thought, one grasps the compound of form and matter (Met.1036a2–8). But since form by itself does not make a primary substance, it must be immanent—that is, compounded with matter—in each individual, primary substance. Rather, in a form-matter compound, such as a living thing, the matter is both the prior stuff out of which the thing has become and the contemporaneous stuff of which it is composed. The form is what makes what a thing is made of, its matter, into that thing (Anscombe 1961, 49, 53).

Due to this hylomorphic account, one might worry that natural science seems to explain everything there is to explain about substances. However, Aristotle insists that there is a kind of separable and immovable being that serves as the principle or source of all other beings, which is the special object of wisdom (Met.1064a35–b1). This being might be called the good itself, which is implicitly pursued by substances when they come to be what they are. In any case, Aristotle insists that this source and first of beings sets in motion the primary motion. But since whatever is in motion must be moved by something else, and the first thing is not moved by something else, it is itself motionless (Met.1073a25–34). As we have seen, even the human intellect is “not affected” (DA 429b19–430a9), producing its own object of contemplation in a pure activity. Following this, Aristotle describes the primary being as an intellect or a kind of intellect that “thinks itself” perpetually (Met.1072b19–20). Thus, we can conceive of the Aristotelian god as being like our own intellect but unclouded by what we undergo as mortal, changing, and fallible beings (Marx 1977, 7–8).

4. Practical Philosophy

Practical philosophy is distinguished from theoretical philosophy both in its goals and in its methods. While the aim of theoretical philosophy is contemplation and the understanding of the highest things, the aim of practical philosophy is good action, that is, acting in a way that constitutes or contributes to the good life. But human beings can only thrive in a political community: the human is a “political animal” and thus the political community exists by nature (Pol.1253a2–5, compare EN 1169b16–19). Thus, ethical inquiry is part of political inquiry into what makes the best life for a human being. Because of the intrinsic variability and complexity of human life, however, this inquiry does not possess the exactness of theoretical philosophy (EN 1094b10–27).

In a similar way that he holds animals are said to seek characteristic ends in his biology, Aristotle holds in his “ergon argument” that the human being has a proper ergon—work or function (EN 1097b24–1098a18). Just as craftsmen like flautists and sculptors and bodily organs like eyes and ears have a peculiar work they do, so the human being must do something peculiarly human. Such function is definitive, that is, distinguishes what it is to be the thing that carries it out. For example, a flautist is a flautist insofar as she plays the flute. But the function serves as an implicit success condition for being that thing. For example, what makes a flautist good as a what she is (“good qua flautist” one might say) is that she plays the flute well. Regardless of the other work she does in her other capacities (qua human, qua friend, and so forth) the question “is she a good flautist?” can be answered only in reference to the ergon of the flautist, namely flute playing.

The human function cannot be nutrition or perception, since those activities are shared with other living things. Since other animals lack reason, the human function must be an activity of the psyche not without reason. A human being that performs this function well will be functioning well as a human being. In other words, by acting virtuously one will by that fact achieve the human good (Angier 2010, 60–61). Thus, Aristotle can summarize the good life as consisting of activities and actions in accordance with ­arete—excellence or virtue—and the good for the human being as the activity of the psyche in accordance with excellence in a complete life (EN 1098a12–19). Though it has sometimes been objected that Aristotle assumes without argument that human beings must have a characteristic function, Angier (2010, 73–76) has shown that the key to Aristotle’s argument is his comparison of the human function to a craft: just as a sculptor must possess a wide variety of subordinate skills to achieve mastery in his specialized activity, so in acting well the human being must possess an inclusive set of dispositions and capacities that serve to fulfill the specialized task of reason.

Ethics and politics are, however, not oriented merely to giving descriptions of human behavior but on saying what ends human beings ought to pursue, that is, on what constitutes the good life for man. While the many, who have no exposure to philosophy, should agree that the good life consists in eudaimonia—happiness or blessedness—there is disagreement as to what constitutes this state (EN 1095a18–26). The special task of practical philosophy is therefore to say what the good life consists in, that is, to give a more comprehensive account of eudaimonia than is available from the observation of the diverse ends pursued by human beings. As Baracchi (2008, 81–83) points out, eudaimonia indicates a life lived under the benevolent or beneficial sway of the daimonic, that is, of an order of existence beyond the human. Thus, the view that eudaimonia is a state of utmost perfection and completion for a human being (Magna Moralia 1184a14, b8) indicates that the full actualization of a human depends on seeking something beyond what is strictly speaking proper to the human.

a. Habituation and Excellence

Though the original meaning of ethics has been obscured due to modern confusion of pursuing proper ends with following moral rules, in the Aristotelian works, ethical inquiry is limited to the investigation of what it is for a human being to flourish according to her own nature. For the purposes of this inquiry, Aristotle distinguishes three parts of the psyche: passions, powers, and habits (EN 1105b20). Passions include attitudes such as feeling fear, hatred, or pity for others, while powers are those parts of our form that allow us to have such passions and to gain knowledge of the world. However, while all human beings share passions and powers, they differ with regard to how they are trained or habituated and thus with respect to their dispositions or states of character. Those who are habituated correctly are said to be excellent and praiseworthy, while those whose characters are misshapen through bad habituation are blameworthy (EN 1105b28–a2).

How does a human being become good, cultivating excellence within herself? Aristotle holds that this happens by two related but distinct mechanisms. Intellectual excellences arise by teaching, whereas ethical excellences by character, such as moderation and courage, arise by ethos, habituation, or training (EN 1103a14–26). Since pleasure or pain results from each of our activities (EN 1104b4), training happens through activity; for example, one learns to be just by doing just things (EN 1103a35–b36). Legislators, who aim to make citizens good, therefore must ensure that citizens are trained from childhood to produce certain good habits—excellences of character—in them (EN 1103b23–25).

Such training takes place via pleasure and pain. If one is brought up to take pleasure or suffer pain in certain activities, one will develop the corresponding character (EN 1104b18–25). This is why no one becomes good unless one does good things (EN 1105b11–12). Rather than trying to answer the question of why one ought to be good in the abstract, Aristotle assumes that taking pleasure in the right kinds of activities will lead one to have a good life, where “right kinds” means those activities that contribute to one’s goal in life. Hence the desires of children can be cultivated into virtuous dispositions by providing rewards and punishments that induce them to follow good reason (EN 1119b2–6).

Since Aristotle conceives of perception as the reception of the perceived object’s form without its matter, to perceive correctly is to grasp an object as having a pleasurable or painful generic form (DA 424a17–19, 434a27–30). The cognitive capacity of perception and the motive capacity of desire are linked through pleasure, which is also “in the soul” (EE 1218b35). Excellence is not itself a pleasure but rather a deliberative disposition to take pleasure in certain activities, a mean between extreme states (EN 1106b36–1107a2).

Although he offers detailed descriptions of the virtues in his ethical works, Aristotle summarizes them in a table:

Excess Mean Deficiency
Irascibility Gentleness Spiritlessness
Rashness Courage Cowardice
Shamelessness Modesty Diffidence
Profligacy Temperance Insensitiveness
Envy Righteous Indignation Malice
Greed Justice Loss
Prodigality Liberality Meanness
Boastfulness Honesty Self-deprecation
Flattery Friendliness Surliness
Subservience Dignity Stubborness
Luxuriousness Hardness Endurance
Vanity Greatness of Spirit Smallness of Spirit
Extravagance Magnificence Shabbiness
Rascality Prudence Simpleness

This shows that each excellence is a mean between excessive and defective states of character (EE 1220b35–1221a15). Accordingly, good habituation is concerned with avoiding extreme or pathological states of character. Thus, Aristotle can say that ethical excellence is “concerned with pleasures and pains” (EN 1104b8–11), since whenever one has been properly trained to take the correct pleasure and suffer correct pain when one acts in excess or defect, one possesses the excellence in question.

b. Ethical Deliberation

Human action displays excellence only when it is undertaken voluntarily, that is, is chosen as the means to bring about a goal wished for by the agent. Excellence in general is thus best understood as a disposition to make correct choices (EN 1106b36–1107a2), where “choice” is understood as the product of deliberation or what “has been deliberated upon” (EN 1113a4). Deliberation is not about ends but about what contributes to an end already given by one of the three types of desire discussed above: appetite, thumos, or wish (EN 1112b11–12, 33–34).

But if all excellent action must be chosen, how can actions undertaken in an instant, such as when one acts courageously, be excellent? Since such actions can be undertaken without the agent having undergone a prior process of conscious deliberation, which takes time, it seems that one must say that quick actions were hypothetically deliberated, that is, that they count as what one would have chosen to do had one had time to deliberate (Segvic 2008, 162–163).

Such reasoning can be schematized by the so-called the “practical syllogism.” For example, supposing one accepts the premises

One should not drink heavy water

This water in this cup is heavy

The syllogism concludes with one’s not drinking water from the cup (EN 1142a22–23). If this is how Aristotle understands ethical deliberation, then it seems that all one’s voluntary actions count as deliberated even if one has not spent any time thinking about what to do.

However, Contreras (2018, 341) points out that the “practical syllogism” cannot represent deliberation since its conclusion is an action, whereas the conclusion of deliberation is choice. Though one’s choice typically causes one to act, something external could prevent one from acting even once the choice has been made. Thus, neither are choice and action the same, nor are the processes or conditions from which they result identical. Moreover, even non-rational desires like appetite and thumos present things under the “guise of the good” so that whatever one desires appears to be good. Hence an action based on those desires could still be described by a practical syllogism, though it would not be chosen through deliberation. Deliberation does not describe a kind of deduction but a process of seeking things that contribute to an aim already presented under the guise of the good (Segvic 2008, 164–167).

This “seeking” aspect of deliberation is brought out in Aristotle’s comparison of the deliberator to the geometer, who searches and analyzes by diagrams (EN 1112b20–24). Geometrical analysis is the method by which a mathematician works backwards from a desired result to find the elements that constitute that result. Similarly, deliberation is a search for the elements that would allow the end one has in view to be realized (EN 1141b8–15).

However, while geometrical reasoning is abstracted from material conditions, the prospective reasoning of deliberation is constrained both modally and temporally. One cannot deliberate about necessities, since practical things must admit of being otherwise than they are (DA 433a29–30). Similarly, one cannot deliberate about the past, since what is chosen is not what has become—“no one chooses that Ilium be destroyed”—but what may or may not come about in the future (EN 1139b5–9, DA 431b7–8). One can describe deliberation, then, as starting from premises in the future perfect tense, and as working backwards to discover what actions would make those statements true.

In addition to these constraints, the deliberating agent must have a belief about herself, namely that she is able to either bring about or not bring about the future state in question (EN 1112a18–31). Since rational powers alone are productive of contrary effects, deliberation must be distinctively rational, since it produces a choice to undertake or not to undertake a certain course of action (Met.1048a2–11). In distinction to technical deliberation, the goal of which is to produce something external to the activity that brings it about, in ethical deliberation there is no external end since good action is itself the end (EN 1140b7). So rather than concerning what an agent might produce externally, deliberation is ethical when it is about the agent’s own activity. Thus, deliberation ends when one has reached a decision, which may be immediately acted upon or put into practice later when the proper conditions arise.

c. Self and Others

Life will tend to go well for a person who has been habituated to the right kinds of pleasures and pains and who deliberates well about what to do. Unfortunately, this is not always sufficient for happiness. For although excellence might help one manage misfortunes well and avoid becoming miserable as their result, it is not reasonable to call someone struck with a major misfortune blessed or happy (EN 1100b33–1101a13). So there seems to be an element of luck in happiness: although bad luck cannot make one miserable, one must possess at least some external goods in order to be happy.

One could also ruin things by acting in ignorance. When one fails to recognize a particular as what it is, one might bring about an end one never intended. For example, one might set off a loaded catapult through one’s ignorance of the fact that it was loaded. Such actions are involuntary. But there is a more fundamental kind of moral ignorance for which one can be blamed, which is not the cause of involuntary actions but of badness (EN 1110b25–1111a11). In the first case, one does what one does not want to do because of ignorance, so is not worthy of blame. In the second case, one does what one wants to do and is thus to be blamed for the action.

Given that badness is a form of ignorance about what one should do, it is reasonable to ask whether acting acratically, that is, doing what one does not want to do, just comes down to being ignorant. This is the teaching of Socrates, who, arguing against what appears to be the case, reduced acrasia to ignorance (EN 1145b25–27). Though Aristotle holds that acrasia is distinct from ignorance, he also thinks it is impossible for knowledge to be dragged around by the passions like a slave. Aristotle must, then, explain how being overcome by one’s passions is possible, when knowledge is stronger than the passions.

Aristotle’s solution is to limit acrasia to those cases in which one generically knows what to do but fails to act on it because one’s knowledge of sensibles is dragged along by the passions (EN 1147b15–19). In other words, he admits that the passions can overpower perceptual knowledge of particulars but denies that it can dominate intellectual knowledge of universals. Hence, like Socrates, Aristotle thinks of acrasia as a form of ignorance, though unlike Socrates, he holds that this ignorance is temporary and relates only to one’s knowledge of particulars. Acrasia consists, then, in being unruled with respect to thumos or with respect to sensory pleasures. In such cases, one is unruled because one’s passions or lower desires temporarily take over and prevent one from grasping things as one should (EN 1148a2–22). In this sense, acrasia represents a conflict between the reasoning and unreasoning parts of the psyche (for discussion see Weinman 2007, 95–99).

If living well and acting well are the same (EN 1095a18–20, EE 1219b1–4) and acting well consists in part in taking the proper pleasure in one’s action, then living well must be pleasurable. Aristotle thinks the pleasure one has in living well comes about through a kind of self-consciousness, that of being aware of one’s own activity. In such activity, one grasps oneself as the object of a pleasurable act of perception or contemplation and consequently takes pleasure in that act (Ortiz de Landázuri 2012). But one takes pleasure in a friend’s life and activity almost as one takes pleasure in one’s own life (EN 1170a15–b8). Thus, the good life may be accompanied not only by a pleasurable relation to oneself but also by relationships to others in which one takes a contemplative pleasure in their activities.

The value of friendship follows from the ideas that when a person is a friend to himself, he wishes the good for himself and thus to improve his own character. Only such a person who has a healthy love of self can form a friendship with another person (EN 1166b25–29). Indeed, one’s attitudes towards a friend are based on one’s attitudes towards oneself (EN 1166a1–10), attitudes which are extended to another in the formation of a friendship (EN 1168b4–7). However, because people are by nature communal or political, in order to lead a complete life, one needs to form friendships with excellent people, and it is in living together with others that one comes to lead a happy life. When a true friendship between excellent persons is formed, each will regard one another with the same attitude with which he regards himself, and thus as an “another self” (EN 1170b5–19)

Friendship is a bridging concept between ethics concerning the relations of individuals and political science, which concerns the nature and function of the state. For Aristotle, friendship holds a state together, so the lawgiver must focus on promoting friendship above all else (EN 1155a22–26). Indeed, when people are friends, they treat one another with mutual respect so that justice is unnecessary or redundant (EN 1155a27–29). Aristotle’s ethics are thus part of his political philosophy. Just as an individual’s good action depends on her taking the right kinds of pleasures, so a thriving political community depends on citizens taking pleasure in one another’s actions. Such love of others and mutual pleasure are strictly speaking neither egoistic nor altruistic. Instead, they rest on the establishment of a harmony of self and others in which the completion of the individual life and the life of the community amount to the same thing.

d. The Household and the State

Aristotle’s political philosophy stems from the idea that the political community or state is a creation of nature prior to the individual who lives within it. This is shown by the fact that the individual human being is dependent on the political community for his formation and survival. One who lives outside the state is either a beast or a god, that is, does not participate in what is common to humanity (Pol.1253a25–31). The political community is natural and essentially human, then, because it is only within this community that the individual realizes his nature as a human being. Thus, the state exists not only for the continuation of life but for the sake of the good life (Pol.1280a31–33).

Aristotle holds that the human being is a “political animal” due to his use of speech. While other gregarious animals have voice, which nature has fashioned to indicate pleasure and pain, the power of speech enables human beings to indicate not only this but also what is expedient and inexpedient and what is just and unjust (Pol.1253a9–18). Berns (1976, 188–189) notes that for Aristotle, the speech symbol’s causes are largely natural: the material cause of sound, the efficient cause of the living creatures that produce them, and the final cause of living together, are all parts of human nature. However, the formal cause, the distinctive way in which symbols are organized, is conventional. This allows for a variability of constitutions and hence the establishment of good or bad laws. Thus, although the state is natural for human beings, the specific form it takes depends on the wisdom of the legislator.

Though the various forms of constitution cannot be discussed here (for discussion, see Clayton, Aristotle: Politics), the purpose of the state is the good of all the citizens (Pol.1252a3), so a city is excellent when its citizens are excellent (Pol.1332a4). This human thriving is most possible, however, when the political community is ruled not by an individual but by laws themselves. This is because even the best rulers are subject to thumos, which is like a “wild beast,” whereas law itself cannot be perverted by the passions. Thus, Aristotle likens rule of law to the “rule of God and reason alone” (Pol.1287a16–32). Although this is the best kind of political community, Aristotle does not say that the best life for an individual is necessarily the political life. Instead he leaves open the possibility that the theoretical life, in which philosophy is pursued for its own sake, is the best way for a person to live.

The establishment of any political community depends on the existence of the sub-political sphere of the household, the productive unit in which goods are produced for consumption. Whereas the political sphere is a sphere of freedom and action, the household consists of relations of domination: that of the master and slave, that of marriage, and that of procreation. Hence household management or “economics” is distinct from politics, since the organization of the household has the purpose of production of goods rather than action (Pol.1253b9–14). Crucial to this household production is the slave, which Aristotle defines as a living tool (Pol.1253b30–33) who is controlled by a master in order to produce the means necessary for the survival and thriving of the household and state. As household management, economics is concerned primarily with structuring slave labor, that is, with organizing the instruments of production so as to make property necessary for the superior, political life.

Aristotle thus offers a staunch defense of the institution of slavery. Against those who claim that slavery is contrary to nature, Aristotle argues that there are natural slaves, humans who are born to be ruled by others (Pol.1254a13–17). This can be seen by analogy: the body is the natural slave of the psyche, such that a good person exerts a despotic rule over his body. In the same way, humans ought to rule over other animals, males over females, and masters over slaves (Pol.1254a20–b25). But this is only natural when the ruling part is more noble than the part that is ruled. Thus, the enslavement of the children of conquered nobles by victors in a war is a mere convention since the children may possess the natures of free people. For Aristotle, then, slavery is natural and just only when it is in the interest of slave and master alike (Pol.1255b13–15).

The result of these doctrines is the view that political community is composed of “unlikes.” Just as a living animal is composed of psyche and body, and psyche is composed of a rational part and an appetite, so the family is composed of husband and wife, and property of master and slave. It is these relations of domination, in Aristotle’s view, that constitute the state, holding it together and making it function (Pol.1277a5–11). As noted in the biographical section, Aristotle had close ties to the expanding Macedonian empire. Thus his political philosophy, insofar as it is prescriptive of how a political community should be managed, might have been intended to be put into practice in the colonies established by Alexander. If that is the case, then perhaps Aristotle’s politics is at base a didactic project intended to teach an indefinite number of future legislators (Strauss 1964, 21).

5. Aristotle’s Influence

Aristotle and Plato were the most influential philosophers in antiquity, both because their works were widely circulated and read and because the schools they founded continued to exert influence for hundreds of years after their deaths. Aristotle’s school gave rise to the Peripatetic movement, with his student Theophrastus being its most famous member. In late antiquity, there emerged a tradition of commentators on Aristotle’s works, beginning with Alexander of Aphrodisias, but including the Neo-Platonists Simplicius, Syrianus, and Ammonius. Many of their commentaries have been edited and translated into English as part of the Ancient Commentators on Aristotle project.

In the middle ages, Aristotle’s works were translated into Arabic, which led to generations of Islamic Aristotelians, such as Ibn Bajjah and Ibn Rushd (see Alwishah and Hayes 2015). In the Jewish philosophical tradition, Maimonides calls Aristotle the chief of the philosophers and uses Aristotelian concepts to analyze the contents of the Hebrew Bible. Though Boethius’ Latin commentaries on Aristotle’s logical works were available from the fifth century onwards, the publication of Aristotle’s works in Latin in the 11th and 12th centuries led to a revival of Aristotelian ideas in Europe. Indeed, a major controversy broke out at the University of Paris in the 1260s between the Averroists—followers of Ibn Rushd who believed that thinking happens through divine illumination—and those who held that the active intellect is individual in humans (see McInerny 2002). A further debate, concerning realism (the doctrine that universals are real) and nominalism (the doctrine that universals exist “in name” only) continued for centuries. Although they disagreed in their interpretations, prominent scholastics like Bacon, Buridan, Ockham, Scotus, and Aquinas, tended to accept Aristotelian doctrines on authority, often referring to Aristotle simply as “The Philosopher.”

Beginning in the sixteenth century, the scholastics came under attack, particularly from natural philosophers, often leading to the disparagement of Aristotelian positions. Copernicus’ model made Earth not the center of the universe as in Aristotle’s cosmology but a mere satellite of the sun. Galileo showed that some of the predictions of Aristotle’s physical theory were incorrect; for example, heavier objects do not fall faster than lighter objects. Descartes attacked the teleological aspect of Aristotle’s physics, arguing for a mechanical conception of all of nature, including living things. Hobbes critiqued the theory of perception, which he believed unrealistically described forms or ideas as travelling through the air. Later, Hume disparaged causal powers as mysterious, thus undermining the conception of the four causes. Kantian and utilitarian ethics argued that duties to humanity rather than happiness were the proper norms for action. Darwin showed that species are not eternal, casting doubt on Aristotle’s conception of biological kinds. Frege’s logic in the late nineteenth century developed notions of quantification and predication that made the syllogism obsolete. By the beginning of the twentieth century, Aristotle looked not particularly relevant to modern philosophical concerns.

The latter part of the twentieth century, however, has seen a slow but steady intellectual shift, which has led to a large family of neo-Aristotelian positions being defended by contemporary philosophers. Anscombe’s (1958) argument for a return to virtue ethics can be taken as a convenient starting point of this change. Anscombe’s claim, in summary, is that rule-based ethics of the deontological or utilitarian style is unconvincing in an era wherein monotheistic religions have declined, and commandments are no longer understood to issue from a divine authority. Modern relativism and nihilism on this view are products of the correct realization that without anyone making moral commandments, there is no reason to follow them. Since virtue ethics grounds morality in states of character rather than in universal rules, only a return to virtue ethics would allow for a morality in a secular society. In accordance with this modern turn to virtue ethics, neo-Aristotelian theories of natural normativity have increasingly been defended, for example, by Thompson (2008). In political philosophy, Arendt’s (1958) distinction between the public and private spheres takes the tension between the political community and household as a fundamental force of historical change.

In the 21st century, philosophers have drawn on Aristotle’s theoretical philosophy. Cartwright and Pemberton (2013) revive the concept of natural powers being part of the basic ontology of nature, which explain many of the successes of modern science. Umphrey (2016) argues for the real existence of natural kinds, which serve to classify material entities. Finally, the ‘Sydney School’ has adopted a neo-Aristotelian, realist ontology of mathematics that avoids the extremes of Platonism and nominalism (Franklin 2011). These philosophers argue that, far from being useless antiques, Aristotelian ideas offer fruitful solutions to contemporary philosophical problems.

6. Abbreviations

a. Abbreviations of Aristotle’s Works

Cat.                                         Categoriae Categories
Int. Liber de interpretatione On Interpretation
AnPr. Analytica priora       Prior Analytics
AnPo.  Analytica posteriora  Posterior Analytics
Phys. Physica Physics
Met.   Metaphysica Metaphysics
Meteor. Meteorologica  Meteorology
DC   De Caelo On the Heavens
HA       Historia Animalium The History of Animals
Genn et Corr. De Generatione et Corruptione On Generation and Corruption
EN  Ethica Nicomachea     Nicomachean Ethics
DA  De Anima On the Soul
MA De Motu Animalium On the Motion of Animal
Mem.   De Memoria On Memory
Sens.    De Sensu et Sensibili     On Sense and its Objects
Pol. Politica  Politics
Top.  Topica  Topics
Rhet. Rhetorica Rhetoric
Poet.  Poetica   Poetics
SophElen. De Sophisticiis Elenchiis  Sophistical Refutations

b. Other Abbreviations

DL Diogenes Laertius, The Life of Aristotle.
Bekker “August Immanuel Bekker.” Encyclopedia Britannica. 9th ed., vol. 3, Cambridge University Press, 1910, p. 661.

7. References and Further Reading

a. Aristotle’s Complete Works

  • Aristotelis Opera. Edited by A.I. Bekker, Clarendon, 1837.
  • Complete Works of Aristotle. Edited by J. Barnes, Princeton University Press, 1984.

b. Secondary Sources

i. Life and Early Works

  • Bos, A.P. “Aristotle on the Etruscan Robbers: A Core Text of ‘Aristotelian Dualism.’” Journal of the History of Philosophy, vol. 41, no. 3, 2003, pp. 289–306.
  • Chroust, A-H. “Aristotle’s Politicus: A Lost Dialogue.” Rheinisches Museum für Philologie, Neue Folge, 108. Bd., 4. H, 1965, pp. 346–353.
  • Chroust, A-H. “Eudemus or on the Soul: A Lost Dialogue of Aristotle on the Immortality of the Soul.” Mnemosyne, Fourth Series, vol. 19, fasc. 1, 1966, pp. 17–30.
  • Chroust, A-H. “Aristotle Leaves the Academy.” Greece and Rome, vol. 14, issue 1, April 1967, pp. 39–43.
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ii. Logic

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iii. Theoretical Philosophy

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iv. Practical Philosophy

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v. Aristotle’s Influence

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Author Information

Justin Humphreys
Email: jhh@sas.upenn.edu
University of Pennsylvania
U. S. A.

David Hume: Moral Philosophy

HumeAlthough David Hume (1711-1776) is commonly known for his philosophical skepticism, and empiricist theory of knowledge, he also made many important contributions to moral philosophy. Hume’s ethical thought grapples with questions about the relationship between morality and reason, the role of human emotion in thought and action, the nature of moral evaluation, human sociability, and what it means to live a virtuous life. As a central figure in the Scottish Enlightenment, Hume’s ethical thought variously influenced, was influenced by, and faced criticism from, thinkers such as Shaftesbury (1671-1713), Francis Hutcheson (1694-1745), Adam Smith (1723-1790), and Thomas Reid (1710-1796). Hume’s ethical theory continues to be relevant for contemporary philosophers and psychologists interested in topics such as metaethics, the role of sympathy and empathy within moral evaluation and moral psychology, as well as virtue ethics.

Hume’s moral thought carves out numerous distinctive philosophical positions. He rejects the rationalist conception of morality whereby humans make moral evaluations, and understand right and wrong, through reason alone. In place of the rationalist view, Hume contends that moral evaluations depend significantly on sentiment or feeling. Specifically, it is because we have the requisite emotional capacities, in addition to our faculty of reason, that we can determine that some action is ethically wrong, or a person has a virtuous moral character. As such, Hume sees moral evaluations, like our evaluations of aesthetic beauty, as arising from the human faculty of taste. Furthermore, this process of moral evaluation relies significantly upon the human capacity for sympathy, or our ability to partake of the feelings, beliefs, and emotions of other people. Thus, for Hume there is a strong connection between morality and human sociability.

Hume’s philosophy is also known for a novel distinction between natural and artificial virtue. Regarding the latter, we find a sophisticated account of justice in which the rules that govern property, promising, and allegiance to government arise through complex processes of social interaction. Hume’s account of the natural virtues, such as kindness, benevolence, pride, and courage, is explained with rhetorically gripping and vivid illustrations. The picture of human excellence that Hume paints for the reader equally recognizes the human tendency to praise the qualities of the good friend and those of the inspiring leader. Finally, the overall orientation of Hume’s moral philosophy is naturalistic. Instead of basing morality on religious and divine sources of authority, Hume seeks an empirical theory of morality grounded on observation of human nature.

Hume’s moral philosophy is found primarily in Book 3 of The Treatise of Human Nature and his Enquiry Concerning the Principles of Morals, although further context and explanation of certain concepts discussed in those works can also be found in his Essays Moral, Political, and Literary. This article discusses each of the topics outlined above, with special attention given to the arguments he develops in the Treatise.

Table of Contents

  1. Hume’s Rejection of Moral Rationalism
    1. The Influence Argument
    2. The Divide and Conquer Argument
    3. The Representation Argument
    4. Hume and Contemporary Metaethics
  2. Hume’s Moral Sense Theory
    1. The Moral Sense
    2. The General Point of View
  3. Sympathy and Humanity
    1. Sympathy
    2. Humanity
  4. Hume’s Classification of the Virtues and the Standard of Virtue
  5. Justice and the Artificial Virtues
    1. The Circle Argument
    2. The Origin of Justice
    3. The Obligation of Justice and the Sensible Knave
  6. The Natural Virtues
    1. Pride and Greatness of Mind
    2. Goodness, Benevolence, and the Narrow Circle
    3. Natural Abilities
  7. References and Further Reading
    1. Hume’s Works
    2. Further Reading
    3. Other Works Cited

1. Hume’s Rejection of Moral Rationalism

Many philosophers have believed that the ability to reason marks a strict separation between humans and the rest of the natural world. Views of this sort can be found in thinkers such as Plato, Aristotle, Aquinas, Descartes, and Kant. One of the more philosophically radical aspects of Hume’s thought is his attack on this traditional conception. For example, he argues that the same evidence we have for thinking that human beings possess reason should also lead us to conclude that animals are rational (T 1.3.16, EHU 9). Hume also contends that the intellect, or “reason alone,” is relatively powerless on its own and needs the assistance of the emotions or “passions” to be effective. This conception of reason and emotion plays a critical role in Hume’s moral philosophy.

One of the foremost topics debated in the seventeenth and eighteenth century about the nature of morality was the relationship between reason and moral evaluation. Hume rejected a position known as moral rationalism. The moral rationalists held that ethical evaluations are made solely upon the basis of reason without the influence of the passions or feelings. The seventeenth and eighteenth century moral rationalists include Ralph Cudworth (1617-1688), Samuel Clarke (1675-1729), and John Balguy (1688-1748). Clarke, for instance, writes that morality consists in certain “necessary and eternal” relations (Clarke 1991[1706]: 192). He argues that it is “fit and reasonable in itself” that one should preserve the life of an innocent person and, likewise, unfit and unreasonable to take someone’s life without justification (Clarke 1991[1706]: 194). The very relationship between myself, a rational human being, and this other individual, another rational human being who is innocent of any wrongdoing, implies that it would be wrong of me to kill this person. The moral truths implied by such relations are just as evident as the truths implied by mathematical relations. It is just as irrational to (a) deny the wrongness of killing an innocent person as it would be to (b) deny that three multiplied by three is equal to nine (Clarke 1991[1706]: 194). As evidence, Clarke points out that both (a) and (b) enjoy nearly universal agreement. Thus, Clarke believes we should conclude that both (a) and (b) are self-evident propositions discoverable by reason alone. Consequently, it is in virtue of the human ability to reason that we make moral evaluations and recognize our moral duties.

a. The Influence Argument

Although Hume rejects the rationalist position, Hume does allow that reason has some role to play in moral evaluation. In the second Enquiry Hume argues that, although our determinations of virtue and vice are based upon an “internal sense or feeling,” reason is needed to ascertain the facts required to form an accurate view of the person being evaluated and, thus, is necessary for accurate moral evaluations (EPM 1.9). Hume’s claim, then, is more specific. He denies that moral evaluation is the product of “reason alone.” It is not solely because of the rational part of human nature that we can distinguish moral goodness from moral badness. Not “every rational being” can make moral evaluations (T 3.1.1.4). Purely rational beings that are devoid of feelings and emotion, if any such beings exist, could not understand the difference between virtue and vice. Something other than reason is required. Below is an outline of the argument Hume gives for this conclusion at T 3.1.1.16. Call this the “Influence Argument.”

  • Moral distinctions can influence human actions.
  • “Reason alone” cannot influence human actions.
  • Therefore, moral distinctions are not the product of “reason alone.”

Let us begin by considering premise (1). Notice that premise (1) uses the term “moral distinctions.” By “moral distinction” Hume means evaluations that differentiate actions or character traits in terms of their moral qualities (T 3.1.1.3). Unlike the distinctions we make with our pure reasoning faculty, Hume claims moral distinctions can influence how we act. The claim that some action, X, is vicious can make us less likely to perform X, and the opposite in the case of virtue. Those who believe it is morally wrong to kill innocent people will, consequently, be less likely to kill innocent people. This does not mean moral evaluations motivate decisively. One might recognize that X is a moral duty, but still fail to do X for various reasons. Hume only claims that the recognition of moral right and wrong can motivate action. If moral distinctions were not practical in this sense, then it would be pointless to attempt to influence human behavior with moral rules (T 3.1.1.5).

Premise (2) requires a more extensive justification. Hume provides two separate arguments in support of (2), which have been termed by Rachel Cohon as the “Divide and Conquer Argument” and the “Representation Argument” (Cohon 2008). These arguments are discussed below.

b. The Divide and Conquer Argument

Hume reminds us that the justification for premise (2) of the Influence Argument was already established earlier at Treatise 2.3.3 in a section entitled “Of the influencing motives of the will.” Hume begins this section by observing that many believe humans act well by resisting the influence of our passions and following the demands of reason (T 2.3.3.1). For instance, in the Republic Plato (427–347 B.C.E.) outlines a conception of the well-ordered soul in which the rational part rules over the soul’s spirited and appetitive parts. Or, consider someone who knows that eating another piece of cake is harmful to her health, and values her health, but still eats another piece of cake. Such situations are often characterized as letting passion or emotion defeat reason. Below is the argument that Hume uses to reject this conception.

  1. Reason is either demonstrative or probable.
  2. Demonstrative reason alone cannot influence the will (or influence human action).
  3. Probable reason alone cannot influence the will (or influence human action).
  4. Therefore, “reason alone” cannot influence the will (or influence human action).

This argument is referred to as the “Divide and Conquer Argument” because Hume divides reasoning into two types, and then demonstrates that neither type of reasoning can influence the human will by itself. From this, it follows that “reason alone” cannot influence the will.

The first type of reasoning Hume discusses is demonstrative reasoning that involves “abstract relations of ideas” (T 2.3.3.2). Consider demonstratively certain judgments such as “2+2=4” or “the interior angles of a triangle equal 180 degrees.” This type of reason cannot motivate action because our will is only influenced by what we believe has physical existence. Demonstrative reason, however, only acquaints us with abstract concepts (T 2.3.3.2). Using Hume’s example, mathematical demonstrations might provide a merchant with information about how much money she owes to another person. Yet, this information only matters because she has a desire to square her debt (T 2.3.3.2). It is this desire, not the demonstrative reasoning itself, which provides the motivational force.

Why can probable reasoning not have practical influence? Probable reasoning involves making inferences on the basis of experience (T 2.3.3.1). An example of this is the judgments we make of cause and effect. As Hume established earlier in the Treatise, our judgments of cause and effect involve recognizing the “constant conjunction” of certain objects as revealed through experience (see, for instance, T 1.3.6.15). Since probable reasoning can inform us of what actions have a “constant conjunction” with pleasure or pain, it might seem that probable reasoning could influence the will. However, the fundamental motivational force does not arise from our ability to infer the relation of cause and effect. Rather, the source of our motivation is the “impulse” to pursue pleasure and avoid pain. Thus, once again, reason simply plays the role of discovering how to satisfy our desires (T 2.3.3.3). For example, my belief that eating a certain fruit will cause good health seems capable of motivating me to eat that fruit (T 3.3.1.2). However, Hume argues that this causal belief must be accompanied with some passion, specifically the desire for good health, for it to move the will. We would not care about the fact that eating the fruit contributes to our health if health was not a desired goal. Thus, Hume sketches a picture in which the motivational force to pursue a goal always comes from passion, and reason merely informs us of the best means for achieving that goal (T 2.3.3.3).

Consequently, when we say that some passion is “unreasonable,” we mean either that the passion is founded upon a false belief or that passion impelled us to choose the wrong method for achieving our desired end (T 2.3.3.7). In this context Hume famously states that it is “not contrary to reason to prefer the destruction of the whole world to the scratching of my finger” (T 2.3.3.6). It can be easy to misunderstand Hume’s point here. Hume does not believe there is no basis for condemning the person who prioritizes scratching her finger. Hume’s point is simply that reason itself cannot distinguish between these choices. A being that felt completely indifferent toward both the suffering and well-being of other human beings would have no preference for what outcome results (EPM 6.4).

The second part of Hume’s thesis is that, because “reason alone” cannot motivate actions, there is no real conflict between reason and passion (T 2.3.3.1). The view that reason and passion can conflict misunderstands how each functions. Reason can only serve the ends determined by our passions. As Hume explains in another well-known quote “Reason is, and ought only to be the slave of the passions” (T 2.3.3.4). Reason and passion have fundamentally different functions and, thus, cannot encroach upon one another. Why do we commonly describe succumbing to temptation as a failure to follow reason? Hume explains that the operations of the passions and reason often feel similar. Specifically, both the calm passions that direct us toward our long-term interest, as well as the operations of reason, exert themselves calmly (T 2.3.3.8). Thus, the person who possesses “strength of mind,” or what is commonly called “will power,” is not the individual whose reason conquers her passions. Instead, being strong-willed means having a will that is primarily influenced by calm instead of violent passions (T 2.3.3.10).

c. The Representation Argument

The second argument in support of premise (2) of the “Influence Argument” is found in both T 3.3.1 and T 2.3.3. This argument is commonly referred to as the “Representation Argument.” It is expressed most succinctly at T 3.3.1.9. The argument has two parts. The first part of the argument is outlined below.

  1. That which is an object of reason must be capable of being evaluated as true or false (or be “truth-apt”).
  2. That which is capable of being evaluated as true or false (or is “truth-apt”) must be capable of agreement (or disagreement) with some relation of ideas or matter of fact.
  3. Therefore, that which can neither agree (nor disagree) with any relation of ideas or matter of fact cannot be an object of reason.

The first portion of the argument establishes what reason can (and cannot) accomplish. Premise (1) relies on the idea that the purpose of reason is to discover truth and falsehood. In fact, in an earlier Treatise section Hume describes truth as the “natural effect” of our reason (T 1.4.1.1). So, whatever is investigated or revealed through reason must be the sort of claim that it makes sense to evaluate as true or false. Philosophers call such claims “truth-apt.” What sorts of claims are truth-apt? Only those claims which can agree (or disagree) with some abstract relation of ideas or fact about existence. For instance, the claim that “the interior angles of a triangle add up to 180 degrees” agrees with the relation of ideas that makes up our concept of triangle. Thus, such a claim is true. The claim that “China is the most populated country on planet Earth” agrees with the empirical facts about world population and, thus, can also be described as true. Likewise, the claims that “the interior angles of a triangle add up to 200 degrees” or that “the United States is the most populated country on planet Earth” do not agree with the relevant ideas or existential facts. Yet, because it is appropriate to label each of these as false, both claims are still “truth-apt.” From this, it follows that something can only be an object of reason if it can agree or disagree with a relation of ideas or matter of fact.

Is that which motivates our actions “truth-apt” and, consequently, within the purview of reason? Hume addresses that point in the second part of the Representation Argument:

4. Human “passions, volitions, and actions” (PVAs) can neither agree (nor disagree) with any relation of ideas or matter of fact.

5. Therefore, PVAs cannot be objects of reason (or reason cannot produce action).

Why does the argument talk about “passions, volitions, and actions” (PVAs) in premise (4)? PVAs are the component parts of motivation. Passions cause desire or aversion toward a certain object, which results in the willing of certain actions. Thus, the argument hinges on premise (4)’s claim that PVAs can never agree or disagree with relations of ideas or matters of fact. Hume’s justification for this claim is again found at T 2.3.3.5 from the earlier Treatise section “Of the Influencing Motives of the Will.” Here Hume argues that for something to be truth-apt it must have a “representative quality” (T 2.3.3.5). That is, it must represent some type of external reality. The claim that “the interior angles of a triangle equal 180 degrees” represents a fact about our concept of a triangle. The claim that “China is the most populated country on planet Earth” represents a fact about the current population distribution of Earth. Hume argues the same cannot be said of passions such as anger. The feeling of anger, just like the feeling of being thirsty or being ill, is not meant to be a representation of some external object (T 2.3.3.5). Anger, of course, is a response to something external. For example, one might feel anger in response to a friend’s betrayal. However, this feeling of anger is not meant to represent my friend’s betrayal. A passion or emotion is simply a fact about the person who feels it. Consequently, since reason only deals with what is truth-apt, it follows that (5) PVAs cannot be objects of reason.

d. Hume and Contemporary Metaethics

Hume’s moral philosophy has continued to influence contemporary philosophical debates in metaethics. Consider the following three metaethical debates.

Moral Realism and Anti-Realism: Moral realism holds that moral statements, such as “lying is morally wrong,” describe mind-independent facts about the world. Moral anti-realism denies that moral statements describe mind-independent facts about the world.

Moral Cognitivism and Noncognitivism: Moral cognitivism holds that moral statements, such as “lying is morally wrong,” are capable of being evaluated as true or false (or are “truth-apt”). Moral noncognitivism denies that such statements can be evaluated as true or false (or can be “truth-apt”).

Moral Internalism and Externalism: Moral internalism holds that someone who recognizes that it is one’s moral obligation to perform X necessarily has at least some motive to perform X. Moral externalism holds that one can recognize that it is one’s moral obligation to perform X and simultaneously not have any motive to perform X.

While there is not just one “Humean” position on each of these debates, many contemporary meta-ethicists who see Hume as a precursor take a position that combines anti-realism, noncognitivism, and internalism. Much of the support for reading Hume as an anti-realist comes from consideration of his moral sense theory (which is examined in the next section). Evidence for an anti-realist reading of Hume is often found at T 3.1.1.26. Hume claims that, for any vicious action, the moral wrongness of the action “entirely escapes you, as long as you consider the object.” Instead, to encounter the moral wrongness you must “turn your reflexion into your own breast” (T 3.1.1.26). The wrongness of murder, taking Hume’s example, does not lie in the act itself as something that exists apart from the human mind. Rather, the wrongness of murder lies in how the observer reacts to the murder or, as we will see below, the painful sentiment that such an act produces in the observer.

The justification for reading Hume as an internalist comes primarily from the Influence Argument, which relies on the internalist idea that moral distinctions can, by themselves, influence the will and produce action. The claim that Hume is a noncognitivist is more controversial. Support for reading Hume as a noncognitivist is sometimes found in the so-called “is-ought” paragraph. There Hume warns us against deriving a conclusion that we “ought, or ought not” do something from the claim that something “is, and is not” the case (T 3.1.1.27). There is significant debate among Hume scholars about what Hume means to say in this passage. According to one interpretation, Hume is denying that it is appropriate to derive moral conclusions (such as “one should give to charity”) from any set of strictly factual or descriptive premises (such as “charity relieves suffering”). This is taken to imply support for noncognitivism by introducing a strict separation between facts (which are truth-apt) and values (which are not truth-apt).

Some have questioned the standard view of Hume as a noncognitivist. Hume does think (as seen in the Representation Argument) that the passions, which influence the will, are not truth-apt. Does the same hold for the moral distinctions themselves? Rachel Cohon has argued, to the contrary, that moral distinctions describe statements that are evaluable as true or false (Cohon 2008). Specifically, they describe beliefs about what character traits produce pleasure and pain in human spectators. If this interpretation is correct, then Hume’s metaethics remains anti-realist (moral distinctions refer to facts about the minds of human observers), but it can also be cognitivist. That is because the claim that human observers feel pleasure in response to some character trait represents an external matter of fact and, thus, can be denominated true or false depending upon whether it represents this matter of fact accurately.

2. Hume’s Moral Sense Theory

Hume claims that if reason is not responsible for our ability to distinguish moral goodness from badness, then there must be some other capacity of human beings that enables us to make moral distinctions (T 3.1.1.4). Like his predecessors Shaftesbury (1671-1713) and Francis Hutcheson (1694-1745), Hume believes that moral distinctions are the product of a moral sense. In this respect, Hume is a moral sentimentalist. It is primarily in virtue of our ability to feel pleasure and pain in response to various traits of character, and not in virtue of our capacity of “reason alone,” that we can distinguish between virtue and vice. This section covers the major elements of Hume’s moral sense theory.

a. The Moral Sense

Moral sense theory holds, roughly, that moral distinctions are recognized through a process analogous to sense perception. Hume explains that virtue is that which causes pleasurable sensations of a specific type in an observer, while vice causes painful sensations of a specific type. While all moral approval is a sort of pleasurable sensation, this does not mean that all pleasurable sensations qualify as instances of moral approval. Just as the pleasure we feel in response to excellent music is different from the pleasure we derive from excellent wine, so the pleasure we derive from viewing a person’s character is different from the pleasure we derive from inanimate objects (T 3.1.2.4). So, moral approval is a specific type of pleasurable sensation, only felt in response to persons, with a particular phenomenological quality.

Along with the common experience of feeling pleasure in response to virtue and pain when confronted with vice (T 3.1.2.2), Hume also thinks this view follows from his rejection of moral rationalism. Everything in the mind, Hume argues, is either an impression or idea. Hume understands an impression to be the first, and most forceful, appearance of a sensation or feeling in the human mind. An idea, by contrast, is a less forceful copy of that initial impression that is preserved in memory (T 1.1.1.1). Hume holds that all reasoning involves comparing our ideas. This means that moral rationalism must hold that we arrive at an understanding of morality merely through a comparison of ideas (T 3.1.1.4). However, since Hume has shown that moral distinctions are not the product of reason alone, moral distinctions cannot be made merely through comparison of ideas. Therefore, if moral distinctions are not made by comparing ideas, they must be based upon our impressions or feelings.

Hume’s claim is not that virtue is an inherent quality of certain characters or actions, and that when we encounter a virtuous character we feel a pleasurable sensation that constitutes evidence of that inherent quality. If that were true, then the moral status of some character trait would be inferred from the fact that we are experiencing a pleasurable sensation. This would conflict with Hume’s anti-rationalism. Hume reiterates this point, stating that spectators “do not infer a character to be virtuous, because it pleases: But in feeling that it pleases [they] in effect feel that it is virtuous” (T 3.1.2.3). Because moral distinctions are not made through a comparison of ideas, Hume believes it is more accurate to say that morality is a matter of feeling rather than judgment (T 3.1.2.1). Since virtue and vice are not inherent properties of actions or persons, what constitutes the virtuousness (or viciousness) of some action or character must be found within the observer or spectator. When, for example, someone determines that some action or character trait is vicious, this just means that your (human) nature is constituted such that you respond to that action or character trait with a feeling of disapproval (T 3.1.1.26). One’s ability to see the act of murder, not merely as a cause of suffering and misery, but as morally wrong, depends upon the emotional capacity to feel a painful sentiment in response to this phenomenon. Thus, Hume claims that the quality of “vice entirely escapes you, as long as you consider the object” (T 3.1.1.26). Virtue and vice exist, in some sense, through the sentimental reactions that human observers toward various “objects.”

This provides the basis for Hume’s comparison between moral evaluation and sense perception, which lies at the foundation of his moral sense theory. Just like the experiences of taste, smell, sight, hearing, and touch produced by our physical senses, virtue and vice exist in the minds of human observers instead of in the actions themselves (T 3.1.1.26). Here Hume appeals to the primary-secondary quality distinction. Sensory qualities and moral qualities are both observer-dependent. Just as there would be no appearance of color if there were no observers, so there would also be no such thing as virtue or vice without beings capable of feeling approval or disapproval in response to human actions. Likewise, a human being who lacked the required emotional capacities would be unable to understand what the rest of us mean when we say that some trait is virtuous or vicious. For instance, imagine a psychopath who has the necessary reasoning ability to understand the consequences of murder, but lacks aversion toward it and, thus, cannot determine or recognize its moral status. In fact, the presence of psychopathy, and the inability of psychopaths to understand moral judgments, is sometimes taken as an objection to moral rationalism.

Furthermore, our moral sense responds specifically to some “mental quality” (T 3.3.1.3) of another person. We can think of a “mental quality” as a disposition one has to act in certain ways or as a character trait. For example, when we approve of the courageous individual, we are approving of that person’s willingness to stand resolute in the face of danger. Consequently, actions can only be considered virtuous derivatively, as signs of another person’s mental dispositions and qualities (T 3.3.1.4). A single action, unlike the habits and dispositions that characterize our character, is fleeting and may not accurately represent our character. Only settled character traits are sufficiently “durable” to determine our evaluations of others (T 3.3.1.5). For this reason, Hume’s ethical theory is sometimes seen as a form of virtue ethics.

b. The General Point of View

Hume posits an additional requirement that some sentiment must meet to qualify as a sentiment of moral approval (or disapproval). Imagine a professor unfairly shows favor toward one student by giving her an “A” for sub-standard work. In this case, it is not difficult to imagine the student being pleased with the professor’s actions. However, if she was honest, that student would likely not think she was giving moral approval of the professor’s unfair grading. Instead, she is evaluating the influence the professor’s actions have upon her perceived self-interest. This case suggests that there is an important difference between the evaluations we make of other people based upon how they influence our interests, and the evaluations we make of others based upon their moral character.

This idea plays a significant role in Hume’s moral theory. Moral approval only occurs from a perspective in which the spectator does not take her self-interest into consideration. Rather, moral approval occurs from a more “general” vantage point (T 3.1.2.4). In the conclusion to the second Enquiry Hume makes this point by distinguishing the languages of morality and self-interest. When someone labels another “his enemy, his rival, his antagonist, his adversary,” he is evaluating from a self-interested point of view. By contrast, when someone labels another with moral terms like “vicious or odious or depraved,” she is inhabiting a general point of view where her self-interest is set aside (EPM 9.6). Speaking the language of morality, then, requires abstracting away from one’s personal perspective and considering the wider effects of the conduct under evaluation. This unbiased point of view is one aspect of what Hume refers to as the “general” (T 3.3.1.15) or “common” (T 3.3.1.30, EPM 9.6) point of view. Furthermore, he suggests that the ability to transcend our personal perspective, and adopt a general vantage point, ties human beings together as “the party of humankind against vice and disorder, its common enemy” (EPM 9.9). Thus, Hume’s theory of moral approval is related in important ways to his larger goal of demonstrating that moral life is an expression of human sociability.

The general vantage point from which moral evaluations are made does not just exclude considerations of self-interest. It also corrects for other factors that can distort our moral evaluations. For instance, adoption of the general point of view corrects our natural tendency to give greater praise to those who exist in close spatial-temporal proximity. Hume notes that someone might feel a stronger degree of praise for her hardworking servant than she feels for the historical representation of Marcus Brutus (T 3.3.1.16). From an objective point of view, Brutus merits greater praise for his moral character. However, we are acquainted with our servant and frequently interact with him. Brutus, on the other hand, is only known to us through historical accounts. Temporal distance causes our immediate, natural feelings of praise for Brutus to be less intense than the approval we give to our servant. Yet, this variation is not reflected in our moral evaluations. We do not judge that our servant has a superior moral character, and we do not automatically conclude that those who live in our own country are morally superior to those living in foreign countries (T 3.3.1.14).  So, Hume needs some explanation of why our considered moral evaluations do not match our immediate feelings.

Hume responds by explaining that, when judging the quality of someone’s character, we adopt a perspective that discounts our specific spatial-temporal location or any other special resemblance we might have with the person being evaluated. Hume tells us that this vantage point is one in which we consider the influence that the person in question has upon his or her contemporaries (T 3.3.3.2). When we evaluate Brutus’ character, we do not consider the influence that his qualities have upon us now. As a historical figure who no longer exists, Brutus’ virtuous character does not provide any present benefit. Instead, we evaluate Brutus’ character based upon the benefits it had for those who lived in Brutus’ own time. We recognize that if we had lived in Brutus’ own time, and were a fellow Roman citizen with him, then we would express much greater praise and admiration for his character (T 3.3.1.16).

Hume identifies a second type of correction that the general point of view is responsible for as well. Hume observes that we have the capacity to praise someone whose character traits are widely beneficial, even when unfortunate external circumstances prevent those traits from being effective (T 3.3.1.19). For example, we might imagine a generous, kind-hearted individual whose generosity fails to make much of an impact on others because she is of modest means. Hume claims, in these cases, our considered moral evaluation is not influenced by such external circumstances: “Virtue in rags is still virtue” (T 3.3.1.19). At the same time, we might be puzzled how this could be the case since we naturally give stronger praise to the person whose good fortune enables her virtuous traits to produce actual benefits (T 3.3.1.21). Hume makes a two-fold response here. First, because we know that (for instance) a generous character is often correlated with benefits to society, we establish a “general rule” that links these together (T 3.3.1.20). Second, when we take up the general point of view, we ignore the obstacles of misfortune that prevent this virtuous person’s traits from achieving their intended goal (T 3.3.1.21). Just as we discount spatial-temporal proximity, so we also discount the influence of fortune when making moral evaluations of another’s character traits.

So, adopting the general point of view requires spectators to set aside a multitude of considerations: self-interest, demographic resemblance, spatial-temporal proximity, and the influence of fortune. What motivates us to adopt this vantage point? Hume explains that doing so enables us to discuss the evaluations we make of others. If we each evaluated from our personal perspective, then a character that garnered the highest praise from me might garner only than mild praise from you. The general point of view, then, provides a common basis from which differently situated individuals can arrive at some common understanding of morality (T 3.3.1.15). Still, Hume notes that this practical solution may only regulate our language and public judgments of our peers. Our personal feelings often prove too entrenched. When our actual sentiments are too resistant to correction, Hume notes that we at least attempt to conform our language to the objective standard (T 3.3.1.16).

In addition to explaining why it is that we adopt the general point of view, one might also think that Hume owes us an explanation of why this perspective constitutes the standard of correctness for moral evaluation. In one place Hume states that the “corrections” we make to our sentiments from the general point of view are “alone regarded, when we pronounce in general concerning the degrees of vice and virtue” (T 3.3.1.21). Nine paragraphs later Hume again emphasizes that the sentiments we feel from the general point of view constitute the “standard of virtue and morality” (T 3.3.1.30). What gives the pronouncements we make from the general point of view this authoritative status?

Hume scholars are divided on this point. One possibility, developed by Geoffrey Sayre-McCord, is that adopting the general point of view enables us to avoid the practical conflicts that inevitably arise when we judge character traits from our individual perspectives (Sayre-McCord 1994: 213-220). Jacqueline Taylor, focusing primarily on the second Enquiry, argues that the normative authority of the general point of view arises from the fact that it arises from a process of social deliberation and negotiation requiring the virtues of good judgment (Taylor 2002). Rachel Cohon argues that evaluations issuing from the general point of view are most likely to form true ethical beliefs (Cohon 2008: 152-156). In a somewhat similar vein, Kate Abramson argues that the general point of view enables us to correctly determine whether some character trait enables its possessor to act properly within the purview of her relationships and social roles (Abramson 2008: 253). Finally, Phillip Reed argues that, to the contrary, the general point of view does not constitute Hume’s “standard of virtue” (Reed 2012).

3. Sympathy and Humanity

a. Sympathy

We have seen that, for Hume, a sentiment can qualify as a moral sentiment only if it is not the product of pure self-interest. This implies that human nature must possess some capacity to get outside of itself and take an interest in the fortunes and misfortunes of others. When making moral evaluations we approve qualities that benefit the possessor and her associates, while disapproving of those qualities that make the possessor harmful to herself or others (T 3.3.1.10). This requires that we can take pleasure in that which benefits complete strangers. Thus, moral evaluation would be impossible without the capacity to partake of the pleasure (or pain) of any being that shares our underlying human nature. Hume identifies “sympathy” as the capacity that makes moral evaluation possible by allowing us to take an interest in the public good (T 3.3.1.9). The idea that moral evaluation is based upon sympathy can also be found in the work of Hume’s contemporary Adam Smith (1723-1790). However, the account of sympathy found in Smith’s work also differs in important ways from what we find in Hume.

Because of the central role that sympathy plays in Hume’s moral theory, his account of sympathy deserves further attention. Hume tells us that sympathy is the human capacity to “receive” the feelings and beliefs of other people (T 2.1.11.2). That is, it is the process by which we experience what others are feeling and thinking. This process begins by forming an idea of what another person is experiencing. This idea might be formed through observing the effects of another’s feeling (T 2.1.11.3). For instance, from my observation that another person is smiling, and my prior knowledge that smiling is associated with happiness, I form an idea of the other’s happiness. My idea of another’s emotion can also be formed prior to the other person feeling the emotion. This occurs through observing the usual causes of that emotion. Hume provides the example of someone who observes surgical instruments being prepared for a painful operation. He notes that this person would feel terrified for the person about to suffer through the operation even though the operation had not yet begun (T 3.3.1.7). This is because the observer already established a prior mental association between surgical instruments and pain.

Since sympathy causes us to feel the sentiments of others, simply having an idea of another’s feeling is insufficient. That idea must be converted into something with more affective potency. Our idea of what another feels must be transformed into an impression (T 2.1.11.3). The reason this conversion is possible is that the only difference between impressions and ideas is the intensity with which they are felt in the mind (T 2.1.11.7). Recall that impressions are the most forceful and intense whereas ideas are merely “faint images” of our impressions (T 1.1.1.1). Hume identifies two facts about human nature which explain what causes our less vivacious idea of another’s passion to be converted into an impression and, notably, become the very feeling the other is experiencing (T 2.1.11.3). First, we always experience an impression of ourselves which is not surpassed in force, vivacity, and liveliness by any other impression. Second, because we have this lively impression of ourselves, Hume believes it follows that whatever is related to that impression must receive some share of that vivacity (T 2.1.11.4). From these points, it follows that our idea of another’s impression will be enlivened if that idea has some relation to ourselves.

Hume explains the relationship between our idea of another’s emotion and ourselves in terms of his more general conception of how the imagination produces associations of ideas. Hume understands the association of ideas as a “gentle force” that explains why certain mental perceptions repeatedly occur together. He identifies three such ways in which ideas become associated: resemblance (the sharing of similar characteristics), contiguity (proximity in space or time), and causation (roughly, the constant conjunction of two ideas in which one idea precedes another in time) (T 1.1.4.1). Hume appeals to each of these associations to explain the relationship between our idea of another’s emotion and our impression of self (T 2.1.11.6). However, resemblance plays the most important role. Although each individual human is different from one another, there is also an underlying commonality or resemblance within all members of the human species (T 2.1.11.5). For example, when we form an idea of another’s happiness, we implicitly recognize that we ourselves are also capable of that same feeling. That idea of happiness, then, becomes related to ourselves and, consequently, receives some of the vivacity that is held by the impression of our self. In this way, our ideas of how others feel become converted into impressions and we “feel with” our fellow human beings.

Although sympathy makes it possible for us to care for others, even those we have no close or immediate connection with, Hume acknowledges that it does not do so in an entirely impartial or egalitarian manner. The strength of our sympathy is influenced both by the universal resemblance that exists among all human beings as well as more parochial types of resemblances. We will sympathize more easily with those who share various demographic similarities such as language, culture, citizenship, or place of origin (T 2.1.11.5). Consequently, when the person we are sympathizing with shares these similarities we will form a stronger conception of their feelings, and when such similarities are absent our conception of their feeling will be comparatively weaker. Likewise, we will have stronger sympathy with those who live in our own city, state, country, or time, than we will with those who are spatially or temporally distant. In fact, it is this aspect of sympathy which prompts Hume to introduce the general point of view (discussed above). It is our natural sympathy that causes us to give stronger praise those who exist in closer spatial-temporal proximity, even though our considered moral evaluations do not exhibit such variation. Hume poses this point as an objection to his claim that our moral evaluations proceed from sympathy (T 3.3.1.14). Hume’s appeal to the general point of view allows him to respond to this objection. Moral evaluations arise from sympathetic feelings that are corrected by the influence of the general point of view.

b. Humanity

While sympathy plays a crucial role in Hume’s moral theory as outlined in the Treatise, explicit mentions of sympathy are comparatively absent from the Enquiry. In place of Hume’s detailed description of sympathy, we find Hume appealing to the “principle of humanity” (EPM 9.6). He understands this as the human disposition that produces our common praise for that which benefits the public and common blame for that which harms the public (EPM 5.39). The principle of humanity explains why we prefer seeing things go well for our peers instead of seeing them go badly. It also explains why we would not hope to see our peers suffer if that suffering in no way benefited us or satisfied our resentment from a prior provocation (EPM 5.39). Like sympathy, then, Hume uses humanity to explain our concern for the well-being of others. However, Hume’s discussion of humanity in the Enquiry does not appeal (at least explicitly) to the cognitive mechanism that underlies Hume’s account of sympathy, and he even expresses skepticism about the possibility of explaining this mechanism. So, the Enquiry does not discuss how our idea of another’s pleasures and pains is converted into an impression. This does not necessarily mean that sympathy is absent from the Enquiry. For instance, in Enquiry Section V Hume describes having the feelings of others communicated to us (EPM 5.18) and details how sharing our sentiments in a social setting can strengthen our feelings (EPM 5.24, EPM 5.35).

As he did with sympathy in the Treatise, Hume argues that the principle of humanity makes moral evaluations possible. It is because we naturally approve of that which benefits society, and disapprove of that which harms society, that we see some character traits as virtuous and others as vicious. Hume’s justification for this claim follows from his rejection of the egoists (EPM 5.6). Here Hume has in mind those like Thomas Hobbes (1588-1679) and Bernard Mandeville (1670-1733), who each believed that our moral judgments are the product of self-interest. Those qualities we consider virtuous are those that serve our interests, and those that we consider vicious are those that do not serve our interests. Hume gives a variety of arguments against this position. He contends that egoism cannot explain why we praise the virtues of historical figures (EPM 5.7) or recognize the virtues of our enemies (EPM 5.8). If moral evaluations are not the product of self-interest, then Hume concludes that they must be caused by some principle which gives us real concern for others. This is the principle of humanity. Hume admits that the sentiments produced by this principle might often be unable to overpower the influence that self-interest has on our actions. However, this principle is strong enough to give us at least a “cool preference” for that which is beneficial to society, and provides the foundation upon which we distinguish the difference between virtue and vice (EPM 9.4).

4. Hume’s Classification of the Virtues and the Standard of Virtue

Since Hume thinks virtuous qualities benefit society, while vicious qualities harm society, one might conclude that Hume should be placed within the utilitarian moral tradition. While Hume’s theory has utilitarian elements, he does not think evaluations of virtue and vice are based solely upon considerations of collective utility. Hume identifies four different “sources” of moral approval, or four different effects of character traits that produce pleasure in spectators (T 3.3.1.30). Hume generates these categories by combining two different types of benefits that traits can have (usefulness and immediate agreeability) with two different types of benefactor that a trait can have (the possessor of the trait herself and other people) (EPM 9.1). Below is an outline of the four resulting sources of moral approval.

  • We praise traits that are useful to others. For example, justice (EPM 3.48) and benevolence (EPM 2.22).
  • We praise traits that are useful to the possessor of the trait. For example, discretion or caution (EPM 6.8), industry (EPM 6.10), frugality (EPM 6.11), and strength of mind (EPM 6.15).
  • We praise traits with immediate agreeability to others. For example, good manners (EPM 8.1) and the ability to converse well (EPM 8.5).
  • We praise traits that are immediately agreeable to the possessor. For example, cheerfulness (EPM 7.2) and magnanimity (EPM 7.4-7.18).

What does Hume mean by “immediate agreeability”? Hume explains that immediately agreeable traits please (either the possessor or others) without “any further thought to the wider consequences that trait brings about” (EPM 8.1). Although being well-mannered has beneficial long-term consequences, Hume believes we also praise this trait because it is immediately pleasing to company. As we shall see below, this distinction implies that a trait can be praised for its immediate agreeability even if the trait has harmful consequences more broadly.

There is disagreement amongst Hume scholars about how this classification of virtue is related to Hume’s definition of what constitutes a virtue, or what is termed the “standard of virtue.” That is, what is the standard which determines whether some character trait counts as a virtue? The crux of this disagreement can be found in two definitions of virtue that Hume provides in the second Enquiry.

First Definition: “personal merit consists altogether in the possession of mental qualities, useful or agreeable to the person himself or to others” (EPM 9.1).

Second Definition: “It is the nature, and, indeed, the definition of virtue, that it is a quality of the mind agreeable to or approved of by every one who considers or contemplates it” (EPM 8.n50).

The first definition suggests that virtue is defined in terms of its usefulness or agreeableness. On this basis, we might interpret Hume as believing that a trait fails to qualify as a virtue if it is neither useful nor agreeable. This interpretation is also supported by places in the text where Hume criticizes approval of traits that fail to meet the standard of usefulness and agreeableness. One prominent example is his discussion of the religiously motivated “monkish virtues.” There he criticizes those who praise traits such as “[c]elibacy, fasting, penance, mortification, self-denial, humility, silence, solitude” on the grounds that these traits are neither useful to society nor agreeable to their possessors (EPM 9.3). The second definition, however, holds that what determines whether some character trait warrants the status of virtue is the ability of that trait to generate spectator approval. On this view, some trait is a virtue if it garners approval from a general point of view, and the sources of approval (usefulness and agreability) simply describe those features of character traits that human beings find praiseworthy.

5. Justice and the Artificial Virtues

The four-fold classification of virtue discussed above deals with the features of character traits that attract our approval (or disapproval). However, in the Treatise Hume’s moral theory is primarily organized around a distinction between the way we approve (or disapprove) of some character trait. Hume tells us that some virtues are “artificial” whereas other virtues are “natural” (T 3.1.2.9). In this context, the natural-artificial distinction tracks whether the entity in question results from the plans or designs of human beings (T 3.1.2.9). On this definition, a tree would be natural whereas a table would be artificial. Unlike the former, the latter required some process of human invention and design. Hume believes that a similar type of distinction is present when we consider different types of virtue. There are natural virtues like benevolence, and there are artificial virtues like justice and rules of property. In addition to justice and property, Hume also classifies the keeping of promises (T 3.1.2.5), allegiance to government (T 3.1.2.8), laws of international relations (T 3.1.2.11), chastity (T 3.1.2.12), and good manners (T 3.1.2.12) as artificial virtues.

The designs that constitute the artificial virtues are social conventions or systems of cooperation. Hume describes the relationship between artificial virtues and their corresponding social conventions in different ways. The basic idea is that we would neither have any motive to act in accordance with the artificial virtues (T 3.2.1.17), nor would we approve of artificially virtuous behavior (T 3.2.1.1), without the relevant social conventions. No social scheme is needed for us to approve of an act of kindness. However, the very existence of people who respect property rights, and our approval of those who respect property rights, requires some set of conventions that specify rules regulating the possession of goods. As we will see, Hume believes the conventions of justice and property are based upon collective self-interest. In this way, Hume uses the artificial-natural virtue distinction to carve out a middle position in the debate between egoists (like Hobbes and Mandeville), who believe that morality is a product of self-interest, and moral sense theorists (like Shaftesbury and Hutcheson), who believe that our sense of virtue and vice is natural to human nature. The egoists are right that some virtues are the product of collective self-interest (the artificial virtues), but the moral sense theorists are also correct insofar as other virtues (the natural virtues) have no relation to self-interest.

a. The Circle Argument

In Treatise 3.2.1 Hume provides an argument for the claim that justice is an artificial virtue (T 3.2.1.1). Understanding this argument requires establishing three preliminary points. First, Hume uses the term “justice,” at least in this context, to refer narrowly to the rules that regulate property. So, his purpose here is to prove that the disposition to follow the rules of property is an artificial virtue. That is, it would make no sense to approve of those who are just, nor to act justly, without the appropriate social convention. Second, Hume uses the concept of a “mere regard to the virtue of the action” (T 3.2.1.4) or a “sense of morality or duty” (T 3.2.1.8). This article uses the term “sense of duty.” The sense of duty is a specific type of moral motivation whereby someone performs a virtuous action only because she feels it is her ethical obligation to do so. For instance, imagine that someone has a job interview and knows she can improve her chances of success by lying to the interviewers. She might still refrain from lying, not because this is what she desires, but because she feels it is her moral obligation. She has, thus, acted from a sense of duty.

Third, a crucial step in Hume’s argument involves showing that a sense of duty cannot be the “first virtuous motive” to justice (T 3.2.1.4). What does it mean for some motive to be the “first motive?” It is tempting to think that Hume uses the phrase “first motive” as a synonym for “original motive.” Original motives are naturally present in the “rude and more natural condition” of human beings prior to modern social norms, rules, and expectations (T 3.2.1.9). For example, parental affection provides an original motive to care for one’s children (T 3.2.1.5). As we will see, Hume does not believe that the sense of duty can be an original motive to justice. One can only act justly from a sense of duty after some process of education, training, or social conditioning (T 3.2.1.9). However, while Hume does believe that many first motives are original in human nature, it cannot be his position that all first motives are original in human nature. This is because he does not believe there is any original motive to act justly, but he does think there is a first motive to act justly. Therefore, it is best to understand Hume’s notion of the first motive to perform some action as whatever motive (whether original or arising from convention) first causes human beings to perform that action.

With these points in place, let us consider the basic structure of Hume’s reasoning. His fundamental claim is that there is no original motive that can serve as the first virtuous motive of just actions. That is, there is nothing in the original state of human nature, prior to the influence of social convention, that could first motivate someone to act justly. While in our present state a “sense of duty” can serve as a sufficient motive to act justly, human beings in our natural condition would be bewildered by such a notion (T 3.2.1.9). However, if no original motive can be found that first motivates justice, then it follows that justice must be an artificial virtue. This is implied from Hume’s definition of artificial virtue. If the first motive for some virtue is not an original motive, then that virtue must be artificial.

Against Hume, one might argue that human beings have a natural “sense of justice” and that this serves as an original motive for justice. Hume rejects this claim with an argument commonly referred to as the “Circle Argument.” The foundation of this argument is the previously discussed claim that when making a moral evaluation of an action, we are evaluating the motive, character trait, or disposition that produced that action (T 3.2.1.2). Hume points out that we often retract our blame of another person if we find out they had the proper motive, but they were prevented from acting on that motive because of unfortunate circumstances (T 3.2.1.3). Imagine a good-hearted individual who gives money to charity. Suppose also that, through no fault of her own, her donation fails to help anyone because the check was lost in the mail. In this case, Hume argues, we would still praise this person even though her donation was not beneficial. It is the willingness to help that garners our praise. Thus, the moral virtue of an action must derive completely from the virtuous motive that produces it.

Now, assume for the sake of argument that the first virtuous motive of some action is a sense of duty to perform that action. What would have to be the case for a sense of duty to be a virtuous motive that is worthy of praise? At minimum, it would have to be true that the action in question is already virtuous (T 3.2.1.4). It would make no sense to claim that there is a sense of duty to perform action X, but also hold that action X is not virtuous. Unfortunately, this brings us back to where we began. If action X is already virtuous prior to our feeling any sense of duty to perform it, then there must likewise already be some other virtuous motive that explains action X’s status as a virtue. Thus, since some other motive must already be able to motivate just actions, a sense of duty cannot be the first motive to justice. Therefore, our initial assumption causes us to “reason in a circle” (T 3.2.1.4) and, consequently, must be false. From this, it follows that an action cannot be virtuous unless there is already some motive in human nature to perform it other than our sense, developed later, that performing the action is what is morally right (T 3.2.1.7). The same, then, would hold for the virtue of justice. This does not mean that a sense of duty cannot motivate us to act justly (T 3.2.1.8), nor does it necessarily mean that a sense of duty cannot be a praiseworthy motive. Hume’s point is simply that a sense of duty cannot be what first motivates us to act virtuously.

Having dispensed with the claim that a sense of duty can be an original motive, Hume then considers (and rejects) three further possible candidates of original motives that one might claim could provide the first motive to justice. These are: (i) self-interest, (ii) concern for the public interest, (iii) concern for the interests of the specific individual in question. Hume does not deny that each of these are original motives in human nature. Instead, he argues that none of them can adequately account for the range of situations in which we think one is required to act justly. Hume notes that unconstrained self-interest causes injustice (T 3.2.1.10), that there will always be situations in which one can act unjustly without causing any serious harm to the public (T 3.2.1.11), and that there are situations in which the individual concerned will benefit from us acting unjustly toward her. For example, this individual could be a “profligate debauchee” who would only harm herself by keeping her possessions (T 3.2.1.13). Consequently, if there is no original motive in human nature that can produce just actions, it must be the case that justice is an artificial virtue.

b. The Origin of Justice

Thus far Hume has established that justice is an artificial virtue, but has still not identified the “first motive” of justice. Hume begins to address this point in the next Treatise section entitled “Of the origin of justice and property.” We will see, however, that Hume’s complete account of what motivates just behavior goes beyond his comments here. Hume begins his account of the origin of justice by distinguishing two questions.

Question 1: What causes human beings in their natural, uncultivated state to form conventions that specify property rights? That is, how do the conventions of justice arise?

Question 2: Once the conventions of justice are established, why do we consider it a virtue to follow the rules specified by those conventions? In other words, why is justice a virtue?

Answering Question 1 requires determining what it is about the “natural” human condition (prior to the establishment of modern, large-scale society) that motivates us to construct the specific rules, norms, and social expectations associated with justice. Hume does this by outlining an account of how natural human beings come to recognize the benefits of establishing and preserving practices of cooperation.

Hume begins by claiming that the human species has many needs and desires it is not naturally equipped to meet (T 3.2.2.2). Human beings can only remedy this deficiency through societal cooperation that provides us with greater power and protection from harm than is possible in our natural state (T 3.2.2.3). However, natural humans must also become aware that societal cooperation is beneficial. Fortunately, even in our “wild uncultivated state,” we already have some experience of the benefits that are produced through cooperation. This is because the natural human desire to procreate, and care for our children, causes us to form family units (T 3.2.2.4). The benefits afforded by this smaller-scale cooperation provide natural humans with a preview of the benefits promised by larger-scale societal cooperation.

Unfortunately, while our experience with living together in family units shows us the benefits of cooperation, various obstacles remain to establishing it on a larger scale. One of these comes from familial life itself. The conventions of justice require us to treat others equally and impartially. Justice demands that we respect the property rights of those we love and care for just as we respect the property rights of those whom we do not know. Yet, family life only strengthens our natural partiality and makes us place greater importance on the interests of our family members. This threatens to undermine social cooperation (T 3.2.2.6). For this reason, Hume argues that we must establish a set of rules to regulate our natural selfishness and partiality. These rules, which constitute the conventions of justice, allow everyone to use whatever goods we acquire through our labor and good fortune (T 3.2.2.9). Once these social norms are in place, it then becomes possible to use terms such as “property, right, [and] obligation” (T 3.2.2.11).

This account further supports Hume’s claim that justice is an artificial virtue. Justice remedies specific problems that human beings face in their natural state. If circumstances were such that those problems never arose, then the conventions of justice would be pointless. Certain background conditions must be in place for justice to originate. John Rawls (1921-2002) refers to these conditions as the “circumstances of justice” (Rawls 1971: 126n). The remedy of justice is required because the goods we acquire are vulnerable to being taken by others (T 3.2.2.7), resources are scarce (T 3.2.2.7), and human generosity is limited (T 3.2.2.6). Regarding scarcity and human generosity, Hume explains that our circumstances lie at a mean between two extremes. If resources were so prevalent that there were enough goods for everyone, then there would be no reason to worry about theft or establish property rights (EPM 3.3). On the other hand, if scarcity were too extreme, then we would be too desperate to concern ourselves with the demands of justice. Nobody worries about acting justly after a shipwreck (EPM 3.8). In addition, if humans were characterized by thoroughgoing generosity, then we would have no need to restrain the behavior of others through rules and restrictions (EPM 3.6). By contrast, if human beings were entirely self-interested, without any natural concern for others, then there could be no expectation that others would abide by any rules that are established (EPM 3.9). Justice is only possible because human life is not characterized by these extremes. If human beings were characterized by universal generosity, then justice could be replaced with “much nobler virtues, and more valuable blessings” (T 3.2.2.16).

Another innovative aspect of Hume’s theory is that he does not believe the conventions of justice are based upon promises or explicit agreements. This is because Hume believes that promises themselves only make sense if certain human conventions are already established (T 3.2.2.10). Thus, promises cannot be used to explain how human beings move from their natural state to establishing society and social cooperation. Instead, Hume explains that the conventions of justice arise from “a general sense of common interest” (T 3.2.2.10) and that cooperation can arise without explicit agreement. Once it is recognized that everyone’s interest is served when we all refrain from taking the goods of others, small-scale cooperation becomes possible (T 3.2.2.10). In addition to allowing for a sense of security, cooperation serves the common good by enhancing our productivity (T 3.2.5.8). Our understanding of the benefits of social cooperation becomes more acute by a gradual process through which we steadily gain more confidence in the reliability of our peers (T 3.2.2.10). None of this requires an explicit agreement or promise. He draws a comparison with how two people rowing a boat can cooperate by an implicit convention without an explicit promise (T 3.2.2.10).

Although the system of norms that constitutes justice is highly advantageous and even necessary for the survival of society (T 3.2.2.22), this does not mean that society gains from each act of justice. An individual act of justice can make the public worse off than it would have otherwise been. For example, justice requires us to pay back a loan to a “seditious bigot” who will use the money destructively or wastefully (T 3.2.2.22). Artificial virtues differ from the natural virtues in this respect (T 3.3.1.12). This brings us to Hume’s second question about the virtue of justice. If not every act of justice is beneficial, then why do we praise obedience to the rules of justice? The problem is especially serious for large, modern societies. When human beings live in small groups the harm and discord caused by each act of injustice is obvious. Yet, this is not the case in larger societies where the connection between individual acts of justice and the common good is much weaker (T 3.2.2.24).

Consequently, Hume must explain why we continue to condemn injustice even after society has grown larger and more diffuse. On this point Hume primarily appeals to sympathy. Suppose you hear about some act of injustice that occurs in another city, state, or country, and harms individuals you have never met. While the bad effects of the injustice feel remote from our personal point of view, Hume notes that we can still sympathize with the person who suffers the injustice. Thus, even though the injustice has no direct influence upon us, we recognize that such conduct is harmful to those who associate with the unjust person (T 3.2.2.24). Sympathy allows our concern for justice to expand beyond the narrow bounds of the self-interested concerns that first produced the rules.

Thus, it is self-interest that motivates us to create the conventions of justice, and it is our capacity to sympathize with the public good that explains why we consider obedience to those conventions to be virtuous (T 3.2.2.24). Furthermore, we can now better understand how Hume answers the question of what first motivates us to act justly. Strictly speaking, the “first motive” to justice is self-interest. As noted previously, it was in the immediate interest of early humans living in small societies to comply with the conventions of justice because the integrity of their social union hinged upon absolute fidelity to justice. As we will see below, this is not the case in larger, modern societies. However, all that is required for some motive to be the first motive to justice is that it is what first gives humans some reason to act justly in all situations. The fact that this precise motive is no longer present in modern society does not prevent it from being what first motivates such behavior.

c. The Obligation of Justice and the Sensible Knave

Given that justice is originally founded upon considerations of self-interest, it may seem especially difficult to explain why we consider it wrong of ourselves to commit injustice in larger modern societies where the stakes of non-compliance are much less severe. Here Hume believes that general rules bridge the gap. Hume uses general rules as an explanatory device at numerous points in the Treatise. For example, he explains our propensity to draw inferences based upon cause and effect through the influence of general rules (T 1.3.13.8). When we consistently see one event (or type of event) follow another event (or type of event), we automatically apply a general rule that makes us expect the former whenever we experience the latter. Something similar occurs in the present context. Through sympathy, we find that sentiments of moral disapproval consistently accompany unjust behavior. Thus, through a general rule, we apply the same sort of evaluation to our own unjust actions (T 3.2.2.24).

Hume believes our willingness to abide by the conventions of justice is strengthened through other mechanisms as well. For instance, politicians encourage citizens to follow the rules of justice (T 3.2.2.25) and parents encourage compliance of their children (T 3.2.2.26). Thus, the praiseworthy motive that underlies compliance with justice in large-scale societies is, to a large extent, the product of social conditioning. This fact might make us suspicious. If justice is an artificial virtue, and if much of our motivation to follow its rules comes from social inculcation, then we might wonder whether these rules deserve our respect.

Hume recognizes this issue. In the Treatise he briefly appeals to the fact that having a good reputation is largely determined by whether we follow the rules of property (T 3.2.2.27). Theft, and the unwillingness to follow the rules of justice, does more than anything else to establish a bad reputation for ourselves. Furthermore, Hume claims that our reputation in this regard requires that we see each rule of justice as having absolute authority and never succumb when we are tempted to act unjustly (T 3.2.2.27). Suppose Hume is right that our moral reputation hangs on our obedience to the rules of justice. Even if true, it is not obvious that this requires absolute obedience to these rules. What if I can act unjustly without being detected? What if I can act unjustly without causing any noticeable harm? Is there any reason to resist this temptation?

Hume takes up this question directly in the Enquiry, where he considers the possibility of a “sensible knave.” The knave recognizes that, in general, justice is crucial to the survival of society. Yet, the knave also recognizes that there will always be situations in which it is possible to act unjustly without harming the fabric of social society. So, the knave follows the rules of justice when he must, but takes advantage of those situations where he knows he will not be caught (EPM 9.22). Hume responds that, even if the knave is never caught, he will lose out on a more valuable form of enjoyment. The knave forgoes the ability to reflect pleasurably upon his own conduct for the sake of material gain. In making this trade, Hume judges that knaves are “the greatest dupes” (EPM 9.25). The person who has traded the peace of mind that accompanies virtue in order to gain money, power, or fame has traded away that which is more valuable for something much less valuable. The enjoyment of a virtuous character is incomparably greater than the enjoyment of whatever material gains can be attained through injustice. Thus, justice is desirable from the perspective of our own personal happiness and self-interest (EPM 9.14).

Hume admits it will be difficult to convince genuine knaves of this point. That is, it will be difficult to convince someone who does not already value the possession of a virtuous character that justice is worth the cost (EPM 9.23). Thus, Hume does not intend to provide a defense of justice that can appeal to any type of being or provide a reason to be just that makes sense to “all rational beings.” Instead, he provides a response that should appeal to those with mental dispositions typical of the human species. If the ability to enjoy a peaceful review of our conduct is nearly universal in the human species, then Hume will have provided a reason to act justly that can make some claim upon nearly every human being.

6. The Natural Virtues

After providing his Treatise account of the artificial virtues, Hume moves to a discussion of the natural virtues. Recall that the natural virtues, unlike the artificial virtues, garner praise without the influence of any human convention. Hume divides the natural virtues into two broad categories: those qualities that make a human great and those that make a human good (T 3.3.3.1). Hume consistently associates a cluster of qualities with each type of character. The great individual is confident, has a sense of her value, worth, or ability, and generally possesses qualities that set her apart from the average person. She is courageous, ambitious, able to overcome difficult obstacles, and proud of her achievements (EPM 7.4, EPM 7.10). By contrast, the good individual is characterized by gentle concern for others. This person has the types of traits that make someone a kind friend or generous philanthropist (EPM 2.1). Elsewhere, Hume explains the distinction between goodness and greatness in terms of the relationship we would want to have with the good person or the great person: “We cou’d wish to meet with the one character in a friend; the other character we wou’d be ambitious of in ourselves” (T 3.3.4.2).

Alexander of Macedonia exemplifies an extreme case of greatness. Hume recounts how Alexander responded when his general Parmenio suggested he accept the peace offering made by the Persian King Darius III. When Parmenio advises Alexander to accept Darius’ offering, Alexander responds that “So would I too […] were I Parmenio” (EPM 7.5). There are certain constraints that apply to the average person that Alexander does not think apply to himself. This is consistent with the fact that the great individual has a strong sense of self-worth, self-confidence, and even a sense of superiority.

a. Pride and Greatness of Mind

Given the characteristics Hume associates with greatness, it should not be a surprise that Hume begins the Treatise section entitled “Of Greatness of Mind” by discussing pride (T 3.3.2). Those qualities and accomplishments that differentiate one from the average person are also those qualities most likely to make us proud and inspire confidence. Thus, Hume notes that pride forms a significant part of the hero’s character (T 3.3.2.13). However, Hume faces a problem—how can a virtuous character trait be based upon pride? He observes that we blame those who are too proud and praise those with enough modesty to recognize their own weaknesses (T 3.3.2.1). If we commonly find the pride of others disagreeable, then why do we praise the boldness, confidence, and prideful superiority of the great person?

Hume must explain when pride is praiseworthy, and when it is blameworthy. In part, Hume believes expressions of pride become disagreeable when the proud individual boasts about qualities she does not possess. This results from an interplay between the psychological mechanisms of sympathy and comparison. Sympathy enables us to adopt the feelings, sentiments, and opinions of other people and, consequently, participate in that which affects another person. Comparison is the human propensity for evaluating the situation of others in relation to ourselves. It is through comparison that we make judgments about the value of different states of affairs (T 3.3.2.4). Notice that sympathy and comparison are each a stance or attitude we can take toward those who are differently situated. For example, if another individual has secured a desirable job opportunity (superior to my own), then I might sympathize with the benefits she reaps from her employment and participate in her joy. Alternatively, I might also compare the benefits and opportunities her job affords with my own lesser situation. The result of this would be a painful feeling of inferiority or jealousy. Thus, each of these mechanisms has an opposite tendency (T 3.3.2.4).

What determines whether we will respond with sympathy or comparison to another’s situation? This depends upon how lively our idea of the other person’s situation is. Hume supports this by considering three different scenarios (T 3.3.2.5). First, imagine someone is sitting safely on a beach. Taken by itself, this fact would not provide much enjoyment or satisfaction. This individual might try to imagine some other people who are sailing through a dangerous storm to make her current safety more satisfying by comparison. Yet, since this is an acknowledged fiction, and Hume holds that ideas we believe are true have greater influence than mere imaginations (T 1.3.7.7), doing so would produce neither sympathy nor comparison. Second, imagine that the individual on the beach could see, far away in the distance, a ship sailing through a dangerous storm. In this case, the idea of their precarious situation would be more lively. Consequently, the person on the beach could increase her satisfaction with her own situation by comparison. Yet, it is crucial that this idea of the suffering experienced by those in danger does not become too lively. In a third scenario Hume imagines that those in danger of shipwreck were so close to shore that the observer could see their expressions of fear, anxiety, and suffering. In this case, Hume holds that the idea would be too lively for comparison to operate. Instead, we would fully sympathize with the fear of the passengers and we would not gain any comparative pleasure from their plight.

From this example, Hume derives the following principle: comparison occurs whenever our idea of another’s situation is lively enough to influence our passions, but not so lively that it causes us to sympathize (T 3.3.2.5). Hume uses this principle to explain why we are offended by those who are proud of exaggerated accomplishments. When someone boasts about some quality she does not actually have, Hume believes our conception of her pride has the intermediate liveliness that allows for comparison. Our conception of her pride gains liveliness from her presence directly before us (the enlivening relation of contiguity in space and time). Yet, because we do not believe her claims about her merit, our conception of her pride is not so lively that it causes us to sympathize (T 3.3.2.6). Consequently, we disapprove of someone’s exaggerated arrogance because it makes us compare ourselves unfavorably against the pretended achievements and accomplishments of the conceited individual (T 3.3.2.7).

Importantly, Hume does not categorically condemn pride. Justified pride in real accomplishments is both useful (T 3.3.2.8) and agreeable to the possessor (T 3.3.2.9). However, direct expressions of pride, even if based on legitimate accomplishments, still cause disapproval. Recall that sympathizing with another’s pride requires that we believe their self-evaluation matches their actual merit. Yet, it is difficult for us to have such a belief. This is because we know that people are likely to overestimate the value of their own traits and accomplishments. The consequence is that, as a “general rule,” we are skeptical that another person’s pride is well-founded, and we blame those who express pride directly (T 3.3.2.10). It is because boasting and outward expressions of pride cause discomfort through drawing us into unfavorable comparisons that we develop rules of good manners (T 3.3.2.10). Just as we create artificial rules of justice to preserve the harmony of society, so artificial rules of good manners preserve the harmony of our social interactions. Among these unspoken rules is a prohibition against directly boasting about our accomplishments in the presence of others. However, if others infer indirectly through our actions and comportment that we feel pride, then our pride can garner approval (T 3.3.2.10). Thus, Hume believes that pride can be a virtuous trait of character provided it is not overtly expressed and based upon actual accomplishments (T 3.3.2.11).

Hume uses these points to combat attacks on the worth of pride from two different fronts. First, there are those “religious declaimers” who criticize pride and, instead, favor the Christian view which instead prizes humility (T 3.3.2.13). These religious moralists hold, not just that humility requires us to avoid directly boasting about our accomplishments, but that humility requires sincerely undervaluing our character and accomplishments (T 3.3.2.11). Here Hume seems to have in mind something like the view that we should keep in mind the comparative weakness of our own intellect in comparison to that of God. Or, perhaps, that proper worship of God requires that one humble oneself before the divine with an appropriate sense of relative worthlessness. Hume argues that such conceptions do not accurately represent the common regard we pay to pride (T 3.3.2.13).

The second criticism of pride comes from those who charge that the pride of the great individual often causes personal and social harm. The concern is that praising pride and self-assurance can overshadow the more valuable virtues of goodness. This can be seen most clearly in Hume’s discussion of military heroism. The military hero may cause great harm by leaving the destruction of cities and social unrest in his wake. Yet, despite this acknowledged harm, Hume claims that most people still find something “dazzling” about the military hero’s character that “elevates the mind” (T 3.3.2.15). The pride, confidence, and courage of the hero seem, at least temporarily, to blind us to the negative consequences of the hero’s traits. This pride is not communicated directly, but it is communicated indirectly through observing the hero overcoming daunting challenges. As a result, those who admire the military hero participate via sympathy in the pleasure the military hero derives from his own pride and self-assured courage, and this causes us to overlook the negative consequences of the hero’s actions (T 3.3.2.15).

This passage provides additional confirmation that Hume’s ethics cannot be placed neatly into the utilitarian or consequentialist moral tradition. Just as the religious moralist fails to recognize the common praise given to warranted pride in one’s accomplishments, so the consequentialist fails to recognize the human tendency to praise certain traits of character without considering their social utility. Hume’s ethics reminds us of the value of human greatness. In this vein, he writes that the heroes of ancient times “have a grandeur and force of sentiment, which astonishes our narrow souls, and is rashly rejected as extravagant and supernatural” (EPM 7.17). Likewise, Hume contends that if the ancients could see the extent to which virtues like justice and humanity predominate in modern times, that they would consider them “romantic and incredible” (EPM 7.18). Hume’s ethical theory attempts to give proper credit to the qualities of greatness prized by the ancients, as well as the qualities of goodness emphasized by the moderns.

b. Goodness, Benevolence, and the Narrow Circle

Hume turns to a discussion of goodness in a Treatise section entitled “Of Goodness and Benevolence.” Under the heading of “goodness,” Hume lists the following traits: “generosity, humanity, compassion, gratitude, friendship, fidelity, zeal, disinterestedness, liberality, and all those other qualities, which form the character of the good and benevolent” (T 3.3.3.3). Again, these traits are united by their tendency to make us considerate friends, generous philanthropists, and attentive caregivers.

Hume explains that we praise such qualities both because of their tendency to promote the good of society as well as their immediate agreeability to those who possess them. Generosity, of course, is socially useful insofar as it benefits other people. Hume also sees the gentle virtues of goodness as correctives to the destructive excesses of greatness, ambition, and courage (T 3.3.3.4). A complication here is that evaluating another’s generosity depends significantly upon the scope of benefactors we take into consideration. Praise for socially useful traits comes from sympathizing with the pleasure that is caused to those who benefit from them. How far should our sympathy extend when making this evaluation? How wide is the scope of potential benefactors we must consider when judging whether someone is generous or selfish? For example, if we interpret this scope more narrowly, then we might think that the person who takes good care of her children, helps her friends in need, and pushes for positive change in local politics exhibits admirable generosity with her time, energy, and attention. Contrastingly, if we interpret the scope more expansively, then the fact that she fails to make any positive impact on many people who are suffering all over the world will count against her.

Hume answers that when judging another’s generosity, because we do not expect “impossibilities” from human nature, we limit our view to the agent’s “narrow circle” (T 3.3.3.2). Broadly, Hume’s claim is that we limit our focus to those people that the agent can reasonably be expected to influence. A more detailed explanation of this point requires answering two further questions. First, what is the “impossibility” we do not expect of others? Second, just how “narrow” is the “narrow circle” that Hume believes we focus on when evaluating generosity?

Let’s begin with the first question. Given Hume’s statement that recognition of the “impossibility” comes from our knowledge of human nature (T 3.3.3.2), we might think that Hume is making a claim about the naturally confined altruism of human beings. We do not expect that the generous person will be beneficial to those who live far away because human beings rarely concern themselves with those who are spatio-temporally distant or with whom we infrequently interact (T 3.3.3.2). This reading fits naturally with Hume’s previously discussed claim that the strength of sympathy is influenced by our relation to the person sympathized with. It also coheres well with Hume’s claim, emphasized in his discussion of the “circumstances of justice,” that human beings are naturally selfish (although not completely selfish).

An alternative reading, however, holds that the “impossibility” Hume identifies is not primarily the human inability to care about distant strangers. Hume sometimes discusses the possibility of “extensive sympathy” that enables us to care about those who are distant and unrelated (T 3.3.6.3). This suggests Hume might have some other sort of “impossibility” in mind. One possibility would be the “impossibility” of undertaking effective action outside one’s “narrow circle.” In support of this reading, Hume mentions being “serviceable and useful within one’s sphere” (T 3.3.3.2). Perhaps Hume’s point is just that, given human motivational structure and the practical realities of human life, it is unreasonable to expect someone to be able to have a significant impact beyond the sphere of one’s daily interactions. Although, we should note that the practical boundaries to acting effectively outside one’s “narrow circle” are significantly more relaxed today than they were in Hume’s time.

Moving to the second question, how we understand the “impossibility” of expecting benevolence outside of one’s “narrow circle” may depend upon just how close the boundaries of the “narrow circle” are drawn. Many of the ways Hume refers to the agent’s proper sphere of influence suggest he did not think of it as simply a tightly bound group of personal acquaintances and close relations. In a few passages Hume suggests that we consider all those who have “any” connection or association with the agent (T 3.3.1.18; T 3.3.1.30; T 3.3.3.2). Each of these passages leaves open the possibility that the agent’s “sphere” may be much more expansive than the phrase “narrow circle” would immediately suggest.

The proper sphere of influence may also depend upon the role, position, and relationships that the person in question inhabits. In one place, Hume claims that a perfect moral character is one that is not deficient in its relationships with others (T 3.3.3.9). In the second Enquiry Hume imagines a virtuous individual, Cleanthes, whose excellent character is evidenced by the fact that his qualities enable him to perform all his various personal, social, and professional roles (EPM 9.2). Thus, how “narrow,” or expansive, one’s circle is may depend upon the extent to which that person’s attachments and position make her conduct matter to others. For example, when evaluating the character traits of an elected public official we would consider a wider sphere of influence than we would when considering the same traits in most private citizens.

Benevolence is not only praised for its utility to others. Hume also discusses how it is immediately agreeable to the benevolent individual herself. This is a feature that is found in all emotions associated with love, just as it is a feature of all emotions associated with hatred to be immediately disagreeable (T 3.3.3.4). Mirroring his discussion of military heroism, Hume points out that we cannot help but praise benevolence, generosity, and humanity even when excessive or counter-productive (T 3.3.3.6). We say that someone is “too good” as a way of laying “kind” blame upon them for a harmful act with good-hearted intentions (EPM 7.22). Thus, the virtue of benevolence is praised, at least to some extent, in all its forms (T 3.3.3.6; EPM 2.5). However, Hume notes that we react much more harshly to excesses of anger. While not all forms of anger should be criticized (T 3.3.3.7), excessive anger or cruelty is the worst vice (T 3.3.3.8). Whereas cruelty is both immediately disagreeable and harmful, the harms of excessive benevolence can at least be compensated by its inherent agreeability.

c. Natural Abilities

Hume’s ethics is based upon the idea that virtues are mental traits of persons that garner praise. The resulting “catalogue of virtues” (T 3.3.4.2), then, paints a portrait of what human beings believe to be the ideal member of their species. One might argue that this approach to ethics is fundamentally flawed because a mental trait can garner praise without being a moral quality. For example, the rare ability to learn and understand complex concepts is often seen as a natural talent. Such talent is admirable, but is it a moral virtue? Does it not make more sense to feel pity for someone who lacks some natural ability instead of blaming her for failing her moral duty?

Hume’s position is that there is not a significant difference between the supposed categories of moral virtue and natural ability. To understand his view, we need to answer the following question: why must a virtuous trait be a mental quality or disposition? It is not because other types of traits do not garner the approval of spectators. Hume discusses our approval of sex appeal (T 3.3.5.2), physical fitness (T 3.3.5.3), and health (T 3.3.5.4). He also recognizes how the same principle of sympathy which produces approval of virtue also produces our approval of these physical attributes and our admiration for the wealthy (T 3.3.5.6). Instead, the reason virtue is limited to mental qualities is that virtue is supposed to constitute personal merit, or the set of qualities, dispositions, and characteristics that we specifically admire in persons (EPM 1.10). The implication, then, is that the qualities of the mind constitute who we are as persons. So, while Hume does not deny that there is such a thing as bodily merit, he does not see bodily merit as the proper scope of moral philosophy.

If the “catalogue of virtues” is a list of the mental traits we admire in persons, then the catalogue must include certain qualities not normally placed in the category of moral virtue and vice. Common usage of the terms “virtue” and “vice” is narrower than the set of those qualities that we find admirable about persons (EPM App. 4.1). For example, it is common to think that an extraordinary genius is someone with an exceptional talent (instead of a virtue), or a person who is especially lacking in common sense as having some type of defect (instead of a vice). Despite this common language convention, Hume emphasizes that intelligence and common sense are still mental qualities that we admire in persons. Consequently, Hume states that he will leave it to the “grammarians” to decide where to draw the line between virtue, talent, and natural ability (T 3.3.4.4, EPM App 4.1). It is not a distinction Hume believes is philosophically important since, regardless of precisely where the line is drawn, natural abilities like understanding and intelligence are undoubtedly characteristics we praise in persons. Hume quips that nobody, no matter how “good-natured” and “honest,” could be considered virtuous if he is an “egregious blockhead” (EPM App 4.2).

Hume faced criticism from contemporaries on this point. For example, James Beattie (1753-1803) argued that, while it is entirely appropriate to blame someone for failing to act with generosity or justice, it would be entirely inappropriate to blame someone because they lack beauty or intelligence (Beattie 1773: 294). Beattie holds that some quality can only be considered a moral virtue if it is within our control to develop or, at least, act in ways that are consistent with it. Hume anticipates this objection. He agrees that it would be inappropriate to blame someone for a natural lack of intelligence. Yet, he denies that this shows that natural abilities such as intelligence should not be considered part of personal merit. The reason we do not blame someone for their natural defects is that doing so would be pointless. We blame the person who is unjust, or unkind, because these behavior patterns and dispositions can be changed through exerting social pressure. However, we cannot shame someone into being more intelligent (T 3.3.4.4). Yet, we still think a penetrating mind is a quality possessed by the ideal person. So, while those who lack some natural ability are not to blame, this lack still influences our evaluation of their personal merit.

This issue is important for the for the overall plausibility of Hume’s account of the natural virtues. Specifically, the question of natural abilities has an important connection with the role greatness should play in the catalogue of virtue. Beattie claims that he wants nothing to do with the term “great man.” This is because the person who possesses the natural abilities of Hume’s “great man” is better able to cause destruction and harm. Here we should recall Hume’s description of the military hero. For this reason, Beattie holds that virtue is concerned with the qualities of the “good man” that can be acquired by anyone and tend to the good of society (Beattie 1773: 296). If Beattie is correct that the qualities of greatness are natural abilities, then Hume’s attempt to include both goodness and greatness within the catalogue of virtue requires him to provide a satisfactory defense of this point.

7. References and Further Reading

a. Hume’s Works

  • Hume, David (2007 [1739-1740]) A Treatise of Human Nature: A Critical Edition, ed. David Fate Norton and Mary J. Norton. Oxford: Clarendon Press.
    • Cited in text as “T” followed by Book, part, section, and paragraph numbers.
  • Hume, David (2000 [1748]) An Enquiry concerning Human Understanding: A Critical Edition, ed. Tom L. Beauchamp. Oxford: Clarendon Press.
    • Cited in text as “EHU” followed by section and paragraph.
  • Hume, David (1998 [1751]) An Enquiry concerning the Principles of Morals: A Critical Edition, ed. Tom L. Beauchamp. Oxford: Clarendon Press.
    • Cited in text as “EPM” followed by section and paragraph.
  • Hume, David Essays Moral, Political, and Literary, ed. Eugene F. Miller, revised edition, (Indianapolis: Liberty Fund, 1987).
    • Cited in text as “EMPL” followed by the page number.

b. Further Reading

  • Baier, Annette (1991) A Progress of Sentiments. Cambridge: Harvard University Press.
    • An account of the Treatise that emphasizes the continuity between Hume’s ethics and his epistemology, metaphysics, and skepticism.
  • Botros, Sophie (2006) Hume, Reason, and Morality: A Legacy of Contradiction.
    • Focuses on Hume’s theory of motivation, and arguments against the moral rationalist, and develops an account of why these arguments are still relevant for contemporary metaethical debates.
  • Bricke, John (1996) Mind and Morality: An Examination of Hume’s Moral Psychology. New York: Oxford University Press.
    • Discusses Hume’s theory of agency, the will, and defends a noncognitivist interpretation of Hume on moral evaluation.
  • Cohon, Rachel (2008) Hume’s Morality: Feeling and Fabrication. New York: Oxford University Press.
    • Argues against “standard” views of Hume’s moral philosophy by arguing that Hume’s philosophy is both non-realist and cognitivist. Also includes novel and influential interpretations of the artificial virtues.
  • Darwall, Stephen (1995) The British Moralists and the Internal ‘Ought.’ Cambridge: Cambridge University Press.
    • Places Hume’s theory in its historical context and situates Hume as a member of an empirical, naturalist tradition in ethics alongside thinkers such as Hobbes, Locke, and Hutcheson.
  • Gill, Michael (2006) The British Moralists on Human Nature and the Birth of Secular Ethics. Cambridge: Cambridge University Press.
    • Provides further historical context for Hume’s place within seventeenth and eighteenth-century moral philosophy with a particular focus on the way in which the British moralists founded morality on human nature and disentangled morality from divine and religious sources.
  • Harrison, Jonathan (1976) Hume’s Moral Epistemology. Oxford: Clarendon Press.
  • Harrison, Jonathan (1981) Hume’s Theory of Justice. Oxford: Clarendon Press.
    • Each of these works provides a detailed, textual, and critical commentary on the major arguments Hume puts forward in service of his metaethical views and his conception of justice.
  • Herdt, Jennifer (1997) Religion and Faction in Hume’s Moral Philosophy. Cambridge: Cambridge University Press.
    • An account of sympathy that focuses on its connection to human sociability and the tendency that sympathy has for allowing human beings to overcome faction and division.
  • Mackie, J.L. (1980) Hume’s Moral Theory. London: Routledge.
    • Situates Hume’s moral theory within the context of his predecessors and successors and provides critical discussion of the main doctrines of Hume’s ethical thought: Hume’s anti-rationalism, sentimentalism, and a detailed discussion and critique of Hume’s artificial-natural virtue distinction.
  • Mercer, Philip. (1972) Sympathy and Ethics: A Study of the Relationship between Sympathy and Morality with Special Reference to Hume’s Treatise. Oxford: Clarendon Press.
    • Provides critical, detailed commentary on Hume’s account of sympathy and its relationship to his moral philosophy.
  • Norton, David Fate (1982) David Hume: Common-Sense Moralist, Sceptical Metaphysician. Princeton:Princeton University Press.
    • Discusses the relation between Hume’s epistemology and ethics. Puts forward the view that Hume was only skeptical regarding the former, but was a realist about morality.
  • Reed and Vitz (eds.) (2018) Hume’s Moral Philosophy and Contemporary Psychology. New York: Routledge.
    • A collection of essays that draws discusses the relevance of Hume’s moral philosophy for a wide array of topics in psychology. These topics include: mental illness, the situationist critique of virtue ethics, character development, sympathy, and the methodology of Hume’s science of human nature among other topics.
  • Swanton, Christine (2015) The Virtue Ethics of Hume and Nietzsche. Malden, MA: Wiley Blackwell.
    • Argues that Hume should be placed within the tradition of virtue ethics. Includes discussion of how a virtue theoretic interpretation can be reconciled with his rejection of rationalism and his sentimentalism, as well as the problem of why justice is a virtue.

c. Other Works Cited

  • Abramson, Kate (2008) “Sympathy and Hume’s Spectator-centered Theory of Virtue.” In Elizabeth Radcliffe (ed.), A Companion to Hume. Malden, MA: Blackwell Publishing.
  • Beattie, James (1773) An essay on the nature and immutability of truth, in opposition to sophistry and scepticism. The third edition. Dublin, MDCCLXXIII. Eighteenth Century Collections Online. Gale.
  • Clarke, Samuel (1991[1706]) A Discourse of Natural Religion. Indianapolis: Hackett Publishing Company.
  • Rawls, John (1971) A Theory of Justice. Cambridge: Harvard University Press.
  • Reed, Philip (2012) “What’s Wrong with Monkish Virtues? Hume on the Standard of Virtue.” History of Philosophy Quarterly 29.1: 39-53.
  • Sayre-McCord, Geoffrey. (1994) “On Why Hume’s ‘General Point of View’ Isn’t Ideal–and Shouldn’t Be.” Social Philosophy and Policy 11.1: 202-228.
  • Taylor, Jacqueline (2002) “Hume on the Standard of Virtue.” The Journal of Ethics 6: 43-62.

Author Information

Ryan Pollock
Email: pollocrc@gmail.com
Grand Valley State University
U. S. A.

Robert Boyle (1627—1691)

Robert Boyle was one of the most prolific figures in the scientific revolution and the leading scientist of his day. He was a proponent of the mechanical philosophy which sought to explain natural phenomena in terms of matter and motion, rather than appealing to Aristotelian substantial forms and qualities. He was a champion of experimental science, claiming that theory should conform to observation and advocating openness in the publication of experimental results, the replication of experiments for empirical corroboration, and the importance of recording even those experiments that failed, at a time when these ideas were revolutionary. He defended and developed the distinction between primary and secondary qualities and supported it with detailed experimental evidence. With the help of his colleague Robert Hooke (1635-1703), he designed and improved an air pump capable of creating and sustaining a vacuum and used it to perform many famous experiments, investigating things like respiration, disease, combustion, sound, and air pressure. He discovered Boyle’s law, which shows that the volume and pressure of a gas are proportionally related. He used empirical evidence to refute both the four-element theory of Aristotle and the more recent three-principle theory of Paracelsus (1493-1541). Finally, many historians of science consider him to be the father of modern chemistry.

This article focuses on the philosophical significance of Boyle’s work, but it is important to note that Boyle was a polymath with diverse interests ranging from animal husbandry to underwater respiration, from the study of ancient languages to finding ways of extending the human lifespan. Furthermore, Boyle had both the intellect and the financial resources to pursue such a wide research agenda. Focusing on his philosophy, or even his chemistry, runs the risk of ignoring the true complexity of his thought. Nevertheless, much of Boyle’s work has had enduring philosophical significance.

Table of Contents

  1. Life
  2. Natural Philosophy
    1. Rejection of Aristotelianism
    2. The Mechanical Philosophy
    3. Chemistry
    4. Alchemy
    5. Medicine
    6. Pneumatics
  3. Philosophy of Science
  4. Substance Dualism
  5. Causation
  6. God
  7. Ethics
  8. Casuistry
  9. References and Further Reading
    1. Recent Editions of Boyle’s Works
    2. Chronological List of Boyle’s Publications
    3. Correspondence
    4. Work Diaries
    5. Biographies
    6. Selected Works on Boyle
    7. Other Important Works

1. Life

Robert Boyle was born on the 25th of January, 1627, at Lismore Castle, County Waterford, Ireland. He was the fourteenth child of Richard Boyle, the first Earl of Cork, who had come to Ireland from Canterbury, essentially penniless, in 1588. By the time of Boyle’s birth, through a series of shrewd and sometimes shady real estate ventures, Cork had become the wealthiest man in Ireland. This incredible wealth can be seen in Boyle’s lavish upbringing and education. After the death of his mother in 1630, Boyle’s daily care and supervision went to a local Irish woman, known today only as Nurse Allen. Allen raised Boyle, teaching him the Irish language, until his eighth year when he was sent away, along with his brother Francis, for a formal education at Eton.

After only three years at Eton, Cork decided to send Boyle, along with his brother Francis, on a grand tour of the continent under the tutelage of Isaac Marcombes. Marcombes was a renowned teacher from Switzerland and had just returned from a similar tour in which he had tutored Boyle’s older brothers. Boyle spent most of the tour in Geneva, at Marcombes’s home, where he studied a variety of subjects, including French, Latin, Italian, geometry, Roman history, philosophy, tennis, fencing, and horseback riding.

During his initial stay in Geneva in 1641, Boyle had a life-changing experience.  One night during a terrible storm, he thought the Day of Judgment had come and that he had wasted his life on trivial pursuits. Boyle made an oath that he would dedicate himself to the Christian service of humanity if he was allowed to survive. The next morning, after the storm had passed, the young Boyle swore the oath again to demonstrate his sincerity. For the rest of his life he dedicated himself to various charitable endeavors. Even much of his later scientific work was directly motivated by what Boyle perceived as his religious duty. This event also led Boyle to a renewed dedication to his studies, as well as a lifelong aversion to swearing oaths. Later in life, for example, he declined the presidency of the Royal Society because it required swearing an oath. He even wrote a treatise, A Free Discourse Against Customary Swearing (1695).

During the grand tour, Boyle also travelled in France and Italy. They tried to visit Galileo, and Boyle studied Italian to read Galileo’s works in preparation, but the great scientist died before Boyle could meet him. The grand tour came to an end when Boyle received the news that his father had died. After sufficient finances were secured, Boyle returned to England and eventually settled at the family estate at Stalbridge, where he devoted himself to writing chivalric romances, a common literary form at the time, and moral treatises.

It is hard to determine when Boyle developed a serious interest in natural philosophy, but a few events are noteworthy. The Boyle scholar Michael Hunter puts it in the early1650s, warning against an interpretation that makes it seem inevitable that Boyle would become a scientist. However, we should not ignore events in Boyle’s life that indicate an early interest in natural philosophy, and the more one looks into the matter, the more a steady interest in natural philosophy becomes apparent. While it was not inevitable that Boyle would become a scientist, neither is it surprising.

Boyle had been familiar with the work of Aristotle, Bacon, and Galileo since his days at Eton. As early as 1646, events in Boyle’s life show an increasing interest in chemistry. An important letter to his sister Katherine Ranelagh (1615-1691) from May of that year shows that Boyle made a serious attempt to design and construct a chemical laboratory at Stalbridge. The attempt was unsuccessful, since an essential furnace was delivered “crumbled into as many pieces as we are into sects!” But the attempt itself is sufficient evidence of a serious interest in natural philosophy. Nevertheless, ethics was still Boyle’s primary philosophical concern during this period.

A trip to Leiden to attend his brother’s wedding in 1648 is also pertinent because at that time there was a thriving intellectual community of natural philosophers, with multiple schools of anatomy and the controversial mechanical philosophy of Rene Descartes (1596-1650) being discussed all over Holland. During this trip Boyle visited the University of Leiden and viewed an experiment on the nature of light in which the image of the city was projected onto the wall in the room of a high tower. This event may be the cause of the once-common view that Boyle studied there. However, these early experiences do pale in importance next to a conversion experience Boyle had in the early 1650s, when he essentially became a scientist. Boyle had found a way to combine his interests in natural philosophy with his pledge to dedicate his life to philanthropic pursuits.

He was encouraged in these endeavors by his older sister and best friend, the Lady Katherine Ranelagh (1615-1691). His relationship with Ranelagh would be the closest one of his life. Ranelagh was an important natural philosopher in her own right, respected and consulted by her contemporaries, who found a way to pursue her scientific research within the confines of the strict gender norms of seventeenth-century England. Later in life, at her London estate on Pall Mall, she would become Boyle’s intellectual companion, editor, and most trusted collaborator. In the early 1650s, her main contribution to Boyle’s philosophical development was her participation in the Hartlib Circle.

Samuel Hartlib (1600-1662) was a German polymath who moved to England in 1628 and recruited intellectuals and experts in all sorts of fields for a variety of religious philanthropic endeavors, including projects in medicine, public education, agriculture, animal husbandry, and translations of the Bible into other languages (Boyle would eventually help with projects to translate the Bible into Irish, Malay, and Algonquin). The members of the circle included Heinrich Appelius, Friedrich Clodius, Cheney Culpeper, John Dury, Theordore Haack, Godofred Hotton, Joachim Hubner, Katherine Ranelagh, Johann Moriaen, John Pell, William Petty, Johann Rulicius, John Sadler, George Starkey, and Benjamin Worsley. Hartlib, like Marine Mersenne (1588-1648), had a vast network of correspondence, with so many individuals that it is hard to establish a comprehensive list. However, it is important to note that by the time Boyle began participating in the circle, Ranelagh was already an established member. Furthermore, Ranelagh was a very important member, since out of the 766 names mentioned in Hartlib’s correspondence, Ranelagh’s is the sixth most mentioned. The group’s activities were inspired by the utopian writings of Francis Bacon (1561-1626), and it is Bacon who would have the single greatest influence on Boyle’s philosophy. The Hartlib Circle became a prototype of the modern scientific research society. It was eventually replaced by formal scientific societies, such as the Royal Society, of which Boyle was a founding member.

In 1652, Boyle briefly returned to Ireland to settle matters involving his inheritance. Although he was in Ireland only a short time, Hartlib recruited Boyle to work on a number of projects. Boyle was asked to create a Baconian natural history of Ireland, and research ways of developing new agricultural and animal husbandry techniques there, but these projects never got off the ground. By now, Boyle’s primary interest was to learn the empirically oriented chemistry of Jean Baptise Van Helmont (1580-1644). He was being helped in this endeavor through correspondence with the American alchemist George Starkey (1628-1665). However, unable to establish a chemical laboratory in Ireland, Boyle spent his time reading up to 12 hours a day and learning anatomy from William Petty (1623-1687), who had learned anatomy in Leiden before teaching it at Oxford, then following Cromwell to Ireland as Physician General.

Boyle’s serious investigations into natural philosophy really began when he became Starkey’s pupil. In Alchemy Tried in the Fire: Starkey, Boyle, and the Fate of Helmontian Chymistry (2002), William Newman and Lawrence Principe present a detailed analysis of Starkey’s influence on Boyle’s chemical education. They suggest using the term Chymistry to refer to the general group of issues concerning alchemy and chemistry in the early modern period, noting that the terms were then often used synonymously, while they have very different connotations in contemporary discourse.

Starkey was greatly influenced by Van Helmont, and Boyle eventually replicated many of Van Helmont’s experiments. By the time Boyle returned to England he was thoroughly absorbed in natural philosophy, wasting little time in moving to Oxford, networking with other scientists, and establishing the laboratory for which he is now famous. From this point, and for the rest of his life, Boyle was constantly conducting experiments. His published works, correspondence, and work notes—many of which survive—became full of detailed accounts of them. Boyle spent this important part of his career in one of the most thriving intellectual environments in the world at the time, working on a variety of projects involving both chemical analysis as well as experiments involving medicine, pneumatics, and hydraulics. He became involved with a group of like-minded, anti-Aristotelian, natural philosophers, which included John Locke (1632-1704) and eventually Isaac Newton (1643-1727), who regarded Boyle’s work on pneumatics as a paradigm of science.

The natural philosopher Robert Hooke (1635-1703) began his career as Boyle’s laboratory assistant. Together, they made improvements on the air-pump design made by Otto von Guericke (1602-1686), and produced a machine capable of evacuating most of the air from an observable glass chamber. They did a large number of experiments with it, and by presenting these to noble and socially influential audiences, they produced useful publicity for the scientific activities of the Royal Society. Inspired by Bacon’s conception of science, Boyle developed and used new technological instruments that enabled detailed, replicable observations which he thought revealed the hidden structure of the natural world.

Boyle also became close friends with the young John Locke, who went to Oxford in 1652 to study medicine. They even worked on a few medical projects together. Boyle had a significant influence on Locke’s philosophical development, including his distinction between primary and secondary qualities, and the difference between real and nominal essences.

Some of Boyle’s scientific claims were criticized by Thomas Hobbes (1588-1679), and the two philosophers became involved in a heated public debate over the role of experimental observation in natural philosophy. Poor health caused Boyle to move to London in 1668. There he lived with his sister Katherine for the rest of his life. For over twenty years they worked together on various projects in medicine, natural philosophy, and philanthropy. They received many important visitors who would come to witness his famous experiments.

Boyle died of grief a week after the death of his beloved sister, on December 31, 1691.     Locke was the executer of his estate. He left funds to establish a series of annual lectures to defend Christianity against objections to its basic tenets. The lectures continue to this day.

2. Natural Philosophy

Boyle considered natural philosophy to be an important part of philosophy. He believed God gave humans three books to aid in their salvation: “the book of scripture,” “the book of conscience, and “the book of nature.” In works such as Of the Study of the Book of Nature and Some Considerations Touching the Usefulness of Experimental Natural Philosophy (1663), Boyle argues that the natural world had been not only intentionally designed by God, but had been designed specifically to be understood, at least in part, by rational human minds. He believed that humans equipped with reason could make use of detailed observation, under controlled experimental conditions, to uncover the hidden structure of nature. Boyle’s efforts to bring chemistry out of the disreputable shadows of alchemy, as well as all sorts of other projects he undertook in natural philosophy, were justified as part of the theologically acceptable study of the natural world, God’s great automaton, the study of which Boyle believed too many people neglected. Boyle saw it as a religious duty to investigate natural phenomena and publish the knowledge he gained for the benefit of humanity. This Baconian approach to science can be seen throughout his research, including his chemical analyses of medicines, his investigations of air pressure, his study of human anatomy, his invention of the friction match, his efforts to expand the human lifespan, and even his work to advance agriculture and animal husbandry techniques.

Boyle seems to have spent nearly equal time doing experimental natural philosophy, studying the Bible as well as the ancient languages associated with it, and analyzing his own conscience. He put the same intellectually rigorous effort, aided by significant financial resources, into all three. Boyle’s entire philosophy, his metaphysics, his epistemology, and his ethics, are all intertwined with these three religiously motivated projects. Though Boyle is known today mostly for his work in various areas of natural philosophy, these achievements cannot be fully appreciated without understanding their place in Boyle’s religion.

It is important to emphasize that Boyle’s approach to natural philosophy, though influenced by Descartes, is more explicitly indebted to philosophers such as Francis Bacon and Pierre Gassendi (1592-1655). In the article “Pacere Nominibus: Boyle, Hooke and the Rhetorical Interpretation of Descartes” (1994), Edward Davis explores Descartes’s influence on Boyle during the 1660s, under the influence of Hooke, who taught Boyle Cartesian philosophy. However, it is misleading to describe Boyle as a Cartesian.

Descartes’s influence both occurred earlier and was also less extensive than this view implies. Boyle read Descartes’s Passions of the Soul in 1648, before his association with Hooke. While this has been downplayed as a minor work compared to Descartes’s Meditations on First Philosophy and the Principles of Philosophy, it does give an accurate and succinct presentation of Descartes’s philosophy, including his mechanical account of the human body. Furthermore, along with the works of Galileo and Gassendi, it represents one of Boyle’s earliest exposures to the mechanical philosophy. And while Boyle does later present many of his views in Cartesian terms and agrees with his basic dualistic and theist ontology, there are fundamental differences between their philosophies, such as their views on the essence of matter, the possibility of a vacuum, the role of experiment in science, and the possibility and extent of knowledge based on experience. On the other hand, Boyle had been exposed to Bacon’s conception of science since his time at Eton. The provost of Eton, Henry Wotton, was Bacon’s cousin. Furthermore, Bacon’s influence can be seen in the work of many of the members of the Hartlib Circle. Thus, it is more accurate to say that in natural philosophy Boyle was primarily a Baconian who agreed with Gassendi on many important issues, Descartes on others, and often expressed his ideas in Cartesian terms.

In works such as A Discourse on Things Above Reason (1681) and On the High Veneration Man’s Intellect owes to God (1684), Boyle distinguishes between demonstrative rational arguments and what can be inductively inferred from experience. Like Bacon, Boyle believed that theory should conform to observation. He tried to avoid premature metaphysical speculation—with mixed results—in favor of theories that could be tested by experiment. He agreed with Bacon’s claim in Novum Organum (1620) that the hidden structure of the natural world is too subtle to be penetrated by the Aristotelian, deductive approach to science, and that technology can aid in our investigation of the natural world. Boyle thought this approach yielded new scientific information that could be potentially used for the benefit of humanity. Boyle tried to put into practice something like the science Bacon envisioned in works such as Novum Organum (1620), and New Atlantis (1627).

Many areas of Boyle’s philosophy are intimately connected to his natural philosophy, including his rejection of scholastic Aristotelianism, his acceptance of the corpuscular mechanical philosophy, his work in chemistry, alchemy, medicine, and pneumatics, as well as his philosophical views regarding the nature of knowledge, perception, substance, real and nominal essences, causation, and alternative possible worlds.

a. Rejection of Aristotelianism

Central to Boyle’s natural philosophy is his general rejection of scholastic Aristotelianism. In works such as About the Excellency and Grounds of the Mechanical Hypothesis (1674), he rejects Aristotle’s theory of motion as the actualization of a potential, as well as his distinction between natural and unnatural motion, holding that the local motion involved in the mechanical interactions of corpuscles was inherently more intelligible. He also rejected the scholastic notion of substantial form and used controlled experiments to investigate the Aristotelian terrestrial elements, forms, and qualities. For example, Boyle was the first philosopher to write an entire book about cold, a property the scholastics claimed to be one of the four primary qualities of matter, but had actually only discussed in the most general terms. Boyle’s book included all sorts of experiments he had conducted on the nature of cold, each described in meticulous detail.

Boyle rejected the scholastics’ deductive syllogistic approach to science. He agreed with Bacon that the natural world was too complex for the categorical syllogism to penetrate. He thought that scientific progress requires an inductive method that posits a hypothesis that can then be tested by experiment involving multiple controlled observations. Because the theories could be modified in light of new empirical evidence, Boyle believed the experimental method was fundamentally superior to the scholastic syllogistic model of science.

Boyle’s rejection of scholastic Aristotelianism in works such as The Sceptical Chymist (1661), and The Origin of Forms and Qualities (1666), was also based in part on his acceptance of the mechanical philosophy. This early modern philosophical movement sought to explain natural phenomena in terms of matter and motion, rather than, for example, the composition and proportion of Aristotelian terrestrial elements. Boyle thought mechanical explanations were inherently more intelligible than explanations based on the elemental model because they appealed to properties which themselves were more intelligible, such as size, shape, and motion, rather than to ultimately obscure causes such as real qualities or substantial forms. For Boyle, generation, corruption, and alteration could all be explained mechanically, as various types of interaction between microscopic particles of matter he called corpuscles.

This rejection of the elemental model of explanation also extended to other theories of natural philosophy that were popular in his day, such as the alchemical theory of Paracelsus (1493-1541), involving three chemical “principles”: salt, sulfur, and mercury, as well as even the more recent five-element theories of chemists such as Nicolas Le Fevre (1615-1669). When fire-analysis experiments revealed that some compound bodies could be reduced to five, rather than only four, homogenous elements, some natural philosophers thought this was evidence of a fifth element. Boyle rejected the elemental explanatory model altogether. Instead, he argued that there was only one kind of material substance, and what appear at the macroscopic level to be different elements are actually structural modifications of this universal matter’s mechanical properties.

In a similar way, Boyle also rejected the Aristotelian notion of natural motion. In Book 8 of the Physics, Aristotle argued that each element has a natural location in the universe and a natural tendency to return to this location. This was used to explain such things as why rocks fall and smoke rises. In contrast, Boyle argued that all matter was essentially passive and insensible, lacking any tendencies or dispositions beyond its mechanical properties. Matter can be acted upon but contains no internal force, source of motion, substantial form, or disposition.

The traditional Aristotelian qualities of hot, cold, wet, and dry could be mechanically explained in a similar way. For example, Boyle thought that heat was not a primary quality of matter, but instead a property that is reducible to a particular type of rapid corpuscular motion. The conception of heat as molecular motion is a direct descendent of this view. In a similar way, Boyle thought the power of a key to open a lock is not due to some real quality, substantial form, or occult power of the key; rather, it is an emergent power, ultimately reducible to the size, shape, and motion of the key and the lock, which Boyle called their mechanical affections.

It is important to note that Boyle’s objections against Aristotelian natural philosophy were usually directed more toward the views of his contemporary scholastics, such as Julius Caesar Scaliger (1484-1558), than those of Aristotle himself, for whom he had great respect. Boyle’s approach to ethics, for example, shows this respect was more than lip service, since it provides what is essentially an Aristotelian analysis of the causes of moral virtue. It is also important not to conflate the mechanical philosophy, the corpuscular hypothesis (Boyle’s own version of the mechanical philosophy), and the experimental philosophy (the method by which Boyle often tested theories).

b. The Mechanical Philosophy

Boyle coined the term Mechanical Philosophy and used it to describe any attempt to explain natural phenomena in terms of matter and motion, rather than in terms of substantial forms, real properties, or occult qualities. For Boyle, this included the work of a wide variety of philosophers that otherwise differed in many respects. His list of mechanical philosophers included the ancient atomists Democritus, Leucippus, Epicurus, and Lucretius—names synonymous with atheism at the time—as well as his contemporaries Galileo, Descartes, Gassendi, Hobbes, Locke, and Newton.

Boyle’s own corpuscular version of the mechanical philosophy makes him both an empirical representationalist and an indirect realist. Though Galileo’s The Assayer (1923) is likely the first early modern work to raise the influential distinction between primary and secondary qualities, Boyle developed this distinction and made it an important part of his natural philosophy. In the Origin of Forms and Qualities, among other works, he argued that our senses provide a representation of an independently existing, external physical world, which is ultimately composed of material particles moving through empty space. Boyle held that these corpuscles have mechanical affections, properties such as size, shape, and motion, which are the primary qualities of matter, real properties that exist in any bit of material substance, no matter how small. The secondary qualities we perceive, such as color, sound, taste, odor, and warmth, are mental perceptions that are produced by these primary qualities causally interacting with our sense organs, but do not actually exist as real qualities in the object of perception itself. Thus, perception involves information about the external world entering the brain as a result of the causal interaction between the conscious perceiver and the object perceived.

Boyle used the term “corpuscle” to describe the microscopic material particles, and their clusters, of which he believed the material world was composed. Boyle thought God has the power to infinitely divide matter, even if this is beyond our rational comprehension, but the actual physical world is composed of minima or prima naturalia, microscopic particles of matter which never are, as a matter of fact, divided. These basic corpuscles interact and combine to form larger and larger clusters until they form the ordinary macroscopic material substances with which we are familiar.

On the surface, Boyle’s mechanical philosophy seems very similar to Descartes’s, but their views differ in several important respects. Briefly looking at their differences helps us understand the uniqueness of Boyle’s view. Descartes argues that the “attribute,” or essence, of matter is extension in space. He also held that there is no real distinction between a substance and its attribute. Just as there is no body that lacks extension, Descartes held that there is no extension that lacks body. Descartes held that the universe was a plenum, completely filled with material substance. He even thought that the famous mercury vacuum created by Evangelista Torricelli (1608-1647), while devoid of air, was filled with “subtle matter”—particles small enough to penetrate the pores of the glass—and that we could deduce the existence of such particles from the nature of matter itself.

Boyle agreed that all matter was extended in space, but he wasn’t committed to Descartes’s elegant metaphysical system. Boyle thought theory had to be subordinate to observation. Extension, rather than being the essence of matter through which all other properties were mere modifications, is only another empirically manifest mechanical affection like size, shape, texture, arrangement, and solidity. For Boyle, empty space is not only logically possible but also empirically corroborated by experiments like those performed by Torricelli, Otto von Guericke (1602-1686), and himself, with Robert Hooke. Boyle also thought motion in empty space was more intelligible than in a plenum. Descartes had to resort to a complex theory of circular motion to explain it. Until there is empirical evidence to support the existence of subtle matter, Boyle believed its postulation violated Ockham’s razor.

Boyle believed that mechanical explanations were inherently more intelligible than those of the Aristotelians or the Paracelsians because they involved easily understandable concepts like size, shape, and motion. He thought the local motion involved in the mechanical interaction of corpuscles is inherently more intelligible than the Aristotelian conception of motion as the actualization of a potential. Boyle thought the appeal to substantial forms in natural philosophy produced explanations that were vacuous when compared to mechanical explanations. The Paracelsians seemed no better, appealing to vague notions such as the “archeus,” “astral beings,” and “blas.” Furthermore, being firmly rooted in alchemy, they were often secretive and intentionally obscure. However, explanations that appealed only to mechanical properties were clear, intelligible, and often had the advantage of being empirically testable.

In About the Excellency and Grounds for the Mechanical Hypothesis (1674), Boyle points out that no one appeals to substantial forms when mechanical explanations are available, as, for example, when one is shown how the moon is eclipsed by the shadow caused by the position of the earth relative to the sun. Likewise, there is no reason to appeal to witchcraft to explain how a concave mirror can project the image of a man into the air, once catoptrics is understood. Boyle thought Aristotelians and Paracelsians failed to realize that this mechanical approach can be applied to natural phenomena in general.

Boyle was interested in occult qualities, natural phenomena in which the effect is observable, but the cause is not, such as magnetic and electrical attraction. Boyle thought such phenomena could be explained mechanically in terms of corpuscular effluvia, the emission of small corpuscular clusters. In A Discourse of Things above Reason (1681), though, Boyle also recognized that some phenomena cannot be mechanically explained. These included the miracles featured in the Bible, as well as more traditional philosophical problems such as whether or not matter is infinitely divisible, how mind-body interaction is possible, and how human free will and moral responsibility can be compatible with divine foreknowledge. Perhaps these might be explained by future philosophical investigation, but they resist straightforward mechanical explanation.

The influence of the mechanical philosophy can be seen throughout Boyle’s other intellectual endeavors and provides his basic approach to philosophy. This influence is apparent in his metaphysical views on the nature of substance and causation, his defense of the corpuscular hypothesis, his epistemological views on role of experiment in scientific explanation and the limits of reason, and his theological views on the importance of studying the book of nature and its potential for medicine.

c. Chemistry

Boyle is considered by many to be the father of modern experimental chemistry. Through years of diligent work he became a skilled chemist. His interest and work in chemistry lasted from the early 1650s to the end of his life. His social status and efforts to show that natural philosophy was a theologically acceptable pursuit did much to make the science of chemistry socially respectable. Boyle’s most important contribution to chemistry is his systematic critique of both the Aristotelian and Paracelsian theories of natural philosophy.

In The Sceptical Chymist (1661), Boyle points out the limitations of fire analysis as a universal method of separating compound substances into their homogenous components, a method many Aristotelians and Paracelsians used. For example, a green stick burned in open fire seems to separate into four homogenous parts, demonstrating its compound nature: The smoke was the element of air being separated, the hissing and snapping of the sap indicated the water element, the quantity of fire grew as the stick burned, and the remaining ash was the element of earth that was left. Pacracelsians had a similar explanation, separating the stick into the chemical principles of salt, sulfur and mercury.

Boyle thought the separation could be better explained by the rapid mechanical bombardment of corpuscles from the fire onto the structure of the corpuscles composing the stick, setting them in motion. Chemical analysis revealed that the smoke and ash are not homogenous elements but are compound bodies themselves. Some compound substances, such as gold, could be burned for extended periods at extreme temperatures without separating into other homogenous substances. Furthermore, chemical distillation of other compound substances, such as raisins, could produce five homogenous substances.

Boyle was able to chemically sublimate several substances, such as sulfur, turning them from a solid state to a gas and back without going through a liquid phase. Boyle thought such experiments had serious consequences for the elemental model since, according to it, the release of a gas involved the separation of an element or chemical principle, which would require a diminution of the whole. If a substance can be turned back and forth from a solid to a gas again and again without any sign of disintegration, then such a diminution clearly has not taken place. The only alternative explanation on the elemental model would be that the substance has transmuted back and forth into different elements. However, if this is the case, then neither can be considered a true element.

Inspired by Bacon’s utopian model of science, Boyle tried to compile “experimental histories” of different substances. Some of these projects led to completed works, such as An Essay about the Origin and Virtues of Gems (1672) and Short Memoirs for the Natural Experimental History of Mineral Waters (1685). Others, such as the Philosophical History of Minerals, never came to fruition, though much of the research was completed. These projects were records of chemical experiments and other empirical observations concerning the given substance. The goal was to create a sort of publicly accessible database of the chemical analysis of every known substance. Boyle prioritized substances such as the traditional Aristotelian elements and Paracelsian chemical principles, “noble” metals like gold, and bodily fluids such a blood, due to their potential medical value. Concerning salt, a basic chemical principle according to the Paracelsians, Boyle claimed to be able to distinguish three different kinds, each of which he could chemically produce.

Boyle believed colors were caused by the mechanical properties of material corpuscles. In works such as Experiments and Considerations Touching Colours (1664) and New Experiments Concerning the Relation between Light and Air (1668), Boyle presents a chemical analysis of colors and light. He also analyzed samples of phosphorous he had acquired, which produce light chemically. Boyle achieved significant success in these endeavors, though this pales in comparison to the success of later philosophers on the nature of color. This line of investigation also led Boyle to discover things not directly related to color, such as a reliable method of distinguishing an acid from a base.

Developing an interpretation of a laboratory accident of Hennig Brandt, in 1680 Boyle saturated some coarse paper in phosphorous and drew a stick coated with sulfur across it, creating a steady flame. This was the first friction match. The creation of a reliable and eventually safe way to easily produce fire was a major technological advancement that changed the world.

Boyle spent the last twenty years of his life engaged, often with the help of Ranelagh, in the chemical analysis of medical recipes. These efforts did much to bring chemistry out of the shadows of alchemy and into the light of social respectability. Throughout his work in chemistry, Boyle advocated openness in the publication of experimental results, including even those experiments that were unsuccessful. Nonetheless, there were exceptions to this openness involving alchemy.

d. Alchemy

Many of the early modern philosophers, most notably Isaac Newton, had a significant interest in alchemy, and Boyle was no exception. Lawrence Principe in The Aspiring Adept: Robert Boyle and his Alchemical Quest (1998), and William Newman and Lawrence Principe in Alchemy Tried in the Fire: Starkey, Boyle, and the Fate of Helmontian Chymistry (2002), present a detailed analysis of Boyle’s alchemical pursuits, though one should also read Hunter’s account. The early Boyle scholars Henry Miles and Thomas Birch actually destroyed much of Boyle’s work in alchemy, fearing it would tarnish his reputation as a scientist. During his lifetime, however, Boyle’s interest in alchemy was extensive and well known. Though Boyle often tried to distance chemistry from its alchemical association, many of his projects in natural philosophy were clearly alchemical.

Boyle’s alchemical endeavors were motivated by three goals: to uncover the hidden nature of physical reality, to find “extraordinary and noble medicines,” and to acquire accurate accounts of supernatural events that might help convince religious skeptics. Boyle expressed an interest in finding the philosopher’s stone as early as 1646, though he mentions it more as a humorous exaggeration than a current project. In a letter to Ranelagh in May of that year, he complains that he is not destined to find the philosopher’s stone, since his initial attempts at chemical analysis had been so unsuccessful.

Boyle believed it was possible to transmute one substance into another, and this included the traditional alchemical quest of turning lead into gold. He believed the possibility of transmutation directly followed from the mechanical philosophy. If there is only one universal type of matter, and the differences between the macroscopic substances we perceive are the result of structural differences at the microscopic level, then it follows that causing changes in the structure and arrangement of corpuscles might cause substantial changes at the macroscopic level. Since gold and lead have similar macroscopic properties, there might be only a subtle difference between them at the microscopic level.

Boyle claimed to have witnessed the transmutation of lead into gold on more than one occasion. As early as 1652 he claimed to have acquired a quantity of philosopher’s mercury, a substance believed to be required for gold transmutation. Boyle also claimed to have turned gold into a base metal, using a powder given to him by a mysterious stranger. In some works, Boyle describes successful transmutation experiments on other substances. Boyle spent a great deal of time, effort, and financial resources in these pursuits, which included searching for the elixir of life, a medicine capable of curing all diseases and extending the human lifespan.

Boyle was hoodwinked on more than one occasion by charlatans who claimed to have alchemical knowledge or the rare substances required for his alchemical pursuits. The most notable incident involved a con man named Georges Pierre. Boyle eventually realized he was being had, and there is evidence that he was aware of the danger of such scams and viewed them as an unfortunate but necessary risk in the pursuit of alchemical knowledge, a risk that his unique wealth allowed him to take.

Influenced by Bacon’s utopian conception of science, Boyle thought scientific information, including his own detailed reports of chemical experiments, should be made public for the benefit of humanity. This allowed his experiments to be reproduced and the knowledge acquired to be used to help people, especially in areas such as medicine, where the benefit to the public was obvious and immediate. There were limits to this support of scientific openness, though. For example, Boyle was concerned that the publication of instructions for turning lead into gold could collapse the world economy, bringing social chaos. Upon Boyle’s death, Newton, also a dedicated alchemist, made attempts to obtain Boyle’s alchemical notes regarding the transmutation of lead to gold. Boyle had anticipated this and left detailed instructions in his will to prevent it.

Furthermore, despite Boyle’s support of scientific openness as well as his aversion to taking oaths, Boyle often employed secrecy in his alchemical pursuits. The sort of secrecy involved here, however, was a part of the cost of networking with other alchemists to share recipes and other experimental data, and was considered common practice in the world of alchemy. Most alchemists were secretive, and would exchange recipes and materials only if their secrets were kept. Boyle was justified in believing that, if he had refused to make such promises, other alchemists would not have shared their work with him. Nevertheless, this is a notable exception to his otherwise deep aversion to taking oaths, as well as his Baconian belief that scientific data should be open to the public for the benefit of humanity.

e. Medicine

Boyle also had a deep interest in medicine. Though he never formally studied it, much of his research in natural philosophy was either directly medical in nature or motivated by medical goals, both practical and theoretical. He nonetheless distrusted physicians, after an event in his youth in which he became gravely ill when a physician at Eton gave him the wrong medicine by mistake. Furthermore, he generally rejected their Galen-based theories in favor of mechanical ones. He noted that chemical remedies often worked better than the Galenist practice of bloodletting, and that many of Galen’s views were based on claims about human anatomy that turned out to be incorrect. Boyle thought most patients were better off not seeking a doctor’s treatment.

At the same time, Boyle knew, respected, and was respected by many of the leading physicians of his day. Boyle’s London neighbor was Thomas Sydenham (1624-1689), one of the greatest physicians of the day. Sydenham read Boyle’s work and liked it so much that he dedicated his own book, Methodus Curandi Febris (1666), to him. He sometimes even asked Boyle and Ranelagh to accompany him on house calls. Boyle’s medical work was so respected that Oxford gave him an honorary Doctorate of Medicine, the only degree he ever received.

Boyle’s work in medicine is entwined with his work in natural philosophy. While the two should not be conflated, as Boyle worked on many nonmedical projects in natural philosophy, neither can be fully understood apart from the other. The development of Boyle’s interest in medicine coincided with his interest in natural philosophy in general, beginning around 1646, increasing in the mid-1650s, and lasting the rest of his life.

One of Boyle’s earliest published works was a collection of medical recipes entitled An Invitation to a Free and Generous Communication of Secrets and Receits in Physick (1655). Though Boyle worked on medical projects throughout his scientific career, a renewed interest in medicine began in the late 1660s. He would go on to steadily publish books on medical topics for the rest of his life, including Memoirs for the Natural History of Human Blood (1684), Of the Reconcileableness of Specifick Medicines to the Corpuscular Philosophy (1685), Some Receipts of Medicines (1688), Medicina Hydrostatica (1690), Experimenta et Observationes Physicae (1691), and Medical Experiments (1692).

Boyle worked with Locke on a few medical projects that are worth noting. Though early 21st century scholars remember Locke primarily for his work in epistemology and political philosophy, he considered himself first and foremost a physician. Boyle and Locke collaborated for several years to create a Baconian experimental history of human blood. This was part of a larger project of Boyle’s to create records of experimental observations regarding every known substance, with priority given to substances, such as blood, with potential value to medicine. Their work was interrupted while Locke was travelling or Boyle was ill, but their persistence resulted in the publication of Memoirs for the Natural History of Human Blood (1684).

A second medical project with Locke was the collection of data for testing the miasma theory of disease. This is particularly noteworthy because this theory proposes the mechanical explanation that disease is caused by noxious vapors moving in the air. The theory holds that these vapors act as a contagion, penetrating the bodies of those who come in contact with them through respiration. Boyle believed the contagions were composed of corpuscles and might originate deep underground, being released by human activity such as mining. Boyle and Locke hypothesized that these noxious corpuscular emanations were then spread far and wide by the wind. Believing disease and weather were linked, they collected data from physicians across the country on both the weather and the patients they had treated, looking for correlations. While this was a relatively minor project compared to some of Boyle’s other achievements, it is noteworthy since it attempted to use empirical data to test a mechanical explanation. One should not conflate the mechanical philosophy with the experimental philosophy, but the points where they intersect provide insight into Boyle’s philosophy.

Another medical collaboration in which Boyle participated was the race to find a cure for the Great Plague of 1666, an epidemic of bubonic plague which killed a fourth of London’s population, including Boyle’s former mentor George Starkey. Boyle’s belief in the miasma theory convinced him to leave London during this time. Despite this, Boyle was still part of a general effort to cure the plague that included Ranelagh, Sydenham, Locke, and many others. Boyle’s particular efforts primarily consisted of developing medical recipes he hoped would be useful to plague victims, which he then sent to Henry Oldenburg (1619-1677).

Boyle spent the last twenty years of his life engaged in medical research with his sister, Katherine Ranelagh. Through their vast network of correspondents, they would find medical recipes which they would then chemically analyze. Through medical research, Boyle found the clearest way to wed his passion for natural philosophy with his philanthropic goals.

Although he sometimes exaggerated his poor health, Boyle also suffered from very real and serious ailments including malaria, edema, seizures, kidney stones, toothaches, and deteriorating eyesight. He also suffered throughout his life from melancholy and complained of imaginative fits he described as “ravings.” During these episodes, he was carried away by his imagination, making it difficult to work. Boyle considered these ravings both a medical condition and a moral defect and spent years seeking a remedy. Since Boyle distrusted doctors and was an expert chemist, he often treated these illnesses with his own concoctions, sometimes making his condition worse. In 1670, Boyle suffered a severe stroke that left him partially paralyzed. He eventually recovered most of the mobility he had lost and continued working on his experiments.

f. Pneumatics

 In 1643, Evangelista Torricelli, a friend and advocate of Galileo, filled a glass tube with mercury, turned it upside down, and placed it in a basin of mercury. The level of mercury in the tube lowered, but some mercury remained in the tube, suspended by the weight of the air—the air pressure—pressing down on the surface of the mercury in the basin. Since the tube was airtight, Torricelli reasoned that the area in the tube above the mercury must be a vacuum. Through Marin Mersenne and his vast correspondence network, news of the experiment quickly spread throughout Europe.

Otto von Guericke (1602-1686) heard of the Torricelli experiment and designed a pump capable of producing an evacuated receiver so strong, due to the outward air pressure, that sixteen horses could not pull the two hemispheres of the receiver apart. Boyle had been interested in the nature of respiration for some time, so when he and Hooke, then Boyle’s laboratory assistant, heard of von Guericke’s impressive feat, they set about to create their own air pump. Boyle designed an improved model which featured a chamber made of glass, allowing direct observation of the phenomena within the evacuated receiver. Boyle first approached the scientific instrument-maker Ralph Greatorex (1625-1675) to build it, but when he failed Hooke took up the difficult challenge and succeeded.

From the spring through the fall of 1659, Boyle and Hooke performed dozens of experiments using the air pump and published the results in New Experiments Physico-Mechanical Touching the Spring of the Air and its Effects (1660). In this book, Boyle provides extremely detailed presentations of 43 of the experiments, giving compelling evidence for such claims as that air is a distinct substance from space, that air is elastic and has a spring, and that air pressure is so powerful that a glass vial of water placed in the receiver explodes when the air is removed. They demonstrated that air is required for phenomena such as combustion, respiration, and sound. They even placed a Torricellian barometer in the receiver, showing that the mercury does not remain suspended in the vacuum. Spring of the Air established Boyle’s scientific reputation. With its success, Boyle went from being an amateur gentleman interested in natural philosophy to being the leading scientist of the day.

The book highlighted Boyle’s genius for developing experiments that revealed important scientific information, and he also included detailed critiques of the other theories he had studied concerning the nature of air. The detail of his analysis astounded even other natural philosophers such as Henry Power (1623-1668), who claimed, “I never read any tract in all my life, wherein all things are so curiously and critically handled, the experiments so judiciously, and accurately tried, and so candidly and intelligently delivered.” It also influenced Newton, who saw it as a paradigm of scientific research.

At many of the early meetings of the Royal Society, Boyle was asked to replicate some of the experiments. Unlike other natural philosophers, Boyle had the financial resources to conduct the experiments and to repair the temperamental air pump when it broke. He even had an additional air pump made at considerable expense, which he gave to the Royal Society on May 15, 1661.

The book was also controversial, and it remains so to this day. Steven Shapin and Simon Schaffer explore the social construction of science, using the controversy between Hobbes and Boyle over the air pump experiments as their focal point in their influential book Leviathan and the Air Pump: Hobbes, Boyle and the Experimental Life (1985). However, one should also read Hunter’s account. The Jesuit Priest Francis Linus (1595-1675) tried to replicate some of the experiments and offered an alternative Aristotelian interpretation of the results, defending the view that nature abhorred a vacuum in Treatise on the Inseparable Nature of Bodies (1661). Christiaan Huygens (1629-1695) also reported that he could not replicate some of the experiments. Boyle praised Linus for his use of experiment, but pointed out the defects in his experimental practice in A Defense of the Doctrine Touching the Spring and Weight of the Air (1662). He added that further experiments with a J-shaped tube corroborated his claim that the reciprocal proportion between the pressure and volume of air was constant. This became known as Boyle’s Law.

This is controversial because Boyle appealed to experiments with the J tube actually performed by other natural philosophers like Henry Power and Richard Towneley (1629-1704). Furthermore, it was Hooke, rather than Boyle, who worked to find the precise numerical relation between air volume and pressure, while Boyle was more interested in the philosophical significance of the proportion being reciprocal and constant.

Even more significant was a series of objections raised by Boyle’s fellow mechanical philosopher Thomas Hobbes, upon which Leviathan and the Air Pump focuses. Hobbes offered a contrary mechanical interpretation that was consistent with observation. Like Descartes’s interpretation of the Torricelli experiment, Hobbes suggested that subtle matter was passing through microscopic pores in the glass so that the receiver was full of matter and not a true vacuum. Since it is possible to give an alternative mechanical explanation consistent with observation, Hobbes argued one cannot use experiments to decide between them. Furthermore, since multiple mechanical interpretations are possible for any experimental observation, observations are never completely independent of theory.

In An Examen of Mr. T. Hobbes his Dialogus Physicus De Natura Aeris (1662), Boyle replied by distinguishing between “matters of fact,” which can be tested, and mere “hypotheses,” which result from metaphysical speculation. It is possible that subtle matter penetrated the glass, but until there is empirical evidence to support this, positing the existence of subtle matter violates Ockham’s razor. Notably, by the early 21st century compelling evidence had emerged that an evacuated receiver contains billions of subatomic particles, such as neutrinos, far smaller than the pores of the glass.

Boyle also was motivated by a desire to show a theistic alternative to the equally mechanical materialism of Hobbes, Gassendi, and the ancient atomists, which was then strongly associated with atheism. For a time, Hobbes’s name was almost synonymous with atheism. Boyle had tried to show, since the early 1650s, that a mechanical philosophy could be compatible with Christianity.

In the end, Boyle wrote some ten books concerning his work with the air pump: New Experiments Physico-Mechanical Touching the Spring of the Air and its Effects (1660); A Defense of the Doctrine Touching the Spring and Weight of the Air (1662); An Examen of Mr. T. Hobbes his Dialogus Physicus De Natura Aeris (1662); New Experiments Concerning the Relation between Light and Air (1668); A Continuation of New Experiments Physico-Mechanical Touching the Spring and Weight of the Air and their Effects (1669); New Pneumatical Experiments about Respiration (1670); Of a Discovery of the Admirable Rarefaction of Air (1670); Flame and Air (1672); A Continuation of New Experiments Physico-Mechanical Touching the Spring and Weight of the Air and their Effects (1680); and The General History of Air (1692). Eventually, though, his attention shifted to medical chemistry.

3. Philosophy of Science

Boyle was well known for his views on the role of experimental evidence in natural philosophy. Boyle’s philosophy of science was primarily influenced by Bacon. In Novum Organum (1620) and New Atlantis (1627), Bacon had challenged natural philosophers to employ an inductive scientific method based on the careful application of technology to make detailed empirical observations, instead of relying on the syllogistic approach favored in the Scholastic tradition, which made deductive inferences from universal principles. Bacon argued that if the universal principles themselves turned out to be false, the conclusions deduced from them would be unjustified. Instead of trying to anticipate what nature should be like according to reason, natural philosophers instead should make detailed observations of what nature is actually like. They should then interpret these observations and form inductive generalizations about the natural world. This approach to science allows observational evidence to have epistemic priority over theory, so that theories can be modified in the face of new empirical evidence. Bacon envisioned a future “history of qualities,” a sort of publicly accessible scientific database of empirical observations.

Boyle took this challenge seriously and developed an experimental method that used detailed observation, aided by new technology, to reveal nature’s hidden structure. This approach is apparent in his work in pneumatics, his chemical research to create experimental histories of substances, and his projects on cold, air, light, color, minerals, and gems. Many of these projects never came to fruition, but on some he worked steadily for years. For instance, Boyle’s natural history of Ireland never even got off the ground, but his empirical approach to the study of blood was fruitful and eventually led to medical advances which now routinely save lives. It is also important to note that this collection of empirical data is not the blind data collection of the “narrow inductivist conception of scientific inquiry” criticized by Carl Hempel in Philosophy of Natural Science (1966). Boyle prioritized the experimental investigation of substances with obvious benefit to society, and Boyle’s empirical data collection was hypothesis driven.

Boyle’s commitment to the mechanical philosophy was consistent with his views on the role of experiment in science. Boyle would often develop mechanical explanations of phenomena that served as hypotheses, for which he would then design experiments to test. He thought that testability was important in hypothesis development as well as in determining what questions science should pursue. He had a genuine talent for creating experiments designed to test theories, and in many cases this provided new scientific information. Following Bacon, Boyle tried to resist non-empirical metaphysical speculation and modify theories in the light of new experimental evidence. The results are mixed, but when he did engage in metaphysical speculation, such as in his treatment of the arguments for body-to-body occasionalism, he prefaced his remarks by noting that none of the theories he discussed could be empirically tested.

Comparison with Descartes on the role of experiment in natural philosophy is insightful. Experimental observation played a much different role for Boyle than it did for Descartes. Descartes is famous for conducting ingenious experiments, but rather than being used to test or falsify a hypothesis, they often played a part in the reduction of a complex scientific question into more basic ones. In Rules for the Direction of Mind (1628) and Discourse on the Method (1637), Descartes describes a scientific method that involves reducing a problem into more and more fundamental problems until a problem is reached that is so basic that a self-evident intuition solves it. One can then use this intuitive solution in a series of deductive inferences, solving the problems until one reaches a solution to the original one.

Furthermore, for Descartes, empirical observation was not a reliable method of testing hypotheses, since he believed the senses provide only confused modes of thought. The only properties of matter about which we can be certain, for Descartes, are the geometric properties of extended space. He believed this method of science could achieve the same level of certainty as mathematics since it restricted itself to clear and distinct deductions from matter’s geometric properties. For Descartes, physics is applied geometry.

By contrast, Boyle thought theory must be epistemically subordinate to observation, so he used experiments to test a theory. Instead of using them in a reductive process of finding self-evident intuitions, he designed experiments specifically to falsify or corroborate a claim. In this way, claims such as “air is needed for respiration” could be empirically supported, while claims such as “air is identical to space,” could be refuted. For Boyle, scientific knowledge was more likely to be inductively inferred than geometrically deduced.

Concerning Boyle’s general epistemology, in works such as A Discourse of Things above Reason (1681), Boyle distinguishes between things that can be known by reason and things that can be known through experience. Boyle also believed that at least some ideas are innate. Examples of innate ideas include the belief that contradictories cannot both be true, that the whole is greater than the part, and that every natural number is either odd or even.

Furthermore, Boyle believed that some truths are beyond a human’s capacity to understand. These are things which are true, and our intellect has sufficient cause to assent to them based on experience, authentic testimony, or mathematical demonstration, but when it reflects on them, it finds itself at a strange disadvantage. Boyle includes three kinds of beliefs in his taxonomy of things above reason.

The first kind he labels “incomprehensible” since it includes belief in things beyond our comprehension. For example, our finite minds cannot grasp the infinite nature of God. Boyle thinks we can comprehend that God exists and some of the things that God is not, but we cannot fully understand the boundless nature of his perfections. Boyle declares this to be truly supra-intellectual.

Boyle calls the second kind of thing above reason “inexplicable.” This includes beliefs for which we are unable to conceive of their manner of existing, or how the predicate can be applied to the subject. Boyle gives examples such as the infinite divisibility of matter and the incommensurability of the diagonal of a square to the length of its sides.

Boyle calls the final kind of thing above reason “unsociable,” but it might better be labeled “incompatible.” This class includes true propositions that seem incompatible with other propositions known to be true. For example, human free will seems to be incompatible with God’s foreknowledge of future events, but necessary for moral responsibility. Mind and body are distinct substances, but they seem to causally interact. Boyle thought these were real problems and had real solutions but were likely beyond a human’s finite capacity to understand, though he also thought philosophers should continue to try.

Like Descartes, Boyle believed that we could have knowledge of things that are beyond our capacity to clearly imagine, such as the mathematical properties of a chiliagon. We can demonstrate necessary truths about a 1000-sided object and show it has different properties that a 1001-sided object. Despite this, the images our minds form of these shapes are indistinguishable.

Boyle also distinguished between real and nominal essences, which, along with his work on primary and secondary qualities, influenced Locke’s epistemology. In A Free Enquiry into the Vulgarly Received Notion of Nature (1686), Boyle begins by listing all the ways the term “nature” is used. He then distinguishes between the “notional” sense, which is the way we choose to use words, from the way nature really is. Boyle also discusses the distinction in the Origin of Forms and Qualities (1666).

4. Substance Dualism

Boyle was a substance dualist, postulating that the universe consists of two types of substance: purely material corpuscles and nonphysical, conscious souls. Boyle accepted Descartes’s definition of substance as a type of entity that was not ontologically dependent on anything but God, whereas a mode is ontologically dependent on a substance. Shape, for example, cannot exist on its own, but is ontologically dependent on the bit of matter that has it.

Boyle’s dualism was influenced by Descartes, especially after his work with Robert Hooke, who taught him Cartesian philosophy, but there are important differences between their similar metaphysics. Descartes held that spatial extension was the “Attribute,” or essence, of matter, while thought was the essence of mind. Accordingly, all true properties of matter were modifications of extension, such as size, shape, and motion. In a similar way, since thought is the essential attribute of mental substance, all properties of mind are modes or types of thought.

Although Boyle agreed that thought was mental and matter was extended, he was not committed to Descartes’s elegant, rationally deduced substance-attribute-mode model. The mechanical affections Boyle associated with matter were derived from experience. For example, Boyle included solidity as another empirically based mechanical affection, but it is not clear how one can explain it as a mode of Cartesian spatially extended matter.

Boyle saw that bodies need some minimal force of resistance for mechanical interaction to be possible, though he emphasized such a force was nothing like a rational disposition or internal source of motion. Boyle also believed God gave matter the power to transfer motion upon collision, another potential problem for Descartes, since modes should not be able to transfer.

Likewise, for Descartes, the existence of a void or vacuum in space—that is, an area of space containing no matter whatsoever—is logically impossible. Since the attribute of body is extension, and there is no real distinction between a substance and its attribute, any extended area of space must contain body. Boyle’s views on the nature of the material world were more influenced by Bacon and Gassendi. He believed the elegance of a metaphysical system is not as important as its correspondence to empirical observation. He thought the air pump experiments supported the idea that a vacuum in space, devoid of all matter, was logically possible, and the existence of a vacuum should be posited until there was empirical evidence for the presence of matter in the evacuated receiver.

A final difference between Boyle’s dualism and that of Descartes was Boyle’s belief in animal consciousness. Descartes thought animals lacked a soul and were merely incredibly complex, divinely designed machines. Although they behaved as if they suffered, nonhuman animals lacked any conscious mental states. Descartes performed many animal dissections, including vivisections of live animals. Boyle saw the scientific need for vivisection since some anatomical features are only observable in living bodies. He even performed some during his sojourn in Ireland during the early 1650s. He gave up the practice, though, because of the observable suffering it caused. Boyle even had a preference for free-range chicken, but this may have been as much about flavor as chicken flourishing.

Boyle believed much instinctual behavior in nonhuman animals is purely mechanical, such as involuntary blinking when an eyelash is touched by a feather. Although he believed nonhuman animals were capable of conscious sensations, he thought they lacked rationality. Like other natural phenomena, nonhuman animal behavior sometimes seems rational, but, contrary to the scholastic Aristotelians, he thought the material world contained no rational dispositions.

5. Causation

Fundamental to Boyle’s philosophy is the belief that matter is passive, having no internal power, force, source of motion, or substantial form beyond the primary qualities of size, shape, solidity, and motion. He rejected the scholastic tendency to see intelligent dispositions everywhere in nature, such as the view that nature abhors a vacuum, or the view that an element has an internal disposition to move toward a natural location in the universe. Boyle acknowledged that the regularity seen in the natural world makes it sometimes seem like there is rational behavior, such as the regular motion of celestial bodies, or the tendencies of chemical substances to repeatedly behave in uniform ways. Despite this, he rejected the view that matter had power beyond its mechanical properties and sought to demonstrate how natural phenomena could be explained in terms of the motion of particles obeying certain laws of motion which he believed God had established. In works such as The Christian Virtuoso (1744), Boyle argued that the regularities we see in nature are a manifestation of God’s power and that divine volitions cause the laws of nature.

Boyle believed that the ultimate cause of motion is God, who created bodies, set them in motion, and maintained the laws of motion by divine will. God does grant matter certain basic powers such as solidity and the power to transfer motion to other bodies upon collision, but these are to be understood as unconscious mechanical properties rather than anything like mental dispositions or the internal sources of motion invoked by scholastic Aristotelian natural philosophy.

Boyle was aware of, and even sympathetic to, occasionalism, the view that God is the cause of anything that requires a cause. However, he never explicitly endorsed it. He does speak of it favorably in folios 38 to 40 of volume 10 of the Boyle Papers.  While not explicitly endorsing it, Boyle presents three arguments intended to show that body-to-body occasionalism is not in itself absurd. Boyle does not here discuss mind-body occasionalism, but rather how God causally interacts with matter to create the natural world.

This is a minor discussion in his vast corpus, and should not be given undue emphasis. Its relevance to Boyle’s views on causation, though, makes it worthy of inclusion here. Boyle generally tried to avoid non-empirical metaphysical speculation or metaphysical system building, and he begins by pointing out that the issue cannot be settled by any testable experiment. Boyle then explicitly appeals to Ockham’s razor. Since God’s concurrence by itself is sufficient to cause the motion of bodies, it is superfluous, and even potentially impious, to attribute such power to finite bodies. If God wills a body to be in location a, and later wills it to be in location b, this alone is sufficient to move it. Attribution of a second cause to matter itself is not necessary.

Boyle’s second argument anticipates the philosophy of David Hume (1711-1776) by claiming that causation itself never appears to the senses. The power of one body to move another body is not directly observable. We only perceive that when one body hits another there follows a motion in the second body. This point is essential to Hume’s formulation of the problem of induction, supporting the claim that our belief in causation cannot be justified as a matter of fact. For Boyle, the fact that the power of causation is not manifest to the senses shows that it could be God. Therefore, occasionalism cannot be ruled out as absurd.

Boyle’s third argument is that it might not be even possible to conceive of one body communicating motion to another. If finite bodies are collections of modes ontologically dependent on the attribute of extension, for example, they should not be able to cause motion in another body. It thus should not be possible for us to conceive of a body transferring its motion to another body on collision. Occasionalism, therefore, cannot be ruled out as absurd since it actually seems more comprehensible than attributing the power of causation to finite bodies.

Boyle incorrectly labels Descartes as a sort of deist. Deists believed that, after the initial divine causal impulse, the universe ran on its own accord, obeying the laws of motion without the constant intervention of God. However, Descartes believed that God is constantly involved in creating the world through one continuous divine act. Boyle was aware of the similar body-body occasionalism of Louis De La Forge, in which God creates motion by recreating an object in different locations at different times. Boyle, however, seems to have preferred what Peter Anstey has described as “nomic occasionalism.” According to this type of body-body occasionalism, bodies are not totally passive but have basic, mechanical powers, such as solidity and the power to transfer their motion to other bodies upon collision. On this view, God causes the initial motion, preserves and conserves that motion, and determines the direction and speed of bodily motions before and after collisions. Like many of his contemporaries, Boyle believed that the laws of nature are divine volitions. In the case of miracles, though, God can suspend a law of nature, a further manifestation of divine power. Yet again, Boyle was cautious and hesitant to proclaim nomic occasionalism over deism, or the so-called cinematic occasionalism of De La Forge, pointing out that none of these views can be easily empirically tested.

In any case, it seems clear that Boyle’s occasionalism was confined to body to body interaction. Boyle thought that human minds were capable of genuine causal agency. This agency played an essential role in his views on the nature of moral responsibility, as well as his theological views about what is necessary for salvation. Our souls are connected to our bodies and somehow causally interact with them. Here again, Boyle is hesitant to commit himself to any specific theory beyond what can be experimentally tested. He believed that how mind-body interaction is possible, as well as how free will is consistent with divine foreknowledge, are likely mysteries beyond the ability of reason to solve.

6. God

By now it should be clear that the single most important influence on Boyle’s philosophy was his personal religious beliefs. His contributions to philosophy, chemistry, pneumatics, and medicine can be all interpreted as the development and fulfillment of a lifelong religious quest. Boyle thought there were three true books of wisdom, the “book of scripture,” the “book of nature,” and the “book of conscience.” He thought all three were important and spent nearly equal amounts of time and energy on each.

Boyle was christened at the chapel at Lismore Castle in Ireland as an infant and brought up as an Anglican protestant, though he was greatly influenced by Puritanism. The terrible storm Boyle witnessed on his grand tour with Isaac Marcombes was a transformative experience for Boyle, and many of his philosophical projects can be seen as attempts to fulfill the oath he took to survive it.

Boyle thought that, of the traditional arguments for the existence of God, the teleological argument was the strongest. Boyle acknowledged that the existence of God could not be rationally demonstrated, but he believed the natural world abounded with empirical evidence of God’s power and wisdom. He thought the incredible complexity and order of the universe was evidence of God’s existence. The vastness of the universe, and the speed with which the earth and celestial objects move, Boyle saw as evidence of God’s unbounded power. He thought that God’s constant concurrence was needed to sustain the universe’s existence.

He was particularly amazed by the human body and the bodies of nonhuman animals, which he interpreted as divinely constructed machines. Internal organs were smaller machines ingeniously and exquisitely designed to work together to sustain the life of the animal. Ignorant of natural selection, Boyle thought the incredible complexity of their mechanical structure was compelling evidence of God’s existence. In one early letter, Boyle claimed to have learned more about God’s creation dissecting fishes than in all the books he had read. At a macroscopic level, he thought that the climates of the different regions of the earth, and other geological features were intentionally designed to sustain the lives of various animals.

Boyle also used the famous clock at Stroudsburg as an analog to “this great automaton the world.” He thought the universe itself was intentionally designed by God to be understood by rational creatures, though parts of this creation are beyond human comprehension. Boyle believed that, since the universe was a manifestation of God’s greatness, one should study the book of nature as an aid to salvation.

Boyle also had a basic modal semantics. He believed God has the power to create alternative universes with different laws of nature. Boyle interpreted these possible worlds as potential divine creations. In addition to possible alternative creations of God, in Of the High Veneration Man’s Intellect Owes to God (1685), Boyle claims the size of the actual universe is so great that distant regions of space might have other areas, the size of our observable universe, that contain different planets and creatures, and even might have different laws of nature.

In the traditional theological debate between divine voluntarism, which holds that God’s will is prior to his reason, and divine intellectualism, which holds that God’s reason is prior to his will, Boyle has been often regarded as an important early modern voluntarist, but the label needs qualification. Boyle believed it was rash to claim that God’s acts had to conform to our finite conception of reason, and he generally rejected the a priori approach to theology advanced by many intellectualists. There is no way for us to deduce a priori which of the countless possible worlds God chose to create. Boyle thought we could learn about God’s magnificent creation through empirical observation. The problem with placing God’s reason above his will was that we are limited by our finite understanding of a priori truths.  The ultimate contingency of the laws of nature calls for their empirical investigation, rather than a priori deduction. On the other hand, Boyle did not think God did things arbitrarily. He thought everything happened according to God’s divine plan, even if we could not completely understand it. Boyle’s rejection of intellectualism has more to do with the limits of our finite reason than a priority of God’s will over his reason.

Boyle believed everyone had the capacity for salvation. Boyle, Ranelagh, and other members of the Hartlib Circle collaborated on a number of projects to make the Bible available to more people, including overseeing the publication of translations of the Bible into Irish, Malay, and Algonquin. This has allowed much of the Algonquin language to be preserved. Such projects were controversial at the time, but Boyle saw them as part of his religious duty.

Boyle spent years mastering ancient Biblical languages to further his understanding of the Bible, including Greek, Syrian, Aramaic, and Arabic. He learned Hebrew to read the Torah and sought out Jewish scholars for advice on his translations. He argued for religious toleration, though he thought Christianity held the only path to salvation.

Boyle believed in the existence of supernatural creatures such as angels, demons, and witches. In Of the High Veneration Man’s Intellect Owes to God (1685), he claimed that angels, both good and evil, are rational but completely incorporeal, and that there could be as many species of angels and demons as there are nonhuman animals, with subtle moral differences between them. On the other hand, he also believed that most witch trials were unjust and not cases of real witchcraft. He tried to apply his empirical scientific method to the investigation of supernatural phenomena by creating a sort of database of reliable accounts of supernatural events, just as his Baconian histories of qualities were records of reliable experimental observations of natural substances. Boyle was convinced that enough reliable accounts of supernatural phenomena would make skepticism of Christianity seem unreasonable. He even saw to the publication of what he believed to be a true account of a poltergeist: Pearreaud’s Devil of Mascon (1658). He also tried to investigate what he thought to be a reliable account of precognition.

Despite a lifetime of religious pursuits, Boyle also had significant religious doubts. These doubts troubled him, and throughout his life he sought spiritual guidance from friends, family, and clergy. He worried that his wealth had been taken from Ireland unjustly and that his philanthropic endeavors were inadequate. He also feared that he had committed a sin against the Holy Ghost by ignoring opportunities to repent for self-acknowledged sins.

Boyle intended to write a book about atheism, but it was never completed. He left a substantial endowment in his will to start a series of annual lectures defending the existence of God and the basic tenets of Christianity against the dangers of atheism he perceived. The sermons started in 1692 and lasted steadily until 1935, after which time they were given frequently, but sporadically. Since 2005, they have been given every year once again.

7. Ethics

Although Boyle is best known for his scientific endeavors, he was also fundamentally concerned with ethics. His earliest attempts at philosophy were in ethics, and ethics dominated his philosophy throughout the years he spent at his estate in Stalbridge during the 1640s, following his return to England from the grand tour with Isaac Marcombes. At some point during the late 1640s to early 1650s, Boyle had a conversion experience in which the focus of his work shifted permanently to natural philosophy. Nonetheless, he never abandoned his ethical concerns.

His most extensive ethical work is the Aretology, a systematic study of virtue. Written between 1645 and 1647 and never published during his lifetime, the treatise defends the claim that the key to human flourishing is the attainment of “felicity,” which Boyle understood as a supreme, sufficient, contenting happiness, ultimately achievable only after the death of the body and the contact of the soul with the divine. Felicity is the goal of eudaimonia because Boyle believes it is the only thing that is good in itself. Boyle rejects pleasure, honor, wealth, and even knowledge as approaches to achieving felicity, arguing instead that “to the palace of felicity the only highway is virtue.” This warrants the systematic study of moral virtue to which the title refers.

Boyle begins by claiming that the proper subject of moral virtue must be the rational soul rather than the affections of the senses. He then adopts a basically Aristotelian causal analysis of moral virtue, complimented with dashes of stoicism. Thus, the final cause of virtue is felicity, as we have seen. The material cause of virtue is the human soul. The formal cause of virtue is what Boyle terms “mediocrity,” the Aristotelian idea that a moral virtue is a mean between a vice of deficiency and a vice of excess, which one obtains only through habitual repetition until it becomes part of one’s character. The efficient cause of virtue is the most complex. Boyle sees it as a combination of God, the capacity that God gave us to develop virtue, mental habit, and living in accordance with right reason.

Boyle was greatly influenced by stoicism, having read the classic works under Isaac Marcombes. This influence is apparent throughout his moral treatises. Boyle’s ethics was also heavily influenced by Johann Alsted (1588-1638), a German Calvinist.

8. Casuistry

Boyle was a dedicated casuist, believing that a detailed analysis of his own conscience was just as important as the study of nature or the study of the Bible, and he devoted just as much of his time and effort to it. Boyle was just as meticulous in the analysis of his own conscience as he was at chemical analysis, scrutinizing his behavior, taking detailed notes, discussing them regularly with close friends and spiritual advisors such as Ranelagh, Locke, Gilbert Burnet (1642-1715), and Edward Stillingfleet (1635-1699).

Boyle’s intense examination of his own conscience likely goes back to the conversion experience he had during the night of the terrible storm on his grand tour, but it was probably also influenced by his study of stoicism. Boyle even provided a stipend for Robert Sanderson to help him publish his Lectures on Human Conscience, a book based on a series of lectures that Sanderson gave at Oxford in the 1640s. It is considered a classic in the field of casuistry.

Throughout his life, Boyle also suffered from manic fits he described as “ravings,” in which his imagination seemed to run away beyond his control, ravishing his attention. He found these fits of restless fancy disturbing and debilitating, and he made all sorts of efforts to treat these episodes both medically and by developing coping mechanisms to calm himself when the fits occurred.

Boyle scrutinized his daily moral behavior. For example, Boyle sometimes had to make promises of secrecy to obtain new alchemical recipes. This not only involved taking an oath, but also ran counter to his general advocation of openness in experimental data. These sorts of tensions gave Boyle and his spiritual advisors plenty of material to analyze. A full understanding of Boyle’s thought has to appreciate his equal dedication to the study of the book of nature, the book of scripture, and the book of conscience.

9. References and Further Reading

a. Recent Editions of Boyle’s Works

  • The Works of Robert Boyle (Pickering & Chatto, 1999-2000), ed. Michael Hunter and Edward B. Davis.
    • This fourteen-volume set is the definitive edition of Boyle’s work.
  • Selected Philosophical Papers of Robert Boyle (Hackett, 1991), ed. M.A. Stewart.
    • An excellent paperback edition of some of Boyle’s most important works.
  • A Free Enquiry into the Vulgarly Received Notion of Nature (Cambridge, 1996), ed. Edward B. Davis and Michael Hunter.
    • A paperback edition of this important later work by Boyle, with a good introduction and chronology.
  • The Works of the Honourable Robert Boyle (Rivington, 1772), ed. Thomas Birch.
    • This was the classic edition, but has been surpassed by the Hunter and Davis edition.

b. Chronological List of Boyle’s Publications

  • An Invitation to a free and generous Communication of Secrets and Receits in Physick (1655)
  • Some Motives and Incentives to the Love of God (Seraphic Love) (1659)
  • New Experiments Physico-Mechanical, touching the Spring of the Air and its Effects (1660)
  • Certain Physiological Essays (1661)
  • The Sceptical Chymist (1661)
  • Some Considerations touching the Style of the Scriptures (1661)
  • A Defense of the Doctrine Touching the Spring and Weight of the Air (1662)
  • An Examen of Mr. T. Hobbes his Dialogus Physicus De Natura Aeris (1662)
  • Some Considerations Touching the Usefulness of Experimental Natural Philosophy (1663)
  • Experiments and Considerations Touching Colours (1664)
  • New Experiments and Observations Touching Cold (1665)
  • Occasional Reflections upon Several Subjects (1665)
  • Hydrostatical Paradoxes (1666)
  • The Origin of Forms and Qualities (1666)
  • New Experiments Concerning the Relation between Light and Air (1668)
  • A Continuation of New Experiments Physico-Mechnical Touching the Spring and Weight of the Air and their Effects (1669)
  • Of Absolute Rest in Bodies (1669)
  • New Pneumatical Experiments about Respiration (1670)
  • Cosmical Qualities (1670)
  • Of a Discovery of the Admirable Rarefaction of Air (1670)
  • The Usefulness of Natural Philosophy, II (1671)
  • An Essay about the Origin and Virtues of Gems (1672)
  • Flame and Air (1672)
  • Essays of Effluviums (1673)
  • The Saltness of the Sea (1673)
  • The Excellency of Theology Compared with Natural Philosophy (1674)
  • About the Excellency and Grounds of the Mechanical Hypothesis (1674)
  • Some Considerations about the Reconcileableness of Reason and Religion (1675)
  • Experiments, Notes, Etc., about the Mechanical Origin of Qualities (1675)
  • Of a Degradation of Gold Made by an Anti-Elixir (1678)
  • Experiments and Notes about the Producibleness of Chemical Principles (1680)
  • A Continuation of New Experiments Physico-Mechnical Touching the Spring and Weight of the Air, and their Effects (1680)
  • The Aerial Noctiluca (1680)
  • New Experiments and Observations, made upon the icy Noctiluca (1682)
  • A Discourse of Things Above Reason (1681)
  • Memoirs for the Natural History of Human Blood (1684)
  • Experiments and Considerations about the Porosity of Bodies (1684)
  • Of the High Veneration Man’s Intellect owes to God (1684)
  • Short Memoirs for the Natural Experimental History of Mineral Waters (1685)
  • An Essay of the Great Effects of Even Languid and Unheeded Motion (1685)
  • Of the Reconcileableness of Specifick Medicines to the Corpuscular Philosophy (1685)
  • A Free Enquiry into the Vulgarly Received Notion of Nature (1686)
  • The Martyrdom of Theodora and of Didymus (1687)
  • A Disquisition about the Final Causes of Natural Things (1688)
  • Some Receipts of Medicines (1688)
  • Medicina Hydrostatica (1690)
  • The Christian Virtuoso (1690)
  • Experimenta et Observationes Physicae (1691)
  • The General History of Air (1692)
  • Medicinal Experiments (1692)
  • A Free Discourse against Customary Swearing (1695)
  • The Christian Virtuoso, The Second Part (1744)

c. Correspondence

  • The Correspondence of Robert Boyle (Pickering & Chatto, 2001), ed. Michael Hunter, Antonio Clericuzo, and Edward B. Davis.
    • This six-volume edition of Boyle’s correspondence is the standard in the field and a companion to the Pickering & Chatto edition of The Works of Robert Boyle.

d. Work Diaries

  • Boyle diligently kept diaries of his experimental work starting in the 1640s. Thanks to the work of Michael Hunter and Charles Littleton, these are available online at http://www.bbk.ac.uk/boyle/workdiaries/.

e. Biographies

  • Hunter, Michael. Boyle: Between God and Science (Yale, 2009).
    • This is the best biography of Boyle to date, and includes important recent discoveries in Boyle studies.
  • Hunter, Michael. Robert Boyle by Himself and His Friends (Cambridge, 1994).
    • This edited volume of biographical and autobiographical essays about Boyle is noteworthy for the inclusion of fragments from William Wotton’s lost Life of Boyle.
  • Maddison, R.E.W. The Life of the Honourable Robert Boyle (Taylor & Francis, 1969).
    • This is another biography of Boyle with excellent coverage of Boyle’s Oxford period, but the coverage of Boyle’s early life is covered by reprinting Boyle’s own account as presented in the autobiographical An Account of Philaretus During his Minority (also included in Hunter 1994 above).
  • Masson, Flora. Robert Boyle: A Biography (Constable and Company, 1914).
    • An early biography of Boyle with many notable anecdotes.

f. Selected Works on Boyle

  • Alexander, Peter. Ideas, Qualities, and Corpuscles: Locke and Boyle on the External World (Cambridge, 1985).
    • This is an exploration of Boyle’s profound influence on John Locke.
  • Anstey, Peter. The Philosophy of Robert Boyle (Routledge, 2000).
    • This is the first book-length treatment of Boyle’s philosophy.
  • Anstey, Peter. “Boyle Against Thinking Matter,” in Late Medieval and Early Modern Corpuscular Matter Theories, Edited by Christoph Luthy, John Murdoch, and William Newman (Brill, 2001).
  • Baxter, Roberta. Skeptical Chemist: The Story of Robert Boyle (Morgan Reynolds Publishing, 2006).
  • Boas, Marie. Robert Boyle and Seventeenth-Century Chemistry (Cambridge, 1958).
  • Boas-Hall, Marie. Robert Boyle on Natural Philosophy (Indiana University Press, 1965).
  • DiMeo, Michelle. “‘Such a Sister Became Such a Brother’: Lady Ranelagh’s Influence on Robert Boyle,” Intellectual History Review 25.1 (2015), pp. 21-36.
  • Eaton, William. Boyle on Fire: The Mechanical Revolution in Scientific Explanation (Continuum, 2005).
    • This work explores the lasting influence of Boyle’s philosophy of science.
  • Harwood, John. The Early Essays and Ethics of Robert Boyle (Southern Illinois University Press, 1991).
    • This is the only book that presents a detailed analysis of Boyle’s ethics.
  • Hunter, Michael. Robert Boyle Reconsidered (Cambridge, 1994).
    • This edited volume of essays brought about a new appreciation of the significance of Boyle’s natural philosophy.
  • Hunter, Michael. “How Boyle became a Scientist,” History of Science 33.1(1995), pp. 59-103.
    • This article is a detailed account of how Boyle became a scientist.
  • Hunter, Michael. Robert Boyle 1627-1691: Scrupulosity and Science (Boydell, 2000).
    • This work is an in-depth exploration of the relationship between Boyle’s religious views and his natural philosophy. It includes Hunter’s essay, “How Boyle became a Scientist.”
  • Hunter, Michael. Boyle Studies: Aspects of the Life and Thought of Robert Boyle (Ashgate, 2015).
  • Kuslan, Louis, and A. Harris Stone. Robert Boyle: The Great Experimenter (Prentice-Hall, 1970).
    • Although written for children, this short book is an excellent introduction to Boyle’s natural philosophy, with detailed explanations of several of his most important experiments.
  • J.R. Jacob. Robert Boyle and the English Revolution: A Study in Social and Intellectual Change (Burt Franklin, 1977).
  • Newman, William, and Lawrence Principe. Alchemy Tried in the Fire: Starkey, Boyle, and the Fate of Helmontian Chymistry (University of Chicago, 2002).
  • Principe, Lawrence. The Aspiring Adept: Robert Boyle and His Alchemical Quest (Princeton, 1998).
  • Sargent, Rose-Mary. The Diffident Naturalist: Robert Boyle and the Philosophy of Experiment (University of Chicago, 1995).
  • Wojcik, Jan W. Robert Boyle and the Limits of Reason (Cambridge University Press, 2002).

g. Other Important Works

  • Ben-Chaim, Micahel. Experimental Philosophy and the Birth of Empirical Science (Routledge, 2004).
  • Evan Bourke. “Female Involvement, Membership, and Centrality: A Social Network Analysis of the Hartlib Circle,” Literature Compass 14.4 (2017).
  • David, Edward. Creation, Contingency, and Early Modern Science: The Impact of Voluntaristic Theology on Seventeenth Century Natural Philosophy (PhD Dissertation, Indiana University, 1984)
  • Duddy, Thomas. A History of Irish Thought (Routledge, 2002).
  • Frank, Robert G. Harvey and the Oxford Physiologists: A Study of Scientific Ideas (University of California Press, 1980).
  • Garber, Daniel. Descartes’ Metaphysical Physics (University of Chicago Press, 1992).
  • Garber, Daniel. Descartes Embodied: Reading Cartesian Philosophy through Cartesian Science (Cambridge University Press, 2000).
  • Harrison, Peter. “Voluntarism and Early Modern Science,” History of Science 40.1 (2002), pp. 63-89.
  • Harrison, Peter. The Fall of Man and the Foundations of Science (Cambridge University Press, 2007).
  • Hempel, Carl. The Philosophy of Natural Science (Prentice Hall, 1966).
  • Klaaren, Eugene. Religious Origins of Modern Science (William B. Eerdmans Publishing Company, 1977).
  • Osler, Margaret. Divine Will and the Mechanical Philosophy: Gassendi and Descartes on Contingency and Necessity in the Created World (Cambridge University Press, 1994).
  • Webster, Charles. The Great Instauration: Science, Medicine, and Reform 1626-1660 (Holmes and Meier Publishers, 1975)

Author Information

William Eaton
Email: weaton@georgiasouthern.edu
Georgia Southern University
U. S. A.

Reduction and Emergence in Chemistry

Most talk of reduction and emergence figures in discussions about the relation between different physical theories, or between physics and biology. The aim of this article is to present a different perspective through which to examine reduction and emergence; namely, the perspective of chemistry’s relation to physics.

Very broadly, reduction is associated with the idea that the sciences are hierarchically ordered and unified. As a universal thesis, reductionism takes physics to be the most fundamental science in the sense that the laws and postulates of all other sciences can, at least in principle, be derived from and explained by physics. Metaphysically, this implies that things like molecules, cells, chairs and consciousness are nothing more than the physical stuff of which they are made. On the other hand, emergence is often associated with the idea that the special sciences and their postulated entities, properties, and so forth are somehow novel and partially autonomous from physics. On this view, while the special sciences comply with physical laws, they are nevertheless autonomous, and their postulated entities are over and above physical ones. In this context, one cannot explain away molecules, cells and their respective properties by reference only to physical stuff.

The philosophy of chemistry examines in detail whether reduction, emergence, or some other notion correctly characterises chemistry’s relation to physics and, in particular, to quantum mechanics. The philosophy of chemistry illuminates possible ways of thinking of chemistry’s relation to physics, but also of reduction and emergence. Moreover, understanding chemistry’s relation to physics has important implications for how one understands the relation between other sciences. For example, biology often refers to chemical entities and processes in order to explain biological phenomena. Given this, examining chemistry’s relation to physics contributes to understanding biology’s relation to physics. Furthermore, the notions of reduction and emergence are associated with more general philosophical questions about the unity or disunity of the sciences, but also about the very nature and structure of the world. Examining reduction and emergence with respect to chemistry can contribute to these issues. A case in point is the nature and reality of entities and properties in special sciences. For example, if chemical entities are reduced to those of physics, then one could formulate an argument against the existence of chemical entities. On the other hand, if chemical entities somehow emerge from physical ones, then this may suffice to support the reality of chemical entities and of their respective properties.

Table of Contents

  1. Introduction
  2. The Significance of This Topic in the Philosophy of Chemistry
  3. Reduction in Chemistry
    1. Epistemological, or Intertheoretic, Reduction
    2. Antireductionism with Respect to Chemistry
    3. Ontological Reduction
    4. Alternative Forms of Reduction
  4. Emergence in Chemistry
    1. British Emergentism in Chemistry
    2. Strong Emergence
    3. Alternative Forms of Emergence
  5. Beyond Reduction and Emergence
    1. Unity without Reduction
    2. Pluralism
  6. Conclusion
  7. References and Further Reading

1. Introduction

What one means by reduction and emergence can vary extensively, and there are positions which argue for an understanding of chemistry’s relation to physics in a manner that goes beyond the dilemma between reduction and emergence. Nevertheless, all positions can be understood as addressing at least one of two distinct, yet often overlapping, questions:

  1. The question of the relation of the formalism of chemistry to that of physics. This is an epistemic question because it focuses on the relation between theories of chemistry and theories of physics.
  2. The question of the relation of the entities, properties, and so forth that are postulated by chemistry to the entities and so forth that are postulated by physics. This is a metaphysical question because it concerns the nature of chemical entities, properties, and so forth.

Chemistry’s relation to physics is examined with respect to different theories, concepts, entities, properties and phenomena of chemistry and of physics (Hendry 2012; van Brakel 2014). Given this, ‘to speak of “the relation between chemistry and physics” is nonsense: a whole variety of possible intertheoretical relations have to be addressed’ (van Brakel 2014: 34). Both chemistry and physics, understood as scientific disciplines, encompass various sub-disciplines and theories which have, among other things, distinct explanatory and heuristic goals. In light of this, various theories have been examined in the context of chemistry’s relation to physics, including: (a) the relation between thermodynamics and statistical mechanics (Hendry 2012: 369; Needham 2009); (b) the relation of chemistry to quantum mechanics; and, (c) the relation of organic chemistry to quantum chemistry (Goodwin 2013).

Given the above, it is not surprising that the relation between chemistry and physics involves examining the relation between different sets of entities, properties, and so forth that the relevant theories postulate. For example, chemistry’s relation to quantum mechanics has been examined with respect to (a) chemical elements and the periodic table (Scerri 2012b: 75-76); (b) molecular structure (Hendry 2010b; Weininger 194; Woolley 1976); (c) orbitals (Villani et al. 2018); (d) chemical reaction rates (Hettema 2017: 69-86); and (e) the chemical bond (Hendry 2008; Weisberg 2008). Another feature of chemistry’s relation to physics concerns examining how macroscopic substances are related to their constituents (van Brakel 2014: 34). Also, another feature involves examining the relation between the ‘vernacular and scientific use of substance names’ (van Brakel 2014: 34).

While none of the above features of chemistry’s relation to physics are independent from each other, each of them deserves its own article, as each involves addressing issues unique to its specific domain of inquiry. Given this, as well as the fact that reduction and emergence are mostly investigated with respect to chemistry’s relation to quantum mechanics, this article reviews reduction and emergence in the context of how chemistry and its postulated chemical entities relate to quantum mechanics and its postulated entities.

Before presenting the existing views on chemistry’s relation to quantum mechanics, it is useful to briefly specify the subject matter of the two relevant sciences. Chemistry is concerned with the composition and transformation of matter into new substances. It achieves the description, explanation, and prediction of the composition and reaction of matter by reference to entities, properties, and so forth that the theory postulates. In other words, chemistry uses concepts which are characteristic of the chemical description and which allegedly refer to entities, properties, and so forth that determine how matter is composed and reacts. Phenomena that are within the purview of chemistry are the rusting of metals, the properties of atoms and molecules, the boiling of water and the volatility of mercury. Quantum mechanics is the non-relativistic theory that describes microscopic systems (Palgrave Macmillan Ltd 2004: 1863). It is distinct from relativistic quantum mechanics and from quantum field theory. Quantum mechanics achieves the description, explanation, and prediction of microscopic systems by reference to entities and properties that the theory postulates. Phenomena that are within the purview of quantum mechanics are black-body radiation, the double-slit experiment, and the behaviour of a free particle under a magnetic field.

Note that quantum chemistry plays a very important role in understanding the relation between chemistry and quantum mechanics. In the Dictionary of Physics quantum chemistry is defined as the ‘branch of theoretical chemistry in which the methods of quantum mechanics are applied to chemical problems’ (Palgrave Macmillan Ltd 2004: 1845; see also Gavroglu and Simões 2012). In the literature on chemistry’s relation to quantum mechanics, it is not clear whether quantum chemistry is regarded as part of the higher-level theory or the lower-level one (that is, chemistry and quantum mechanics respectively). For example, Goodwin (2013) refers to the relation of quantum chemistry to quantum mechanics, implicitly suggesting that quantum chemistry is the higher-level (chemical) theory. On the other hand, there are philosophers of chemistry who compare the explanatory and predictive success of quantum chemistry with that of chemistry proper, thus implicitly suggesting that quantum chemistry is the lower-level theory.

2. The Significance of This Topic in the Philosophy of Chemistry

According to some members of the philosophy of chemistry community, chemistry is a special science that has not been considered in much detail with respect to its relation with other sciences, including physics (Scerri and Fisher 2015: 3). This is because the philosophy of science and the philosophy of physics take the relation between chemistry and physics to be an unproblematic relation of subordination of the former to the latter (for example van Brakel 2014: 13; Bensaude-Vincent 2008: 16). Epistemically, this broadly means that the descriptions, explanations, and predictions of phenomena that are provided by chemistry can at least in principle be derived from the theories of physics. Metaphysically, this broadly means that the entities, properties, and so forth that are postulated by chemistry are nothing over and above physical entities and properties.

There are two main reasons why physics may be considered ‘ontologically prior’ to chemistry (Hendry 2012: 367). First, if one takes physics to examine those things that make up chemical entities and properties, then this establishes the priority of physics in virtue of the existence of a mereological relation between chemical and physical entities (Hendry 2012: 367). Secondly, physics is considered a universal science in the sense that it sets out, at least in principle, to describe, explain, and predict everything in the world, and not just some subset of phenomena, like chemistry does (Hendry 2012: 367). Dirac’s famous quote is indicative of this stance towards chemistry and of chemistry’s status compared to physics:

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. (1929: 714)

In light of this, some members of the community take the investigation of chemistry’s relation to physics to be a central issue in the philosophy of chemistry, as the answer that one gives with respect to this issue determines whether, and in what sense, chemistry is an autonomous scientific discipline (Chang 2015; Lombardi and Labarca 2005). For example, Chang states that

the relationship between physics and chemistry is one of the perennial foundational issues in the philosophy of chemistry. It concerns the very existence and identity of chemistry as an independent scientific discipline. Chemistry is also the most immediate territory that physics must conquer if its “imperialistic” claim to be the foundation for all sciences is to have any promise. (Chang 2015: 193)

Some members of the philosophy of chemistry community take the investigation of chemistry’s relation to physics to be central not only for establishing the autonomy of chemistry, but also for ensuring the legitimacy of the philosophy of chemistry as a worthwhile and autonomous field of philosophy (in particular see Lombardi and Labarca 2005; Lombardi and Labarca 2007; Scerri and Fisher 2015; Schummer 2014a: 1-2; van Brakel 1999). For example, Scerri and Fisher state that

the philosophy of chemistry had been mostly ignored as a field, in contrast to that of physics and, later, biology. This seems to have been due to a rather conservative, and at times implicitly reductionist, philosophy of physics whose voice seemed to speak for the general philosophy of science. It has taken an enormous effort by dedicated scholars around the globe to get beyond the idea that chemistry merely provides case studies for established metaphysical and epistemological doctrines in the philosophy of physics. These efforts have resulted in both definitive declarations of the philosophy of chemistry to be an autonomous field of inquiry and a number of edited volumes and monographs. (2015: 3)

Lombardi and Labarca state something similar regarding the ‘traditional assumption’ of reduction:

This traditional assumption not only deprives the philosophy of chemistry of legitimacy as a field of philosophical inquiry, but also counts against the autonomy of chemistry as a scientific discipline: whereas physics turns out to be a ‘fundamental’ science that describes reality in its deepest aspects, chemistry is conceived as a mere ‘phenomenological’ science, that only describes phenomena as they appear to us. (2005: 126)

Given the above, it is no surprise that chemistry’s relation to physics has received such attention in the philosophy of chemistry. This does not mean that all philosophers who investigate the relation of chemistry to physics do so with the intention of defending the legitimacy of the philosophy of chemistry or the autonomy of chemistry. In fact, many examine the question of chemistry’s relation to physics because they take it to be relevant to the investigation of other philosophical issues, such as the reality of chemical entities and the relation between biology and physics. For example, Needham believes that views regarding biology’s reduction to physics, as they are discussed in the philosophy of mind and biology, presuppose the successful reduction of chemistry to physics (Needham 1999: 169). Therefore, the question of the relation of chemistry to physics is central not only for chemistry and the philosophy of chemistry in the manner outlined above, but also for the sciences and general philosophy as well.

3. Reduction in Chemistry

Discussion of reduction with respect to chemistry primarily occurs in the context of the distinction between epistemological and ontological reduction. In the philosophy of chemistry, epistemological reduction requires ‘that the laws of chemistry be derivable from those of physics’ (Hendry and Needham 2007: 339). Ontological reduction ‘requires only that chemical properties are determined by “more fundamental” properties’ (Hendry and Needham 2007: 339). By and large, this distinction is accepted in the literature, though there are philosophers that argue that this distinction is not helpful in spelling out correctly the relation between the two theories (Needham 2010: 169; Hettema 2012b: 164). It is worth noting that Hendry and Needham prefer using the term ‘intertheoretic reduction’ instead of ‘epistemological reduction’ as they think that the former term captures best the sort of reduction that is investigated; namely a reduction which ‘involves logical relationships between theories, rather than knowledge’ (Hendry and Needham 2007: 339).

a. Epistemological, or Intertheoretic, Reduction

Discussion of epistemological, or intertheoretic, reduction primarily happens in the context of Nagel’s account of reduction. In the philosophy of chemistry, a Nagelian reduction is understood as requiring at least, in principle, the derivation or deduction of chemistry from quantum mechanics (Needham 2010: 164; Hettema 2017: 7). A Nagelian reduction consists of two ‘formal’ requirements, namely the ‘connectability and derivability’ of the two theories ((Scerri 1994: 160), see also (Hettema 2017: 7)). Moreover, the reduction of chemistry to quantum mechanics would fall under the cases of heterogeneous reductions. This is because ‘some typically chemical terms cannot be found in the quantum mechanical language’, thus requiring the existence of bridge laws (Scerri 1994: 160; see also Primas 1983: 5). A successful reduction would allegedly be sufficiently supported if the chemical properties of atoms and molecules can, at least in principle, be calculated by quantum mechanics ‘entirely from first principles, without recourse to any experimental input whatsoever’ (Scerri 1994: 162). Note that the latter form of quantum mechanics is often referred to as ‘ab initio quantum mechanics’ (Scerri 1994; Schwarz 2007).

In the philosophy of chemistry there has been debate on what the appropriate criteria are for a successful Nagelian reduction of chemistry to physics (see for example Hettema 2012a; 2017; Needham 1999; 2010; Scerri 1994). For example, Hettema claims that the use of the term ‘Nagelian’ with reference to the aforementioned understanding of reduction is to an extent misleading because Nagel was not so strict in his account of reduction:

Reduction is too often conceived of as a straightforward derivation or deduction of the laws and concepts of the theory to be reduced to a reducing theory, notwithstanding Nagel’s insistence that heterogeneous reduction simply does not work that way. (Hettema 2017: 1-2; see also Hettema 2012b: 146; Dizadji-Bahmani, Frigg and Hartmann 2010; Fazekas 2009; Klein 2009; Nagel 1979; van Riel 2011)

While Nagel’s account of reduction is the most widely discussed account in the philosophy of chemistry, there are other accounts from philosophy. They include Oppenheim’s and Putnam’s account of micro-reduction (Oppenheim and Putnam 1958; Hendry 2012: 368-369). Very briefly, according to this account of reduction, a theory T1 micro-reduces a theory T2 if (i) the phenomena that are explained by T2 can be explained by T1; and (ii) T1 describes the parts of the entities, properties, and so forth that are postulated by T2. According to Hendry, if ‘the micro reductive explanation takes the form of a deduction’, then Oppenheim’s and Putnam’s account is a kind of Nagelian reduction (Hendry 2012: 369).

Nagel, Oppenheim and Putnam take chemistry’s relation to physics to be a paradigmatic case of their respective accounts of reduction (Hendry 2012: 369). A large, though not the entire, part of the philosophy of chemistry literature discusses reduction by investigating whether these accounts of reduction correctly apply to chemistry’s relation to quantum mechanics. Popper’s understanding of reduction has also been investigated in the context of chemistry’s relation to quantum mechanics (Scerri 1998; Needham 1999).

The epistemological reduction of chemistry to quantum mechanics is primarily examined by looking at how quantum mechanics, via the Schrödinger equation, describes the chemical properties of atoms and molecules. Given this, it is useful to briefly present how quantum chemistry employs the Schrödinger equation in order to describe the chemical properties of atoms and molecules. This sub-section henceforth focuses on the non-relativistic Schrödinger equation since this is the one that is standardly employed for the description of atoms and molecules and that is discussed with respect to chemistry’s relation to quantum mechanics.

The Schrödinger equation is the ‘equation of motion for the wave function’ which describes ‘the state of a quantum-mechanical system, and (more generally) for the corresponding state-vector’ (Palgrave Macmillan Ltd 2004: 2029). The solutions of the time-dependent Schrödinger equation (Ψ(x,t)) are (potentially) the wavefunctions of the system under examination (that is of an electron, atom, molecule and so forth).

The generic form of the time-dependent Schrödinger equation is the following:

iħ ∂Ψ(x,t)/ ∂t = – (ħ2/2m)(∂2Ψ(x,t)/∂x2) + VΨ(x,t),

where

∂: partial derivative

Ψ(x,t): a system’s wavefunction

ħ: Planck’s constant

m: the system’s mass

x: position

t: time

V: potential energy

i: imaginary unit (square root of negative one)

If one assumes that a system’s potential energy is independent of time, then it is possible to solve the Schrödinger equation using the method of separation of variables (Griffiths 2005: 24). In this context, the resulting solutions are wavefunctions of the following form (Griffiths 2005: 24):

Ψ(x,t) = ψ(x)φ(t),

where

ψ: a function of position

φ: a function of time

Based on the ability to separate the variables of the Schrödinger equation, it is possible to formulate the time-independent Schrödinger equation, which is an equation independent of time and whose solutions are a system’s time-independent wavefunctions, ψ(x). These wavefunctions correspond to the stationary states of the system under examination.

The time-independent Schrödinger equation does not yield a unique solution (that is, one wavefunction) (Griffiths 2005: 27). It yields an infinite number of solutions (ψ(x1), ψ(x2), …), each of which corresponds to a different state of the system under examination. In accordance with the superposition principle, any linear combination of the solutions of the time-independent Schrödinger equation is also regarded as a wavefunction that represents a possible state of the system (Griffiths 2005: 27).

The stationary state of a system, through its wavefunction ψ(x), provides useful information about the total state of the system, Ψ(x,t). First, the probability density Ψ(x,t) equals ∣ψ(x)∣2. This means that knowledge of just the stationary state of a system, through the solution of the time-independent Schrödinger equation, provides the probability of finding the system at a particular region in space. Secondly, it is possible to calculate the expectation value of any dynamical variable of a state of the system through the stationary state of the system alone (Griffiths 2005: 26). Stationary states are states of definite total energy, E (Griffiths 2005: 26). Each solution to the time-independent Schrödinger equation is associated with a particular allowed total energy of the system (E1, E2, …). The wavefunction that is associated with the minimum total energy corresponds to the ground state of the system, whereas the wavefunctions whose total energies are larger correspond to the excited states of the system.

The time-independent Schrödinger equation for an isolated molecule provides an infinite number of solutions (that is, wavefunctions), each of which corresponds to different stationary states of the molecule. For example, a stable isolated molecule, in virtue of being stable, is said to be in the ground state. From this, it follows that it is represented by the wavefunction that is associated with the system’s ground state and that it has the minimum total energy.

The Hamiltonian operator plays a central role in the solution of the time-independent Schrödinger equation for quantum systems and isolated molecules in particular. When the system under examination is an isolated molecule, the Hamiltonian operator corresponds to the total energy of the molecule (that is, its eigenvalues are the total energy of each state of the molecule); hence it is called the molecular Hamiltonian. In principle, the molecular Hamiltonian operator includes all the factors that determine the kinetic and dynamic energy of the molecule. That is, it should take into account the kinetic energy of each nucleus and electron in the system, the repulsion between each pair of electrons and between each pair of nuclei, and the attraction between each pair of electron and nucleus.

Because of the mathematical complexity involved in the formulation of the Hamiltonian operator, atomic and molecular systems are examined within the framework of the Born-Oppenheimer approximation (henceforth BO approximation; also referred to as the adiabatic approximation). The BO approximation is a ‘(r)epresentation of the complete wavefunction as a product of an electronic and a nuclear part Ψ(r,R) = Ψe( r,R) ΨN(R)’ (IUPAC 2014: 179). The validity of the BO approximation is ‘founded on the fact that the ratio of electronic to nuclear mass […] is sufficiently small and the nuclei, as compared to the rapidly moving electrons, appear to be fixed’ (IUPAC 2014: 179).

Within the BO approximation, one can in principle formulate the Hamiltonian operator by positioning the nuclei at all the possible fixed positions. Each set of nucleonic positions corresponds to different quantum states of the system (hence to different wavefunctions) and to different values of the total energy, E, of the atom or molecule. However, in practice this process is not followed. By having prior knowledge of the quantum system that is under examination—for example, by knowing the chemical and structural properties of the examined molecule—only particular nucleonic conformations are considered when constructing the Hamiltonian operator.

The BO approximation is a feature of quantum mechanics which plays a central role in the investigation of chemistry’s relation to quantum mechanics (Bishop 2010: 173; van Brakel 2014: 31-33; Woolley 1976; 1978; 1991; 1998; Woolley and Sutcliffe 1977; Sutcliffe and Woolley 2012). It has often been invoked as putative empirical evidence for the rejection of chemistry’s reduction to quantum mechanics as well as for the support of the emergence of chemistry (see next sections). Solving the equation outside the BO approximation in order to describe atomic and molecular properties is currently investigated in chemistry and quantum chemistry (for example Tapia 2006). This implies that there are features of quantum mechanics which may further contribute to our understanding of chemistry’s relation to quantum mechanics (for example Woolley 1991).

Note that even when the nucleonic conformation is fixed in the manner represented by the BO approximation, calculating the solution of the Schrödinger equation remains a complicated task. Each nucleonic conformation is compatible with different quantum states of the system (and thus different wavefunctions). This is compatible with chemistry’s understanding of atoms and molecules because, even if the nuclei are fixed at particular positions, the electrons may behave in more than one possible way within an atom or molecule.

In light of the above, the Schrödinger equation is not solved analytically for all atoms and molecules. As Hendry states:

There is an exact analytical solution to the non-relativistic Schrödinger equation for the hydrogen atom and other one-electron systems, but these are special cases on account of their simplicity and symmetry properties. (Hendry 2010a: 212)

Instead, researchers have developed various approximate methods in order to solve it, most of which employ the BO approximation. In general, the development of computation has led to the proliferation of complex computational methods that solve the equation by following different mathematical strategies and by making different assumptions. These methods include the Valence Bond Approach, the Molecular Orbital Approach, the Hartree-Fock Method and Configuration Interaction.

Based on the above, there are philosophers who argue in favour of the epistemological reduction of chemistry to quantum mechanics. For example, Schwarz argues that ab initio quantum mechanics can in principle derive all ‘well-defined numerical properties’ of the chemical elements (Schwarz 2007: 168). Ab initio quantum mechanics refers to quantum mechanical methods that are ‘independent of any experiment other than the determination of fundamental constants. The methods are based on the use of the full Schrödinger equation to treat all the electrons of a chemical system’ (IUPAC 2014: 5).

While Schwarz does not examine chemistry’s relation to quantum mechanics in terms of a particular philosophical account of reduction (such as Nagel’s account of reduction), he advocates some sort of reductive relation between chemistry and quantum mechanics. He claims that the ‘difficulty’ of ab initio quantum mechanics to (in practice) derive certain chemical properties is due to the fact that ‘basic qualitative chemical concepts are so vaguely defined’ and ‘fuzzy’ (Schwarz 2007: 172, 174). Given the above, he believes that the periodic system is in a ‘transition phase’ from a primarily ‘empirical model of chemistry’ to ‘an understandable model based in physical theory’ (Schwarz 2007: 173).

The epistemological reduction of chemistry to quantum mechanics is alternatively supported by Bader’s Quantum Theory of Atoms in Molecules (QTAIM) (Bader 1990; Bader and Matta 2013; Matta and Boyd 2007; Matta 2013). The QTAIM provides a topological analysis of electron density through which one derives information regarding atomic and bonding properties. The QTAIM provides experimentally verifiable information regarding the properties of large molecules, by reconstructing their properties from ‘smaller fragments’ (Matta 2013). It is a scientific theory which ‘demonstrates that every measurable property of a system, finite or periodic, can be equated to a sum of contributions from its composite atoms’ (Bader 1990).

Bader takes the QTAIM to provide correct descriptions, explanations and predictions of the chemical properties of matter ((Bader 1990: vi), see also (Bader and Matta 2013), (Causá et al. 2014), (Hettema 2012a) and (Hettema 2013)). While Bader does not explicitly talk about the reduction of chemistry to quantum mechanics in philosophical terms, his account is regarded in the philosophy of chemistry as representing ‘a proper, (reductionist) basis for chemistry’ (Hettema 2013: 311). This is because, according to Bader and Matta, the QTAIM allegedly supports the claim that ‘chemistry is physics’ (Bader and Matta 2013: 254). However, Hettema argues that while Bader’s view of the QTAIM suggests that the QTAIM is related to chemistry in a manner that closely resembles Kemeny and Oppenheims’ reductive eliminativist account, the QTAIM fails to be a reductive theory of this sort (Hettema 2013). Moreover, Arriaga, Fortin and Lombardi argue that while the QTAIM manages to ‘provide a rigorous definition of the chemical bond and of atoms in a molecule, it appeals to concepts that are unacceptable in the quantum-chemical context’, thus failing to sufficiently support the reduction of chemistry to quantum mechanics (Arriaga et al. 2019: 125). Van Brakel makes a similar point, arguing that the QTAIM works only after postulating facts from chemistry (van Brakel 2014: 32), thus rendering it insufficient for the support of chemistry’s reduction to quantum mechanics.

b. Antireductionism with Respect to Chemistry

Many members of the philosophy of chemistry community reject the epistemological reduction of chemistry to quantum mechanics, as understood in terms of the aforementioned accounts. As Hettema states:

The idea that chemistry stands in a reductive relationship to physics still is a somewhat unfashionable doctrine in the philosophy of chemistry. (2017: 1)

Indeed, there are alternative and often incompatible positions in the philosophy of chemistry which argue, either explicitly or implicitly, against the reduction of chemistry to quantum mechanics. These antireductionist views can be divided into two main camps (Scerri 2007b). First are those positions which reject the reduction of chemistry tout court (Schummer 1998; Schummer 2014b; van Brakel 2000). That is, they ‘deny the whole enterprise’ of reducing chemistry to quantum mechanics on grounds that have to do with the unique methodological, classificatory or other epistemological features of chemistry (Scerri 2007b: 70). Philosophers that follow this antireductionist approach support, either implicitly or explicitly, the irreducibility of chemistry by arguing that chemistry, in virtue of being a science of substances which employs unique classificatory tools and concepts, cannot be reduced to a science which looks at the micro-constituents of those substances and which disregards the classificatory or methodological tools and concepts that are of interest to chemists.

In the second camp are those positions which examine in detail how quantum mechanics describes, predicts, and explains particular chemical entities, properties, and so forth (such as the chemical bond, molecular structure, orbitals and the periodic system). They consider how quantum mechanics describes particular chemical properties and through this analysis they implicitly or explicitly argue against the reduction of chemistry to quantum mechanics (Bogaard 1978; González et al. 2019; Hendry 1998; 1999; 2010a; 2012; Ramsey 1997; Scerri 1994; 1998; Woolley 1976; 1978; 1985; 1998; Woolley and Sutcliffe 1977; Weininger 1984; Woody 2000).

For example, Scerri evaluates the manner in which the Schrödinger equation is solved so as to yield accurate results about the properties of atoms and molecules. He claims that ab initio quantum mechanics has yielded relatively accurate results regarding the ground-state energy of particular atoms and has acknowledged the success of quantum mechanics in providing a mathematical analysis of chemical phenomena and in generating sufficiently accurate quantitative values of chemical properties such as bond strength and dipole moments (2007b; 2012). However, he takes that this does not sufficiently support the reduction of chemistry to quantum mechanics (Scerri 1994: 164). Specifically, the approximate methods that are employed for the solution of the Schrödinger equation—and without which a solution cannot be provided—involve the use of ad hoc assumptions which, in virtue of being ad hoc and reliant ‘on experimental data’, undermine the thesis that chemistry is reduced in a Nagelian manner to quantum mechanics (Scerri 1994: 165-168; see also Scerri 1991: 320-321). Note that Hofmann (1990) presents how models and approximations have been employed throughout the history of quantum mechanics for the description of chemical properties; see also Gavroglu and Simões (2012).

Scerri invokes the periodic table and the electronic configuration model as examples that support the failure of chemistry’s reduction to quantum mechanics (Scerri 2007b: 74; Scerri 2012b: 79-80; Scerri 1991).

Before presenting Scerri’s argument, it is useful to briefly define the chemical terms that his and subsequent analyses invoke. The electronic configuration is ‘a distribution of the electrons of an atom or a molecular entity over a set of one-electron wavefunctions called orbitals, according to the Pauli principle’ (IUPAC 2014: 317). An orbital, whether atomic or molecular, is a ‘(w)avefunction depending explicitly on the spatial coordinates of only one electron’ (IUPAC 2014: 1034). An atomic orbital is a ‘(o)ne-electron wavefunction obtained as a solution of the Schrödinger equation for an atom’ (IUPAC 2014: 124). Given that orbitals depend on the spatial coordinates of electrons, the electronic configuration of an atom provides a representation of the distribution of electrons in the atom. This is particularly important in chemistry because it serves as a basis for the explanation and prediction of the type of bonds that are formulated between atoms.

With respect to the periodic table then, Scerri’s claim is broadly the following. The manner in which chemical elements are ordered in the periodic table is partially explained and could be regarded as derived by quantum mechanics because quantum mechanics specifies the electronic configuration of the atoms of each element (Scerri 2012b: 75). However, there are certain features of the periodic table, such as the length of its periods, which are not deducible from quantum mechanics (Scerri 2012b: 77-78). Therefore, the derivation of the periodic table from quantum mechanics, and thus the reduction of chemistry, cannot be sufficiently supported.

Moreover, a Nagelian reduction ‘requires axiomatised versions of the theory to be reduced as well as the reducing theory’, which at least with respect to chemistry cannot possibly be argued for (Scerri 2006: 124). A similar point is made by Hettema regarding Nagelian reduction: ’chemistry is a field, whereas reduction tends to be a relation between individual theories, or between laws and theories’ (Hettema 2017: 1). Furthermore, quantum mechanics does not provide on its own ‘a conceptual understanding of chemical phenomena’ (Scerri 2007b: 74). Instead, chemists employ chemical models and theories in order to formulate sufficient descriptions, explanations, and predictions of chemical phenomena and properties. Another problem for the reduction of chemistry is that quantum mechanics is symmetric under time inversion, and thus cannot provide an explanation of why chemical entities evolve in time the way they do. It can only provide a ‘reductive description’ of chemical properties independent of time (Scerri 2007b: 78). In fact, while quantum mechanics provides numerical values to particular chemical properties, it does not provide a complete explanation of a system’s chemical behaviour (Scerri 2007b: 78).

Scerri also rejects the success of an approximate reduction of chemistry to quantum mechanics (1994; 1998). By approximate reduction, Scerri refers to Putnam’s analysis of reduction, which permits the reducing theory to be approximately and not exactly true (Scerri 1994: 161). That is, ‘the relationships postulated by the theory hold not exactly, but with a certain specifiable degree of error’ (Putnam 1965: 206-207). In this context, reduction is not undermined if ab initio quantum mechanics provides only approximate results of the value of atomic and molecular properties, as long as these results are accompanied by a specifiable degree of error. However, Scerri rejects approximate reduction as the errors ‘are seldom computed by independent ab initio criteria’ (Scerri 1994: 168). Scerri also examines approximate reduction in relation to Popper’s analysis of the reduction of chemistry. In this context, Scerri draws a very similar conclusion with respect to the approximate reduction of chemistry (Scerri 1998: 42).

Based on all the above, Scerri concludes that the reduction of chemistry is ambiguous since, depending on what the set criteria for a successful reduction are, chemistry’s reduction to quantum mechanics ‘is both successful and unsuccessful’ (Scerri 2007b: 76; Scerri 2012b: 80).

Other philosophers also argue that chemistry has failed to epistemically reduce to quantum mechanics by pointing out similar issues with respect to the quantum mechanical description of chemical phenomena (see Bogaard 1978; Hendry 1998; Hendry 2010b: 183; Primas 1983; Woolley 1976; 1998; Woolley and Sutcliffe 1977). For example, Primas argues that quantum mechanics is ‘incorrect and should be revised, partly because [it] seems incapable of rendering a robust account of concepts such as molecular shape’ (Hettema 2017: 53, see also Primas 1983). Bogaard points out that chemists disregard a number of features of the behaviour of subatomic particles when specifying an atom’s or molecule’s Schrödinger equation. These features include (a) the behaviour of subatomic particles (namely protons and neutrons); (b) the energetic contribution of the movement of the nuclei; and, (c) relativistic effects (Bogaard 1978: 346). Moreover, the fact that the Schrödinger equation is ‘adapted’ so as to provide an accurate description of each particular system challenges the view that quantum mechanics can, even in principle, deduce complete explanations of chemical phenomena (Bogaard 1978).

González et al. (2019) argue that there is a tension between the theoretical postulates of quantum mechanics and how molecular structure is understood in chemistry. In particular, Heisenberg’s uncertainty principle implies that a ‘quantum “particle” is not an individual in the traditional sense, since it has properties—those represented by its observables—that have no definite value’ (González et al. 2019: 36). Such a metaphysical understanding of quantum particles comes in contrast to chemistry’s understanding of molecular structure, which is defined ‘in terms of the spatial relation of the nuclei conceived as individual localised objects’ (González et al. 2019: 43). The failure of chemistry’s reduction is further supported by the fact that the Schrödinger equation cannot be solved analytically without the use of approximations and models (for example Bogaard 1978: 347; González et al. 2019; Hendry 2010b). These approximations and models are based on ‘theoretical assumptions drawn from chemistry’, thus rendering the quantum chemical description of complex atoms and molecules in a ‘loose relationship to exact atomic and molecular Schrödinger equations’ (Hendry 2010b: 183).

Lastly, Chang argues that since its advent, quantum chemistry was practiced in a manner that required the use of pre-quantum, chemical knowledge (Chang 2015; 2017). The views of Linus Pauling, one of the main founders of quantum chemistry, allegedly corroborate this argument, as Pauling took quantum chemistry to be ‘a direct continuation of nineteenth-century organic structural chemistry’ (Chang 2015: 197-198). Chang also claims that physics consists of many different branches and that the relation of those branches with more fundamental physical theories has not been decisively shown to be reductionist. In light of this, and given that chemistry’s relation to physics is examined in the context of a physical theory (that is, quantum mechanics) which is not the most fundamental theory in physics, one should not assume chemistry to be unproblematically reduced to physics (Chang 2015: 200; Chang 2017: 365). Thirdly, Chang looks at how chemistry is done in practice and claims from this that chemistry is very far from being ‘submitted’ to physics (Chang 2015: 201). This claim allegedly undermines the reduction of chemistry to quantum mechanics since quantum mechanics has never in practice been sufficient for the description, explanation or prediction of phenomena that are within the purview of chemistry (Chang 2015: 201-202).

c. Ontological Reduction

In light of the above objections against the epistemological reduction of chemistry, there are philosophers who have investigated whether it is possible to support chemistry’s ontological reduction to quantum mechanics in a manner that is consistent with the failure of chemistry’s epistemological reduction. Most notable is Le Poidevin, who formulated a detailed account for the ontological reduction of chemical properties which does not depend on the success of an epistemic reduction of chemistry to quantum mechanics. In fact, Le Poidevin accepts that chemistry has not been epistemically reduced to quantum mechanics and argues that, despite this, it can be argued that chemical elements are ontologically reduced to physical properties. He claims that the argument for the ontological reduction of chemical elements can be generalised to all chemical properties in the following manner:

Chemical properties reduce to those properties variation in which is discrete, and combinations of which constitute the series of physically possible chemical properties. (Le Poidevin 2005: 132)

In particular, he takes that the discreteness of chemical elements as specified via the periodic table supports a combinatorial argument for their ontological reduction. According to this argument, ‘a finite number of fundamental entities combine together to give a discrete set of composite elements’ (Scerri 2007a: 929).

Le Poidevin’s argument is based on two premises. The first is the ‘combinatorial criterion for ontological reduction’, which states that

a property type F is ontologically reducible to a more fundamental property type G if the possibility of something’s being F is constituted by a recombination of actual instances of G, but the possibility of something’s being G is not contributed by a recombination of actual instances of F. (Le Poidevin 2005: 132)

The second premise concerns the ‘discreteness of chemical ordering’: ‘between any two elements there is a finite number of physically possible intermediate elements’ (Le Poidevin 2005: 132).

According to Le Poidevin, the combinatorial criterion for the ontological reduction of chemical properties is preferable to existing physicalist accounts regarding the ontological reduction of special science properties because it overcomes two insurmountable problems of physicalism. The first problem is the ‘vacuity problem’, according to which physicalism is in danger of becoming a trivial thesis depending on what one takes to be included in the domain of physics (Le Poidevin 2005: 121-122). The second problem is the ‘asymmetry problem’, according to which the supervenience relation, as postulated by physicalism, does not necessitate an asymmetric relation between higher and lower-level properties (Le Poidevin 2005: 122).

Scerri, Hendry and Needham are sympathetic towards Le Poidevin’s argument of the ontological reduction of chemical elements (Scerri 2007b: 76; Hendry and Needham 2007: 340). As Hendry and Needham state, the combinatorial argument establishes that ‘the discreteness of the elements is explained by the nomologically required discrete variation in a physical quantity, namely nuclear charge’ (Hendry and Nedham 2007: 34). However, all of them take that there are certain problematic features in Le Poidevin’s account.

First, the argument is allegedly not well-supported for all chemical properties. Scerri doubts that the combinatorial argument can be generalised so as to apply to all chemical properties because, unlike chemical elements, most chemical properties are not discreet (such as the solubility and acidity of elements) (Scerri 2007a: 929). Similarly, Hendry and Needham argue that the combinatorial argument is only investigated with respect to chemical elements, thus disregarding a large part of chemistry. This is a central shortcoming of Le Poidevin’s account because there are particular features of chemistry and of quantum mechanics which are often regarded as posing unique challenges to chemistry’s reduction to quantum mechanics. For example, the structure of molecules is a chemical property which some argue is not in principle derivable by quantum mechanics (Hendry and Needham 2007: 341-342). This is regarded problematic for the reduction of chemistry to quantum mechanics, whether epistemic or ontological. Another issue is how chemistry describes the rate of chemical reactions. Kinetic theory and thermodynamics play a fundamental role in explaining and describing the rate of chemical reactions, and thus need to be considered in the context of chemistry’s relation to quantum mechanics (Hendry and Needham 2007: 343-344). These are problems that concern particular chemical properties and which need to be tackled if any account of (ontological) reduction is to be well-supported for all chemical properties.

Secondly, Scerri takes that Le Poidevin’s attempt to circumvent any talk about the epistemic reduction between the two relevant theories is illusory. The latter takes that a ‘periodic ordering is a classification rather than a theory’, thus rendering his account of ontological reduction ‘theory-neutral’ (Le Poidevin 2005: 131). However, Scerri disagrees on this point as he takes reference to the periodic table to inevitably require the investigation of how chemistry and quantum mechanics are epistemically related (Scerri 2007a: 929). Hendry and Needham take this point a step further by suggesting that reference to a theory cannot be avoided when specifying the micro-constituents of chemical elements (Hendry and Needham 2007: 344). In fact, they argue that there is ‘a close evidential connection’ between epistemological and ontological reduction; one cannot entirely avoid the investigation of inter-theoretic reduction when seeking to provide sufficient empirical support to ontological reduction (Hendry and Needham 2007: 351).

Another objection to Le Poidevin’s account is that the combinatorial argument, even if correct, does not succeed in establishing the ontological reduction of chemistry to physics. The asymmetric relation that Le Poidevin allegedly establishes via his combinatorial argument establishes ‘only an asymmetrical relationship between the (actual) physical and the (merely possible) chemical’ (Hendry and Needham 2007: 349). Given this, such a relation does not preclude the possibility of chemical properties having novel causal powers, thus rendering Le Poidevin’s account consistent with non-reductive (metaphysical) accounts (such as emergentist accounts) (Hendry and Needham 2007: 350).

Hendry also offers independent support to the claim that chemistry fails to ontologically reduce to quantum mechanics, outside his critique of Le Poidevin’s account. Specifically, he assumes that ontological reduction involves the acceptance of the causal completeness of physics (Hendry 2010b: 187). Given this, it follows that ontological reduction is committed to the claim that only physical entities, properties, and so forth possess novel causal powers (Hendry 2010b: 187). Based on this understanding of ontological reduction, he argues that what he calls the ‘symmetry problem’ undermines the tenability of ontological reduction. The symmetry problem arises from the fact that, for any atom or molecule, the arbitrary solutions of the Schrödinger equation are spherically symmetrical (Hendry 2010b: 186). This comes in contrast to the asymmetry exhibited by polyatomic molecules and which chemistry invokes in order to explain many of their chemical properties, such as the acidic behaviour and boiling point of the hydrogen chloride molecule (Hendry 2010b: 186). The symmetry problem allegedly challenges the ontological reduction of chemistry because it undermines the tenability of the causal completeness of physics, namely the principle that every physical effect has a physical cause (Hendry 2010b: 187). This is because

  • quantum mechanics is consistent with the view that the asymmetry of molecules ‘is not conferred by the molecule’s physical basis according to physical laws’ (Hendry 2010b: 187); and
  • the symmetry problem ‘removes much of the empirical support that is claimed for’ the causal completeness of physics (Hendry 2010b: 187).

Lastly, it should be noted that there are positions which argue for the ontological autonomy of chemistry in a manner that is implicitly or explicitly incompatible with the ontological reduction of chemistry to quantum mechanics. This includes Lombardi and Labarca (2005) and Schummer (2014b) (see subsection 5b).

d. Alternative Forms of Reduction

Despite the arguments against chemistry’s epistemological and ontological reduction to quantum mechanics, there are philosophers who attempt to establish reduction. For example, Hettema states that ‘the widespread rejection of reduction by philosophers of chemistry might have been premature’ (Hettema 2012b: 147). Hettema argues that, contrary to how Nagel’s account of reduction has been understood and argued against in the philosophy of chemistry, Nagel was in fact not so strict about the requirements for reduction (Hettema 2014: 193; see also Hettema 2012a). In light of this, Hettema proposes ‘a suitable paraphrase of the Nagelian reduction programme’ which is ‘reinforced by a modern notion of both connectibility and derivability’ (Hettema 2017: 24) (italics are in the original text). Hettema’s position is a reductive account which advocates the existence of autonomous areas. Characterising Hettema’s account as a form of reduction is justified given the quotes just mentioned. Nevertheless, it should be noted that Hettema often refers to his proposal as one that advocates a form of unity (for example Hettema 2012b; 2017). In order to explicate his proposal, Hettema analyses the development of the reaction rate theory and presents, among other things, Eyring’s theory of absolute reaction rates (2017: 71-81; see also Hettema 2012b) (see also subsection 5a).

Needham has also investigated reduction and identified those aspects of Nagelian reduction which should be amended for a more convincing defence of chemistry’s reduction to physics to be achieved. As Needham states:

Chemistry is, perhaps, so entwined with physics that what would be left after removal of physics is but a pale shadow of modern chemistry. It is, perhaps, not even clear what the removal of physics from chemistry would amount to. (Needham 2010: 163)

Needham identifies the weaknesses of Nagelian reduction and examines whether historical developments in chemistry and physics are consonant with how reduction tells us that two theories are related (2010: 170). Based on such an analysis, he argues that it is possible to understand Nagelian reduction in a way that permits and takes into account the use of approximations in science (Needham 2010: 168-169).

4. Emergence in Chemistry

The emergence of chemistry was first discussed and defended by British Emergentists. British Emergentism defended the emergence of chemistry before the advent of quantum mechanics. With the development of quantum mechanics and quantum chemistry, the emergence of chemistry, as it was advocated by British emergentists, was mostly rejected in philosophy. However, in the contemporary literature the emergence of chemistry from quantum mechanics has been reformulated and supported on new grounds. Perhaps the most detailed and widely discussed account of emergence with respect to chemistry is Robin Hendry’s account of the strong emergence of molecular structure. However, there are also alternative understandings of emergence within the philosophy of chemistry.

a. British Emergentism in Chemistry

 British Emergentism refers to a group of philosophers in the 19th and 20th centuries which is regarded as the first to provide a detailed and coherent philosophical account of emergence. Among the examples that British Emergentists invoked in order to support the existence of emergence is that of chemistry and in particular of chemical bonding. In particular, J. S. Mill argued that ‘the different actions of a chemical compound will never, undoubtedly, be found to be the sums of the actions of its separate elements’ (quote in McLaughlin 1992: 28; see also Mill 1930). C. D. Broad also advocated the emergence of chemistry on the grounds that it is not ‘theoretically possible to deduce the characteristic behaviour of any element from an adequate knowledge of the number and arrangement of the particles in its atom, without needing to observe a sample of that substance’ (Broad 1925: 70; see also McLaughlin 1992: 47; Hendry 2006: 176-180; Hendry 2010a: 210; Hendry 2010b: 185).

The putative empirical evidence that emergentists invoked for the support of the emergence of chemical bonding is the failure to deduce the chemical behaviour of elements from the entities and properties that constitute those chemical elements. Since one does not describe and predict how chemical elements are bonded to each other only with reference to the entities that compose them, then this suffices to support that chemical bonding is an emergent chemical property which exerts downward causal powers to the entities that constitute the relevant chemical elements (Scerri 2007a: 921).

The British Emergentists’ argument for the emergence of chemical bonding was formulated before the advent of quantum mechanics. According to McLaughlin, once quantum mechanics contributed to the understanding of atomic and molecular properties, including the chemical bond, the emergence of chemical bonding was no longer justified in the manner that British Emergentism advocated:

Quantum mechanical explanations of chemical bonding suffice to refute central aspects of Broad’s Chemical Emergentism: Chemical bonding can be explained by properties of electrons, and there are no fundamental chemical forces. (Mclaughlin 1992: 49; see also Scerri 2007a)

On the other hand, Scerri argues that McLaughlin is mistaken to reject the emergence of chemistry and rejects McLaughlin’s claims that

  • there was no complete or adequate theory of chemical bonding before the advent of quantum mechanics; and
  • quantum mechanics provided a complete theory of chemical bonding (Scerri 2007a: 922-923; see also Scerri 2012a).

In fact, Scerri claims that the quantum mechanical theory of chemical bonding should be viewed as continuous and as enhancing Lewis’s theory of chemical bonding (Scerri 2007a: 922-923). The advent of quantum mechanics does not refute pre-quantum, chemical theories of bonding, but rather offers a deeper understanding of chemical bonding. Chemistry remains vital in the description and explanation of the chemical behaviour of elements because quantum mechanics cannot offer by itself a complete account of chemical bonding and of the overall chemical behaviour of elements. While quantum mechanics provides quantitative information regarding particular chemical properties of elements and compounds, it ‘cannot predict what compounds will actually form’ (Scerri 2007a: 924). Quantum mechanics can neither provide an explanation of how atoms and molecules evolve in time, nor can it provide a complete explanation of their overall chemical behaviour (Scerri 2007b: 78). These two characteristics of quantum mechanics, apart from blocking the possibility of a ‘complete’ reduction of chemistry, also allegedly support the claim that chemical entities and properties emerge at a level ‘over and above what one would expect from the constituents of the system’ (Scerri 2007b: 77; see also Llored 2012: 254). What Scerri means by emergence is, however, unclear since he only specifies this notion contrary to physicalism and does not provide a detailed account of the emergence of chemistry.

b. Strong Emergence

Hendry formulates one of the most detailed and widely discussed accounts of emergence regarding chemistry. Hendry’s account focuses on a metaphysical understanding of emergence that has direct implications on the metaphysical relation between chemical and quantum mechanical entities and properties, as well as on the nature of molecular structure. His account of strong emergence is formulated in terms of downward causation, and the putative empirical evidence that supports his position is drawn from the manner in which quantum mechanics and chemistry each describe molecular structure.

According to Hendry, the structure of a molecule strongly emerges from its quantum mechanical entities in the sense that it exhibits downward causal powers. Specifically, ‘the emergent behaviour of complex systems must be viewed as determining, but not being fully determined by, the behaviour of their constituent parts’ (Hendry 2006: 180).

Strong emergence is supported by the ‘counternomic criterion for downward causation’ (Hendry 2010b: 189). According to this criterion, ‘a system exhibits downward causation if its behavior would be different were it determined by the more basic laws governing the stuff of which it is made’ (Hendry 2010b: 189). The manner in which quantum mechanics describes a molecule’s structure allegedly satisfies the counternomic criterion and thus supports the view that molecular structure strongly emerges.

In order to support this claim, Hendry makes a distinction between ‘resultant’ and ‘configurational’ Hamiltonians. A molecule’s resultant Hamiltonian takes into account all the intra-molecular interactions and is constructed using as input only fundamental physical interactions and the value of the physical properties of the entities (such as masses, charges, and so forth) (Hendry 2010a: 210-211). Given the resultant Hamiltonian, the so-called ‘Coulombic Schrödinger equation’ is constructed, which is a complete and exact description of the relevant molecule. However, the resultant Hamiltonian is in practice never used for the solution of the Schrödinger equation. This is primarily due to the equation’s mathematical complexity. Nevertheless, if the Coulombic Schrödinger equation were to be solved, it would not distinguish between different molecular structures (specifically that of isomers), and it would not explain the symmetry properties of a molecule. Instead, quantum explanations of molecular structure are based on the construction of ‘configurational Hamiltonians’ for the solution of the Schrödinger equation of a molecule (Hendry 2010a: 210-211). Configurational Hamiltonians are constructed on the basis of ad hoc assumptions which impose on the Schrödinger equation the molecular structure that is supposed to be derived from that equation. This situation satisfies the counternomic criterion because we did not recover a molecule’s ‘structure from the “resultant” Hamiltonian, given the charges and masses of the various electrons and nuclei; rather we viewed the motions of those electrons and nuclei as constrained by the molecule of which they are part’ (Hendry 2006: 183).

Hendry presents two examples that illustrate that the counternomic criterion is satisfied with respect to molecular structure. The first example concerns isomers (see also Bishop 2010: 172-173). Isomers are sets of molecules that contain the same number and kind of atoms, but whose atoms are arranged differently. This means that isomers differ only in terms of their structure. Isomers have distinct chemical descriptions and they are invoked for the explanation of a variety of physical and chemical phenomena. If one is to describe an isomer via the use of its resultant Hamiltonian, then the Coulombic Schrödinger equation is identical with the Coulombic Schrödinger equations that describe the other relevant isomers (Hendry 2017: 153). On the other hand, if one is to describe an isomer via the use of its configurational Hamiltonian, then the Schrödinger equation that is subsequently constructed, is not identical to those that describe the other relevant isomers. According to Hendry, this means that this example satisfies the counternomic criterion. He thinks it illustrates that the molecule’s behaviour, as this is described ‘by the more basic laws governing the stuff of which it is made’ (that is, via the resultant Hamiltonian) is different from its behaviour, as this is described by assuming certain chemical properties (namely, its structure) via the configurational Hamiltonian.

The second example that Hendry takes as empirical support for downward causation involves the symmetry properties of molecules. Similarly to the case of isomers, one cannot derive the different chemical symmetry properties from the relevant resultant Hamiltonian because ‘the only force appearing in molecular Schrödinger equations is the electrostatic or Coulomb force: other forces are negligible at the relevant scales. But the Coulomb force has spherical symmetry’ (Hendry 2017: 154).

As is the case with other accounts of strong emergence in philosophy of science, Hendry’s account of strong emergence overcomes the overdetermination problem by postulating that there are certain quantum mechanical effects which do not have purely quantum mechanical causes (Wilson 2015: 353). That is, accounts of strong emergence deny the causal completeness of the physical (CCP), which states that ‘every lower-level physically acceptable effect has a purely lower-level physically acceptable cause’ (Wilson 2015: 352). Instead of the CCP, Hendry proposes an alternative principle; namely the ‘ubiquity of physics’ (UP):

Under the ubiquity of physics, physical principles constrain the motions of particular systems though they may not fully determine them. (Hendry 2010b: 188)

This principle acts as a substitute for the causal completeness of the physical (CCP) which Hendry rejects and which is incompatible with his notion of strong emergence. UP allows for the physical principles (as these are formulated via the physical laws and theories) to ‘apply universally without accepting that they fully determine the motions of the systems they govern’ (Hendry 2010b: 188). According to Hendry, unlike UP, the CCP is not well supported by physics itself, and he follows Bishop in thinking it ‘does not imply its own causal closure’ (Bishop 2006: 45). Note that, given the rejection of the CCP, strong emergence, as understood by Hendry, is incompatible with not only some form of epistemic reduction but also with reductive and non-reductive physicalism.

A critique of Hendry’s account in the philosophy of chemistry literature is provided by Scerri, who argues that the putative empirical evidence invoked by the former for the support of strong emergence is merely a ‘theoretical rather than ontological issue’ (Scerri 2012a: 25).

c. Alternative Forms of Emergence

There are alternative accounts of emergence with respect to chemistry. These are mostly accounts which focus on the unique epistemological features of chemistry and propose an understanding of emergence that is primarily epistemic, rather than metaphysical. For example, Bishop and Atmanspacher (2006) formulate an account of ‘contextual emergence’ which they take to successfully apply in two separate cases: namely to the case of molecular structure and to that of temperature (see also Bishop 2010). With respect to molecular structure, they argue that quantum mechanics provides necessary but not sufficient conditions for the description of molecular structure. This implies that reduction is not the appropriate account to correctly specify the relation between the two relevant descriptions. In order to derive a lower-level (that is, quantum mechanical) description of molecular structure, one introduces sufficient conditions by specifying the particular context in which the relevant lower-level system is considered. This allegedly supports the claim that molecular structure is a novel property which is not derivable by the quantum mechanical description alone but rather emerges from it (Bishop and Atmanspacher 2006: 1774; see also Bishop 2010: 176-177; Llored 2012: 248).

Furthermore, Llored presents ‘a relational form of emergence which pays attention to the constitutive role of the modes of intervention and to the co-definition of the levels of organization’ (Llored 2012: 245). This is not a metaphysical account of emergence; as Llored states, his proposed account is ‘agnostic’ with respect to the ontology of chemistry and rather focuses on ‘what chemists do in their daily work’ (Llored 2012: 245). In particular, Llored looks at how ‘from the Twenties to nowadays, quantum chemical methods have been constitutively concerned with the links between the molecule and its parts’ (2012: 257) (italics are in the original text). Among other things, he presents and analyses the debate between Linus Pauling and Robert Mulliken who both ‘focused on the description and the understanding of the molecule, its reactivity, and thus its transformations’ (Llored 2012: 257). Llored argues that his proposed account of emergence is not one which advocates an asymmetric relation between higher and lower-level properties. Rather, both chemical and quantum mechanical properties ‘co-emerge’ (Llored 2014: 156). Chemical phenomena are understood ‘as relative to a certain experimental context, with no possibility of separating them from this context’ (Llored 2014: 156; see also Llored and Harré 2014).

5. Beyond Reduction and Emergence

Very few accounts consider the relation of chemistry to quantum mechanics without invoking some form of reduction or emergence. In fact, if we are to understand epistemic reduction and strong emergence as the two extremes of a spectrum of inter-theoretic accounts, then there is a variety of positions that have remained to this day relatively unexplored with respect to chemistry. Nevertheless, there are some philosophers who consider the possibility of understanding chemistry’s relation to quantum mechanics without reference to reduction or emergence. This section distinguishes between two main camps. First are those accounts which consider unity without reduction. Secondly, there are accounts which support the autonomy of chemistry without reference to some form of emergence.

a. Unity without Reduction

Two philosophers of chemistry have primarily examined chemistry’s relation to quantum mechanics in terms of unity without reduction. First, Needham examines unity without reduction by presenting Pierre Duhem’s ‘scheme’ of ‘unity without reduction’ (Needham 2010: 166). He states that

unity surely does not require reduction, intuitively understood as the incorporation of one theory within another. […] Consistency, requiring the absence of contradiction, and more generally in the sense of the absence of conflicts, tensions and barriers within scientific theory, would provide weaker, though apparently adequate, grounds for unity. (Needham 2010: 163)

According to Duhem’s scheme of unity, ‘(m)icroscopic principles complement macroscopic theory in an integrated whole, with no presumption of primacy of the one over the other’ (Needham 2010: 167). This implies that Duhem’s understanding of unity is incompatible with reductionism in the sense that it rejects that physics is the most fundamental science.

Moreover, Needham argues that positions on unity can be distinguished into four groups:

(i) Unity in virtue of reduction, with no autonomous areas,

(ii) unity in virtue of consistency and not reduction, but still no autonomy because of interconnections,

(iii) unity in virtue of consistency and not reduction, with no autonomous areas, and

(iv) disunity. (Needham 2010: 163-164)

Hettema engages in the discussion of unity with respect to chemistry and evaluates Needham’s scheme of unity (2017). In particular, Hettema takes that the first form of unity assumes a form of ‘reductionism in which derivation is strict and reduction postulates are identities’ (Hettema 2017: 277). Regarding the second form of unity, Hettema argues that it faces certain challenges. For example, in this form of unity ‘the nature of the “interconnections” is (..) not well specified in Needham’s scheme’ (Hettema 2017: 277). Moreover, ‘the theories of chemistry and physics are not as strongly dependent on each other as implied (though not stated) in position (ii) in the scheme’ (Hettema 2017: 277-278). Hettema rejects the third form of unity because it allegedly disregards the ‘idea that one science may fruitfully explain aspects of another’ (Hettema 2017: 278).

As already mentioned, Hettema proposes a novel account of reduction regarding the relation between chemistry and quantum mechanics (see subsection 3d). In the broader context of unity, Hettema takes his account to propose a form of unity that Needham’s scheme does not capture. Specifically, Hettema’s account does not support ‘a form of unity in virtue of reduction with no autonomous areas’ (in line with (i)) because, unlike (i), it does not require strict derivation nor the existence of identity relations between the reduced and reducing theory. Moreover, Hettema’s account does not advocate unity without reduction either. While he acknowledges that his account shares common features with non-reductive accounts of unity in the philosophy of science literature, he maintains that his account proposes a ‘naturalised Nagelian reduction’ (Hettema 2012b: 143).

Interestingly, there are two features that his account allegedly shares with certain non-reductive accounts of unity. First, Hettema takes his account of reduction to be compatible with an understanding of theories as ‘interfield theories’ which ‘use concepts and data from neighbouring fields’ (in line with Darden and Maull 1977) (Hettema 2012b: 160). In this context, absolute reaction rate theory is characterised as an interfield theory ‘where the theories comprising the interfield are in turn reductively connected’ (Hettema 2012b:168). There is no one-to-one relation between the reduced and reducing theory; rather there is a ‘net of theories’ where ‘connective and derivative links of a Nagelian sort exist between all these theoretical approaches’ (Hettema 2012b:168). As a result, the overall reduction of chemistry is specified in terms of a network of different theories that are reductively connected between them (Hettema 2012b:171). Secondly, Hettema takes his account to be compatible with Bokulich’s non-reductive account of ‘interstructuralism’, according to which two theories are related in virtue of the ‘structural continuities and correspondences’ between them (Bokulich 2008: 173; Hettema 2012b: 163). Indeed, Hettema identifies structural continuities in the case of the absolute reaction rate theory (Hettema 2012b: 171).

Lastly, Seifert (2017) advocates unity without reduction, arguing that chemistry and quantum mechanics are unified in a non-reductive manner because they exhibit particular epistemic and metaphysical inter-connections.

b. Pluralism

The autonomy of chemistry from quantum mechanics has been defended without reference to emergence in the form of pluralist accounts. Accounts of pluralism that have not been explicitly investigated with respect to chemistry’s relation to quantum mechanics are not presented here, such as Chang’s (2012). For example, Lombardi and Labarca argue for a ‘Kantian-rooted ontological pluralism’ which is based on Putnam’s account of internalist realism (Lombardi 2014b: 23; see also Lombardi and Labarca 2005; Putnam 1981). They claim that while the epistemological reduction of chemistry is in general rejected in the philosophy of chemistry, the ontological reduction of chemistry is more or less accepted (Lombardi and Labarca 2005: 132-133). They take the acceptance of chemistry’s ontological reduction to imply an antirealist or eliminativist view of chemical ontology and to undermine philosophy of chemistry’s relevance when it comes to investigating metaphysical issues (Lombardi and Labarca 2005: 134). In this context, they argue that a hierarchical view of ontology, where everything is grounded on more fundamental physical entities, should be substituted by a view of the world where ‘different but equally objective theory-dependent ontologies interconnected by nomological, non-reductive relationships’, coexist (Lombardi and Labarca 2005: 146; Lombardi 2014b).

There are various objections against this account of ontological pluralism (Needham 2006; Manafu 2013; Hettema 2014: 195-196; see also Lombardi and Labarca 2006). For example, Manafu argues that Lombardi and Labarca have insufficiently argued for the ‘equal’ reference of concepts that are postulated by different theories. This is because if a theory is reduced to, superseded by, or merely has different theoretical virtues from another theory, then it is not necessary that such a theory employs concepts that actually refer to things that exist (Manafu 2013: 227).

Schummer also argues in favour of a pluralist position. He claims that chemistry’s relation to physics should be understood in accordance to methodological pluralism (2014b). Chemistry and each of its sub-disciplines have distinct subject matters, pose different research questions and employ distinct methods and concepts. Even when it comes to concepts that are employed by both chemistry and physics, such as ‘molecule’ and ‘molecular structure’, Schummer argues that these concepts frequently have different meanings in each of the two disciplines and are employed in the context of radically distinct models, methods and research goals (Schummer 2014b: 260).

6. Conclusion

Given how chemistry’s relation to quantum mechanics has been investigated in the philosophy of chemistry so far, it is possible to draw the following conclusions. First, in the first decades of the 21st century, the philosophy of chemistry persistently argued that chemistry’s relation to quantum mechanics is not a reductive relation, as philosophers and physicists such as Nagel and Dirac commonly supposed. Another point drawn from this analysis is that one cannot correctly spell out the relation between the two sciences unless one takes into account the role of approximations, assumptions, models and idealisations in the two sciences.

Moreover, it is evident that more can be said about chemistry’s relation to quantum mechanics. There is substantial material from the philosophy of science which has not been considered with respect to chemistry and which could contribute to a richer and more accurate understanding of the relation between the two sciences. For example, given the alleged failure of Nagelian reduction, it would be interesting to examine whether a different understanding of epistemic reduction applies to the case of chemistry. Alternative accounts of epistemic reduction that take into account the unique models, idealisations, and practices that the special sciences employ would contribute to formulating a novel understanding of the relation of chemistry with quantum mechanics. Also, it is worth investigating whether chemistry and quantum mechanics are unified in a way that neither requires some form of epistemic or ontological reduction, nor collapses to a strongly emergent or pluralist worldview. Lastly, there are various understandings of pluralism which have not been applied to the case of chemistry and which could further support general accounts of pluralism in the sciences. All in all, more can be said about chemistry’s relation to quantum mechanics which can fruitfully contribute to one’s analysis of reduction, unity, pluralism and emergence.

7. References and Further Reading

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Author Information

Vanessa A. Seifert
Email: vs14902@bristol.ac.uk
University of Bristol
United Kingdom

The Axiology of Theism

The existential question about God asks whether God exists, but the axiology of theism addresses the question of what value-impact, if any, God’s existence does (or would) have on our world and its inhabitants. There are two prominent answers to the axiological question about God. Pro-theism is the view that God’s existence does (or would) add value to our world. Anti-theism, by contrast, is the view that God’s existence does (or would) detract from the value of our world. Philosophers have observed that the answer to the axiological question may vary depending on its target and scope. For instance, assessments about God’s value-impact could made from an impersonal perspective without reference to individuals, or from a personal perspective with reference to the value-impact of God only for a particular person or persons. Axiological assessments can also take into account one, some, or all of the purported advantages and downsides of God’s existence.

No general consensus has emerged in the literature regarding the correct answer(s) to the axiological question about God. Some philosophers argue that the answer to the question is obvious, or that the very question itself is unintelligible. For instance, it might be unintelligible to the many theists who hold that if God does not exist then nothing else would exist. So, it is impossible to compare a world with God to a world without God. The most promising argument in support of anti-theism in the literature is the Meaningful Life Argument, which suggests that God’s existence would make certain individuals’ lives worse, for those individuals have life plans so intimately connected with God’s non-existence that, if it turned out God exists, their lives would lose meaning if God were to exist. The most promising argument for pro-theism is best understood as a cluster of arguments pointing to many of the purported advantages of God’s existence including divine intervention (that is, God performing miracles that help people) and the impossibility of gratuitous evil on theism. Additionally, some pro-theists claim that since God is infinitely good that any state of affairs with God is also infinitely good. To date, the literature has focused on comparing the axiological value of theism (especially Christianity) to atheism (especially naturalism). Future work will likely include axiological assessments of the other religious and non-religious worldviews.

Table of Contents

  1. The Axiological Question about God
  2. Is the Axiological Question Intelligible?
  3. Different answers to the Axiological Question
  4. Arguments for Pro-Theism
    1. The Infinite Value Argument
    2. The Morally Good Agents Argument
    3. The Goods of Theism Argument
  5. Arguments for Anti-Theism
    1. The Meaningful Life Argument
    2. The Goods of Atheism Argument
  6. Connections to the Existence of God
    1. Divine Hiddenness
    2. Problem of Evil
    3. Anti-Theism entails Atheism
  7. Future Directions
    1. Exploration of Different Answers
    2. Other Worldviews
  8. References and Further Reading

1. The Axiological Question about God

A perennial topic in the philosophy of religion is the existential question of whether God exists. Arguments in support of theism include the ontological, cosmological, teleological, and moral arguments. Arguments in support of atheism, on the other hand, include the arguments from evil, from no best world, and from divine hiddenness. Many of these arguments and topics have a rich philosophical history and sophisticated versions of them continue to be discussed in the literature. The importance of the existential question is obvious: God’s existence is tied to the truth value of the theistic religions. It is of little surprise, then, that philosophers of religion have spilled so much ink over these topics.

This article does not discuss the existential question of whether God exists. Rather, it will examine the question of the axiological question about the value-impact of God’s existence. Some brief remarks by Thomas Nagel are often credited as the starting point in the literature (Kahane 2011, 679; Kraay and Dragos 2013, 159; Penner 2015, 327). In his book The Last Word, Thomas Nagel quips: “I hope there is no God! I don’t want there to be a God; I don’t want the universe to be like that” (1997, 130). Nagel is an atheist who thinks he is rational in his atheism. He thinks that in light of the evidence, atheism is the correct answer to the existential question about God. Yet here he expresses a desire or preference about the non-existence of God. Reflections on this brief quote from Nagel have led to the emergence of discussion about the axiological question in the philosophy of religion. While it is clear Nagel is expressing a preference, philosophers initially wanted to know whether it could be developed into an axiological position.

One interesting aspect of this question is that it seems to be conceptually distinct from the existential question about God. For instance, it seems perfectly consistent for an atheist who denies that God exists to simultaneously believe that God’s existence would be good, though some have denied this claim (for example, Schellenberg 2018).  It also seems consistent for a theist who is convinced that God exists to hold that there are negative consequences of God’s existence. Finally, it’s worth pointing out that the axiological question has come to be understood as a comparative question about the difference in value between different possible worlds or states of affairs (that is, between God worlds and God-less worlds).

2. Is the Axiological Question Intelligible?

In explaining what the axiological question is asking, Guy Kahane writes in an early and influential piece that

We are not asking theists to conceive of God’s death—to imagine that God stopped existing. And given that theists believe that God created the universe, when we ask them to consider His inexistence we are not asking them to conceive an empty void […] I will understand the comparison to involve the actual world [where God exists] and the closest possible world where [God does not exist] (Kahane 2011, 676).

While this makes clear the relevant comparison that Kahane and others have in view, some have suggested that the axiological question itself is unintelligible (Kahane 2012, 35-37; Mugg 2016). This is based on the fact that on a standard (Lewis/Stalnaker) semantics, counterpossibles are trivially true. God is typically understood as a necessary being. This means that if God exists, then God exists in every possible world (that is, in every possible state of affairs). Given this, the statement ‘God does not exist’ is a counterpossible. Now, consider the following conditional: If God does not exist, then the world would be better (or worse). Given theism, any counterpossible with the antecedent in the previous conditional is trivially true because there is no way that the antecedent could be true while the consequent is false. This is because there is no way for the antecedent to be true on theism. If this worry is correct, then cross-world axiological judgements are uninformative at best, and possibly unintelligible or impossible at worst. Notice that the same applies to atheism if the view in mind has it that there is no possible world in which God exists (that is, necessitarian atheism, the view that God necessarily does not exist).

One approach to this objection suggests that this type of axiological comparison is possible as a result of a process called cognitive decoupling. This occurs when an agent extracts information from a representation and then performs computations on it in isolation. Certain information is ‘screened off’ and thus not used in the reasoning process. Likewise, “[t]hose beliefs that are allowed into the reasoning process, along with suppositions, are ‘cognitively quarantined’ from the subject’s beliefs” (Mugg 2016, 448). Consider:

Bugs Bunny might pick up a hole off the ground and throw it on a wall. It is not metaphysically possible to pick up a hole, but we are able to suppose that Bugs has picked up the whole and recognize that Bugs can now jump through the wall. Thus, we can imagine an impossible state of affairs and make judgments about what would obtain within that state of affairs. In representing the impossible state of affairs, we screen out those beliefs that would lead to outright contradiction (Mugg 2016, 449).

In this context, cognitive decoupling occurs in situations in which, “when considering a counterfactual, subjects can screen out those beliefs that (with the antecedent of the counterfactual) imply contradictions” (Mugg 2016, 449). A theist who holds that God necessarily exists could address the axiological question by engaging in cognitive decoupling. This means that when addressing the axiological question, she ‘screens off’ her belief that God necessarily exists (and conversely, a necessitarian atheist could screen off her belief that God necessarily doesn’t exist). This proposal raises a number of questions, including how we can be confident that we have ‘screened off’ the appropriate beliefs, and also whether the comparison made when engaging in cognitive decoupling is relevantly similar to the real-world comparison needed to answer the axiological question.

Another proposal for dealing with this objection suggests that this worry about counterpossibles arises only when the comparison in question is understood as one between metaphysically possible worlds. But, so the proposal goes, when the relevant comparison is one between epistemically possible worlds, the counterpossible problem doesn’t apply (Mawson 2012; see also Chalmers 2011). After all, the theist who believes that God exists of metaphysical necessity holds that there are no metaphysically possible worlds where God doesn’t exist. But for a state-of-affairs to be epistemically possible for such a theist, she only needs to concede that it could obtain, for all she knows. Thus, the theist just needs to concede that, for all she knows, God may not exist. A helpful analogy comes by way of reflecting on the idea that water is H2O. While there are no metaphysically possible worlds where water is not H20, for all one knows, water is not H20. Hence, there are epistemically possible worlds where water is not H20 (Chalmers 60-62). For all the necessitarian theist knows, atheism is true, while for all the necessitarian atheist knows, theism is true. Thus, regardless of whether the comparison between metaphysically possible worlds is intelligible, the comparison between epistemically possible worlds is perfectly intelligible.

Yet another reply to the counterpossible problem holds that value can intelligibly be assigned to metaphysical impossibilities (Kahane2012, 36-37). For if it is possible to assign a value to a metaphysical impossibility, then perhaps the theist who thinks that atheism is metaphysically impossible could still assign a value to the relevant counterpossibles. Consider, for instance, that a mathematical proof could rightly be called beautiful or elegant even if it turns out to be invalid. Of course, it’s controversial whether it’s appropriate to talk of the beauty of an invalid proof. If such judgments turn out not to be appropriate, then it turns out that many of our value assignments will be apparent, not factual (Kahane 2012, 37). We will think we are making a factual value judgment when it is in fact not.

To conclude this section, it’s worth noting that the literature on the axiology of theism often treats rational preference as supervening on axiological judgments (that are understood to be objective). But it is an open question whether an agent’s rational preference need always correspond to correct axiological judgments. Perhaps it could be rational for an agent to prefer a worse state of affairs to a better one, or to disprefer a better state of affairs to a worse one. Kahane (2011) appears to think this is a genuine possibility. I won’t dwell on this issue, but it’s worth keeping in mind as one explores this topic. We’re now in a position to examine different answers that can be proposed to the axiological question.

3. Different answers to the Axiological Question

While some have attempted to address worries about the intelligibility of the axiological question, many philosophers have simply proceeded directly to attempting to answer the question (presumably because they are either unaware of the problem or implicitly assume that it has a reasonable solution). No consensus as to the correct answer to the axiological question has emerged in the literature (and seems unlikely to anytime soon). What has become clear, though, is that there are a great number of different possible answers one could offer to the axiological question.

The two main general positions that have been taken up in the literature are pro-theism and anti-theism. Pro-theism is, roughly, the view that it would be good if God were to exist. Anti-theism, on the other hand, holds that it would be bad if God were to exist. There are, however, other potential answers which haven’t received as much attention. For instance, the neutralist about the axiological question holds that God’s existence has (or would have) a neutral impact on the value of the world. The quietest holds that the axiological question cannot (in principle) be answered. Finally, the agnostic holds that the axiological question might be answerable, but we are currently unable to answer it. Much more remains to be said about the plausibility of these three latter positions. (For more on these answers see Kraay 2018, 10-18.)

There are numerous specific variants of these answers to the question. There is a difference between personal and impersonal judgements about the axiological question. The former focus on the axiological implications of God’s existence with respect to individual persons, while the latter focuses on such implications without any reference to God’s value-impact on persons. Additionally, there are narrow and broad judgements about the axiological question. The former refers to just one advantage (or downside) of God’s existence (or non-existence), while the latter refers to the axiological consequences of God’s existence or non-existence overall. These judgments – personal/impersonal and narrow/broad–combine to form at minimum sixty possible answers to the axiological question when applied to five general answers stated above. Klaas J. Kraay’s (2018, 9) helpful chart enables us to visualize all of these different possibilities:

Axiological Positions
Pro-Theism Anti-Theism Neutralism Agnosticism Quietism
Impersonal Personal
Narrow Wide Narrow Wide
Theism
Atheism
Agnosticism

The first column contains all of the sub-divisions relevant to pro-theism. The other general answers can subdivided in precisely the same way. Likewise, inasmuch as there are additional general answers to the axiological question to the five offered here, this chart will increase in size. These distinctions are important for a number of different reasons. For instance, later we will see that some have claimed that defending wide personal/impersonal anti-theism is a very difficult, if not impossible task. Another interesting idea that has emerged in the literature thus far is that someone can be a narrow personal anti-theist and a wide personal/impersonal pro-theist (Lougheed 2018c). In other words, someone could hold that it would be a bad thing for her, in certain respects, if God exists, while acknowledging that would be a good thing overall if God exists.

4. Arguments for Pro-Theism

This section outlines three different considerations that speak in favour of pro-theism.

a. The Infinite Value Argument

One argument for pro-theism appeals to the idea that God is infinitely valuable (for discussion see Van Der Veen and Horsten 2013). The thought is that if God is infinitely valuable, then any world with God is infinitely valuable because God exists in every world and confers infinite value on each one. From this it follows that any theistic world is more valuable than an atheistic world (or at least not worse if atheistic worlds can be infinitely valuable). There are at least two areas in need of further development regarding this line of argument. First, more work has to be done to show how God’s infinite value can sensibly be thought to make a world (assuming theism is true) infinitely valuable. There is a vast literature on the divine attributes, but the idea of God’s infinite value has been neglected (at least in the contemporary literature). What is it to say God is infinite? How is an abstract concept, infinity, supposed to accurately describe God’s value? Second, the claim that all theistic worlds have the same infinitely high value appears to violate very basic modal and moral intuitions. Consider two worlds in which God exists, one of which includes a genocide that the other does not. These two worlds are otherwise identical. Surely such a world–all else being equal–is axiologically superior to ours.

b. The Morally Good Agents Argument

The Morally Good Agents Argument is another argument in favour of pro-theism. Here is a thought experiment motivating this argument. Imagine that Carl’s car breaks down on the highway. Carl has no phone to call for help, and he doesn’t know anything about car mechanics. First, consider a case in which Susan, a morally good agent, discovers Carl on the side of the highway and offers help. She calls a tow truck for Carl, and when she discovers Carl doesn’t have his wallet, she pays for the tow herself. Second, consider a case in which no one pulls over to assist Carl. He attempts to flag down cars, but no one stops. While Carl is in poor health he has no choice but to attempt to walk to nearest gas station for assistance. These two cases are designed to show that morally good agents tend to add value to states of affairs. If the point generalizes, then a world with morally good agents is better than one without such agents, all else being equal (Penner and Lougheed 2015, 56).

Now consider two additional scenarios. Imagine that George sees Carl attempting to flag down vehicles. George attempts to pull over in order to assist Carl, but his brakes fail and he crashes into Carl, killing him on impact. Or consider Tom, who sees a truck crash into Carl’s car and then drives away. Carl’s car is now on fire with Carl trapped inside. Tom calls 911 but knows that the paramedics won’t arrive in time to save Carl. Tom tries to open the door to save Carl, but he isn’t strong enough to pry the bent door open. The idea behind these two additional cases is to acknowledge that morally good agents, despite good intentions, don’t necessarily have the power to do good. Of course, this doesn’t apply to God. Since God is all-powerful, God won’t be constrained or unable to add value to states of affairs in ways that other morally good agents might be constrained. Inasmuch as it makes sense to think that morally good agents add value to states of affairs, then God adds value to states of affairs. All else being equal, then, a world with God is better than a world without God (Penner and Lougheed 205, 57-58).

There are a number of objections to this line of argument which attempt to show that not all else is equal. One reason to think God’s existence isn’t valuable (at least for certain individuals) is based on the idea that God violates everyone’s privacy. If God exists, then there is a sense in which God automatically violates our privacy (that is, if God is all-knowing, then God knows all of our mental states/thoughts). Without a justifying reason to violate a person’s privacy, this is an aspect in which God’s existence is a bad thing, for part of what’s involved in people forming trusting relationships with each other is that they choose what information about themselves they reveal. But this type of choice is impossible for individuals to make in the case of God. (The issue of privacy will be discussed further in section 5a below.) The question remains, however, whether this worry, assuming it really is a downside, is enough to outweigh all of the goods associated with theism. Another objection invokes a worry about an inverted moral spectrum. Suppose that what we think is good is actually bad according to God, and vice versa. If this is right, then, while it might still be technically true that God is a morally good agent (and adds value), it would make little sense to think we ought to prefer that God exist (Penner and Lougheed 2015, 68).

c. The Goods of Theism Argument

The Goods of Theism Argument represents a family of arguments (some quite informally expressed) that focus on highlighting specific goods of theism. This style of argument need not deny that there are genuine goods associated with atheism. Rather, the goods identified in connection to theism are taken to outweigh any goods associated with atheism. Also, some might acknowledge that these goods need not make it rational for certain individuals, in certain respects, to prefer theism. But, so the thought goes, these goods do show that theism is better than atheism overall.

Various theistic goods that have been identified in the literature include objective meaning or purpose, an afterlife, and cosmic justice. For perhaps only God can be the source of objective meaning, and without God every human life would ultimately be meaningless (Cottingham 2005, 37-57; Metz 2019, 9-21) In addition, theism is often associated with the existence of an afterlife, which is connected to the idea that God’s existence ensures that there will be final justice. Many who are wronged on earth are not compensated for being wronged. Those who perpetrate evil often seem to go unpunished. However, God’s existence is good because God will ensure that everyone will receive their due. This could be a logical consequence of a perfect being. The pro-theist need not be committed to the specific details of how this good is instantiated (Lougheed 2018a).

Perhaps one of the most important putative advantage of theism is that if God exists, there are no instances of gratuitous evil. For many theists hold that the existence of gratuitous evil is logically impossible if God exists (Kraay and Dragos 2013, 166; McBrayer 2010). This is because God would ensure that evil only occurs to achieve some otherwise unobtainable good or that every victim of evil will receive just compensation. Notice that there is no pressure on the pro-theist to explain how certain apparent instances of gratuitous evil are not in fact gratuitous (though this is a problem when defending the existence of God). For the pro-theist is merely claiming that if God exists, then there is no gratuitous evil. She isn’t claiming that in fact there is no gratuitous evil. That there is no gratuitous evil if God exists appears to be a very strong consideration in favour of pro-theism.

One worry for this general line of argument is about whether the goods mentioned here are goods that only obtain on theism. If it could be shown that these goods obtain on atheism (or other religious and non-religious worldviews) then they would be of little help in demonstrating that a world with God is more valuable than one without God (Kahane 2018). A more pressing worry, however, is not whether these goods also obtain on naturalism, but whether theism is exclusively what’s required for them to obtain. Perhaps a very good, very powerful, very knowledgeable being who is only slightly lesser than God could ensure that all the goods in question obtain. If this is right, then theism isn’t required for these goods to obtain. For even if such a being existed, atheism would technically be true since God does not exist in this scenario. This is one area where it becomes problematic for the axiology of the theism literature to use ‘naturalism’ and ‘atheism’ interchangeably.

5. Arguments for Anti-Theism

This section examines two important arguments for anti-theism.

a. The Meaningful Life Argument

Perhaps the most widely discussed argument for anti-theism is an argument which has come to be known as the Meaningful Life Argument. Guy Kahane is responsible for first gesturing at this argument, and his discussion is what sparked much recent interest in the axiological question about God. Kahane takes his cue from well-known objections to utilitarianism raised by Bernard Williams. Williams argues that utilitarianism is so demanding that it requires individuals to sacrifice things which give them meaning (1981, 14.). The problem, then, is that utilitarianism is so demanding that, to follow it, one’s own life would cease to have meaning (or at least one would have to stop pursuing those things which confer meaning on her life). According to Kahane, his worry about utilitarianism has a parallel in the present context:  he claims that theism might be too demanding in the way that utilitarianism is too demanding. It could require that certain individuals give up things which confer meaning on their lives. Kahane writes:

If a striving for independence, understanding, privacy and solitude is so inextricably woven into my identity that its curtailment by God’s existence would not merely make my life worse but rob it of meaning, then perhaps I can reasonably prefer that God not exist—reasonably treat God’s existence as undesirable without having to think of it as impersonally bad or as merely setting back too many of my interests. The thought is that in a world where complete privacy is impossible, where one is subordinated to a superior being, certain kinds of life plans, aspirations, and projects cannot make sense… Theists sometime claim that if God does not exist, life has no meaning. I am now suggesting that if God does exist, the life of at least some would lose its meaning (Kahane 2011, 691-692).

This is the first statement of the Meaningful Life Argument. Note that these thoughts only defend narrow personal anti-theism: according to this argument, it would be worse, in certain respects and for certain individuals, if it turns out that God exists.

The merits of this argument have been debated. For instance, it has been objected that we are often mistaken about what constitutes a meaningful life (Penner 2015, 335). Consider that we often pursue some end thinking it will fulfill us. But when we achieve that end, we often find we are no more fulfilled than we were before. In other words, we often end up thinking we’ve pursued the wrong end. Since we’re highly fallible with respect to what goods contribute to a meaningful life, then we should not be confident in using such judgements to support personal anti-theism. Others have countered that for this objection to succeed, one would have to deny that the goods Kahane mentions such as independence, understanding, privacy, and solitude could contribute to an individual’s meaningful life (Lougheed 2017). But most of us don’t want to deny that these are goods. Still, it seems likely that there are quantitative and qualitative difference between how these goods are instantiated on theism compared to atheism. It remains to be seen whether such differences can successfully be articulated in a way that successfully answers the objection, and hence personal anti-theism.

Additionally, while it has been observed from the very beginning of the debate over the Meaningful Life Argument that for a good like privacy to successfully be harnessed in support of anti-theism, it needs to shown that it is intrinsically valuable, but little has been said in this regard (Kahane 2011, 684). Something is intrinsically valuable if it is valuable in and of itself. Consider that if privacy is only extrinsically valuable, it might turn out not to matter if God violates our privacy. Something is extrinsically valuable if it is only valuable based on what we can get from it. This means that God always knows where we are, what we are doing, and what we are thinking. Also, consider that this issue is one at the very heart of whether personal forms of anti-theism can be defended. For if the anti-theist and pro-theist both agree that privacy is intrinsically valuable, then in order to defend personal anti-theism, it need only be shown that God violates our privacy (as opposed to also explaining why it matters if our privacy is violated). Thus, providing a case for why goods associated with atheism such as privacy are intrinsically valuable would greatly strengthen the case for narrow personal anti-theism.

Finally, a closely related but less developed argument for anti-theism appeals to considerations about dignity to defend personal anti-theism (Kahane 2011, 688-689). Imagine that parents decide to have a child merely in order for the child to become an accomplished musician, or professional athlete, or simply for more help on the farm. The idea here is that a child should have the freedom to choose their own life path. A parent should support a child in doing this inasmuch as possible (and inasmuch as the life path in question is morally permissible). To have a child in order to fulfill some end other than their own fundamentally violates the dignity of the child. It treats the child as a means rather than solely as an end (Lougheed 2017, 350-351). The parallel case, of course, is supposed to be with respect to God’s relationship with humans. Many theistic traditions hold that humans were created solely to fulfill God’s purposes for them. If this is true, then humans aren’t permitted to pursue their own ends; they are obliged to pursue the ends God has set for them. Hence, the existence of God violates the dignity of humans. The next step in developing this line of argument is to provide more details about the conception of dignity this argument requires in order to be successful (Lougheed 2017, 351).

b. The Goods of Atheism Argument

The Goods of Atheism Argument has emerged after the Meaningful Life Argument, and it is also best understood as a cluster of arguments. It has been observed that goods associated with atheism need not necessarily be connected to meaning in order to justify narrow personal anti-theism. With respect to goods such as privacy, autonomy, and understanding, it has seemed to some that a world without God could be better for certain individuals, at least when only considering those specific goods. For if goods such as privacy and autonomy are intrinsically valuable, then they don’t need to be connected to meaning in order to support personal forms of anti-theism (Lougheed 2018c). Of course, given the many advantages associated with theism (for example, no gratuitous evil), it is difficult see how this line of argument could ever justify broad versions of anti-theism. It also remains an open question whether an individual could value these goods enough to justify personal anti-theism in absence of them being connected to her life pursuits and hence meaning.

6. Connections to the Existence of God

This section explores connections that have been drawn between the axiological question about God and the existential question of whether God exists.

a. Divine Hiddenness

The most work that has been done to connect the axiological and existential questions about God to one another is with respect to the argument from divine hiddenness for atheism. This argument runs roughly as follows. If God exists, then a relationship with God is one of the greatest goods possible. Because of this fact, if God exists there would be no instances of non-culpable, non-resistant, non-belief among those capable of a relationship with God. For belief that God exists is a necessarily requirement for a relationship with God. Yet there appear to be instances of non-culpable, non-resistant, non-belief. Or at the very least, it is more likely that such individuals exist than that God exists. Thus, it’s probable that God doesn’t exist (Schellenberg 2006; 2015)

One line of argument in the literature attempts to demonstrate that reflections on the axiological consequences of theism and atheism can be used to object to arguments from divine hiddenness. Assume that an actual good obtaining is axiologically equivalent to the experience of the same good (even when that good doesn’t actually obtain). This is intuitive when one considers that from a first-person perspective there is no difference between a good actually obtaining and the mere experience of that same good (Lougheed 2018). They’re both experienced in exactly the same way from the first person perspective. Now consider some goods often used to defend personal forms of anti-theism: privacy, independence, and autonomy. The key move in the argument is to suggest that these atheistic goods can be experienced in a theistic world where God is hidden. For example, consider the atheistic good of total and complete privacy. One can experience this good in a world where God hides. Indeed, many devoutly religious individuals sometimes report feeling alone and unable to feel God’s presence. Likewise, in a world where God hides one also gets many theistic goods. Maybe God intervenes and does a miracle to help someone, but the cause of the help is sufficiently unclear. So, it’s possible to doubt that God performed a miracle, and hence possible to doubt that God exists. Therefore, in a world where God hides, one is able to experience atheistic goods and also the theistic goods since they actually obtain. But atheistic goods cannot be experienced in a world where God isn’t hidden. If God’s existence were obvious (along with some of the divine attributes), for example, then one could not ever have the experience of total and complete privacy (even if turns out to be, in some sense, an illusion). Finally, in an atheistic world no theistic goods obtain. Thus, a world where God is hidden is axiologically superior to an atheistic world, but more importantly, it’s also superior to a world where God isn’t hidden. These considerations serve to support that idea that God might hide in order to maximize the axiological value of the world (Lougheed 2018a)

One line of thought attempts to complete the axiological solution to divine hiddenness by showing that theistic goods do indeed obtain in a world where God hides. On the one hand, it’s clear that theistic goods obtain in a world where God hides simply because this is logical consequence of God’s existence. However, on the other hand it’s not clear that the experience of theistic goods such as forming a relationship with God, cosmic justice, or the afterlife is the same in both worlds. Indeed, the experience of such goods might be so different that the axiological assessment of them ought to differ too. At best, then, we aren’t in a good position to tell whether a world where God hides is axiologically superior to a world where God isn’t hidden. This suggests that the axiological solution to divine hiddenness is at best incomplete (Lougheed 2018b).

One objection to the axiological solution to divine hiddenness attempts to show that it’s intelligible to say that many of the goods typically associated with theism can be experienced in a world where God does not exist (even if they don’t actually obtain). For instance, an afterlife and divine intervention are goods that could both be experienced in a world where God doesn’t exist (Hendricks and Lougheed 2019). Also consider that a world in which God doesn’t exist is consistent with there being an extremely powerful being who is only slightly less powerful than God.  This less powerful being could intervene to help humans and bring an afterlife, and so forth. Such a being might not be possible on naturalism, but it is perfectly consistent with atheism. One of the benefits of the discussion of divine hiddenness and the axiology of theism is that it has brought into focus the goods associated with both theism and atheism, along with how we should understand the value of the experience of such goods. It seems that this is just the beginning of such discussions and much more work remains to be done on this topic.

b. Problem of Evil

One version of the problem of evil, known as the evidential (or probabilistic) problem of evil, suggests that if it’s probable that gratuitous evil exists, then it’s probable that God doesn’t exist. This is because the existence of God is taken to be logically incompatible with the existence of gratuitous evil. Some have suggested that if an individual endorses this or related arguments from evil, then she must also endorse pro-theism. This is because if she accepts the problem of evil then she believes that certain world bad-making properties (for example, gratuitous evil) are incompatible with God’s existence. But if God exists, then those bad-making properties would not exist, and hence the world would be better. So, the atheist who endorses the problem of evil as a reason for atheism must, in order to be consistent, also be a pro-theist (Penner and Arbour 2018).

c. Anti-Theism entails Atheism

Finally, some have argued that if anti-theism is true, then atheism is true. Since God is perfectly good, God must always bring about the better over the worse. However, if anti-theism is true, then there are ways in which God doesn’t always bring about the better. But if God doesn’t always bring about the better over the worse then God doesn’t exist. So, the truth of anti-theism implies the truth of atheism. More strongly, it has been suggested that any negative feature associated with theism (for example, a lack of certain types of privacy) is evidence for atheism. This is because it is logically impossible that there be any negative features associated with a God who is omnibenevolent (Schellenberg 2018).

7. Future Directions

As noted, pro-theism and anti-theism are by far the two broad answers to the axiological question that have received the most attention in the literature to date. Given that much of contemporary philosophy of religion is focused on Christian theism, it isn’t surprising that many of the advantages and drawbacks associated with theism are also most clearly associated with typically Christian conceptions of God. In light of this, it seems that minority views deserve more attention in their own right. Additionally, comparative axiological analyses of other religious and non-religious worldviews would further expand the debate.

a. Exploration of Different Answers

As noted earlier, there are at least three additional answers to the axiological question worthy of further consideration. The first is quietism.  One reason to hold quietism was alluded to earlier, in Section 2. The necessitarian theist thinks there are no worlds where God doesn’t exist, and the necessitarian atheist thinks that there are no worlds where God exists. Given these views and given that the axiological question is a question about comparative judgments, one might think that it’s impossible to make the relevant comparison. As mentioned above, one way around this counterpossible worry might be to think of the comparison as one between epistemically possible worlds as opposed to metaphysically possible worlds. Another reason for quietism might be that worlds are somehow fundamentally incommensurable with one another and hence can’t be compared (Kraay 2018, 13). Consider that what makes an apple taste good is wholly different from what makes cheese taste good. It doesn’t make sense to compare them axiologically even though they’re both foods. This is a simple example intended to motivate incommensurability (Kraay 2011; Penner 2014).

The second additional answer to the axiological question is agnosticism. This view holds that while the axiological question is perhaps in principle answerable, we aren’t currently in a good position to discover the answer. Hence, we should suspend judgment about the answer to the axiological question. One way of motivating this view is that scepticism about whether we have all of the relevant information required in order to make cross-world value judgments. Not only that, we might worry that even if we could identify particular good-making and bad-making features of a specific world, that we don’t know how to combine those features so as to discover the overall value of that world. So, the agnostic holds that we aren’t in a good position to make value judgments about worlds, though such judgments are in principle possible (Kraay 2018, 10-11).

The third additional answer to the axiological question is neutralism. This involves the claim that God’s existence does not make an axiological difference to worlds. Perhaps God is valuable but shouldn’t be factored into assessments of world value. Or maybe one believes the axiological values of theism and atheism are precisely identical (Kraay 2018, 14). Quietism, agnosticism, and neutralism are surely not the only additional answers to the axiological question, but they represent a starting place for further research into different perspectives on the axiology of theism.

b. Other Worldviews

While the axiological question has only been asked about theism (and atheism), there is no in-principle reason why it couldn’t also be asked about other religious and non-religious worldviews. Indeed, the name ‘axiology of theism’ gives away the rather narrow focus of the literature so far. And it’s even narrower still in focusing not just on ‘theism’ in general but on ‘monotheism’ in particular. There are numerous ways the current debate could be expanded. For instance, pantheism considers God and the Universe to be one. The axiological question might not make sense with respect to pantheism (or might need to be reconstructed) since world value apart from God makes little since if pantheism is true. Panentheism considers the universe to be a proper part of God and thus suffers from a similar worry. Or consider that on a polytheistic religion such as Hinduism the axiological question can be asked with respect to many different Gods. Many of the different deities of Hinduism each have their own unique axiological value. Furthermore, one can explore whether it makes sense to assess the value of each deity separately or whether they need to be assessed together. Finally, consider that it’s far from clear that there is the concept of evil on Buddhism. At the very least, the Buddhist understanding of evil is quite different from how the Judeo-Christian tradition understands it. This brings into focus the question of whether it’s possible to make objective axiological judgments without somehow depending on the values of what one is supposed to be assessing in the first place. These concerns are raised only to show that the axiological question is quite far-ranging, and that much work remains to be done not only in assessing the value of theism and atheism, but also the values of other religious and non-religious worldviews.

8. References and Further Reading

  • Azadegan, E. (2019) “Antitheism and Gratuitous Evil.” The Heythrop Journal 60 (5): 671-677.
    • Argues that personal anti-theism is a form of gratuitous evil.
  • Cottingham, John. (2005) The Spiritual Dimension: Religion, Philosophy and Human Value. Cambridge: Cambridge University Press.
  • Chalmers, David (2011) “The Nature of Epistemic Space,” in Epistemic Modality Andy Egan and Brian Weatherson (eds) Oxford: Oxford University Press, pp. 60-106.
    • Provides a model of epistemic possibility.
  • Davis, S.T. (2014) “On Preferring that God Not Exist (or that God Exist): A Dialogue.” Faith and Philosophy 31: 143-159.
    • A simply written dialogue discussing different ways of defending both anti-theism and pro-theism.
  • Dumsday, T. (2016) “Anti-Theism and the Problem of Divine Hiddenness.” Sophia 55: 179-195.
  • Hedberg, T., and Huzarevich, J. (2017) “Appraising Objections to Practical Apatheism.” Philosophia 45: 257-276.
  • Hendricks, P. and Lougheed, K. (2019) “Undermining the Axiological Solution to Divine Hiddenness.” International Journal for Philosophy of Religion 86: 3-15.
    • Argues that theistic goods could be experienced in a world where God doesn’t exist.
  • Kahane, G. (2011) “Should We Want God to Exist?” Philosophy and Phenomenological Research 82: 674-696.
    • This is responsible for starting the axiology of theism literature is the first statement of the Meaningful Life Argument for anti-theism.
  • Kahane, G. (2012) “The Value Question in Metaphysics.” Philosophy and Phenomenological Research 85: 27-55.
  • Kahane, G. (2018) “If There Is a Hole, It Is Not God-Shaped.” In Kraay, K. [Ed.] Does God Matter? Essays on the Axiological Consequences of Theism. Routledge, 95-131.
    • Argues that God isn’t required to get many of the theistic goods mentioned by pro-theists.
  • Kraay, K.J. Ed. (2018) Does God Matter? Essays on the Axiological Consequences of Theism. Routledge.
    • This is the only edited collection on the axiological question and contains essays addressing a wide variety of issues from well-known philosophers of religion.
  • Kraay, K.J. (2018). “Invitation to the Axiology of Theism.” In Kraay, K.J.[Ed.] Does God Matter? Essays on the Axiological Consequences of Theism. Routledge, 1-36.
    • An extremely detailed survey chapter of the current debate including helpful prompts for further discussion.
  • Kraay, K.J. (2011) “Incommensurability, Incomparability, and God’s Choice of a World. International Journal for Philosophy of religion 69 (2): 91-102.
  • Kraay, K.J. and Dragos, C. (2013) “On Preferring God’s Non-Existence.” Canadian Journal of Philosophy 43: 153-178.
    • Responsible for identifying many of the more fine-grained answers to the axiological question.
  • Linford, D. and Megill, J. (2018) “Cognitive Bias, the Axiological Question, and the Epistemic Probability of Theistic Belief.” In Ontology of Theistic Beliefs: Meta-Ontological Perspectives. Ed. Mirslaw Szatkowski. Berlin: de Gruyter.
  • Lougheed, K. (2017) “Anti-Theism and the Objective Meaningful Life Argument.” Dialogue 56: 337-355.
    • Defends the Meaningful Life Argument against Penner (2018).
  • Lougheed, K. (2018a) “The Axiological Solution to Divine Hiddenness.” Ratio 31: 331-341.
    • Argues that a world where God hides is more valuable than a world where God’s existence is obvious and a world where God doesn’t exist.
  • Lougheed, K. (2018b) “On the Axiology of a Hidden God.” European Journal for Philosophy of Religion 10: 79-95
    • Argues that we cannot tell whether a world where God hides is more valuable than world where God’s existence is obvious.
  • Lougheed, K. (2018c). “On How to (Not) to Argue for the Non-Existence of God.” Dialogue: Canadian Philosophical Review 1-23.
    • Argues that pro-theism is not easier to defend than anti-theism.
  • Luck, M. and Ellerby, N. (2012) “Should we Want God Not to Exist?” Philo 15: 193-199.
  • Mawson, T. (2012) “On Determining How Important it is Whether or Not there is a God.” European Journal for Philosophy of Religion 4: 95-105.
  • McBrayer, J. (2010). “Skeptical Theism.” Philosophy Compass 5: 611-623.
  • McLean, G.R. (2015) “Antipathy to God.” Sophia 54: 13-24.
  • Metz, T. (2019). God, Soul and the Meaning of Life. Cambridge University Press.
    • An introduction to different theories of what constitutes a meaningful life.
  • Mugg, Joshua (2016) “The Quietist Challenge to the Axiology of God: A Cognitive Approach to Counterpossibles.” Faith and Philosophy 33: 441-460.
    • Applies a theory from the philosophy of mind to solve the worries about whether the axiological question is intelligible.
  • Penner, M.A. (2018) “On the Objective Meaningful Life Argument: A Reply to Kirk Lougheed.” Dialogue 57: 173-182.
    • Replies to Lougheed (2017).
  • Penner, M.A. (2015) “Personal Anti-Theism and the Meaningful Life Argument.” Faith and Philosophy 32: 325-337.
    • Develops Kahane (2011) into a more detailed version of the Meaningful Life Argument for anti-theism, but ultimately rejects it.
  • Penner, M.A. (2014) “Incommensurability, incomparability, and rational world-choice.” International Journal for Philosophy of Religion 75 (1): 13-25.
  • Penner, M.A. and Arbour, B.H. (2018) “Arguments from Evil and Evidence for Pro-Theism.” In Kraay, K.J. [Ed.] Does God Matter? Essays on the Axiological Consequences of Theism. Routledge, 192-202.
  • Penner, M.A. and Lougheed, K. (2015) “Pro-Theism and the Added Value of Morally Good Agents.” Philosophia Christi 17: 53-69.
    • Argues that God’s existence adds value to the world since God is a morally good agent.
  • Rescher, N. (1990) “On Faith and Belief.” In Human Interests. Stanford: Stanford University Press, 166-178.
    • The first time the axiology of God’s existence is explicitly mentioned in the contemporary literature.
  • Schellenberg, J.L. (2006). Divine Hiddenness and Human Reason. Cornell University Press.
    • This book represents the first statement of the argument from divine hiddenness as discussed in the contemporary literature.
  • Schellenberg, J.L. (2015) The Hiddenness Argument: Philosophy’s New Challenge to Belief in God. Oxford University Press.
    • A statement on divine hiddenness intended to be accessible to a wide audience.
  • Schellenberg, J.L. (2018) “Triple Transcendence, the Value of God’s Existence, and a New Route to Atheism.” In Kraay, K.J.[Ed.] Does God Matter? Essays on the Axiological Consequences of Theism. Routledge, 181-191.
  • Van Der Veen, J. and Horsten, L. (2013) “Cantorian Infinity and Philosophical Concepts of God.” European Journal for Philosophy of Religion 5: 117-138.
  • Williams, B. (1981) “Persons, Character and Morality,” in Moral Luck. Cambridge: Cambridge University Press.

Author Information

Kirk Lougheed
Email: philosophy@kirklougheed.com
Concordia University of Edmonton
Canada

John Wisdom (1904-1993)

Between 1930 and 1956, John Wisdom set the tone in analytic philosophy in the United Kingdom. Nobody expressed this better than J. O. Urmson in his Philosophical Analysis: Its Development Between the Two World Wars (1956) where, after Bertrand Russell and Ludwig Wittgenstein, Wisdom is the most frequently quoted philosopher. Wisdom was the leading figure of the Cambridge School of Therapeutic Analysis (which included other thinkers such as B. A. Farrell, G. A. Paul, M. Lazerowitz, and Norman Malcolm); the other major British school of analytic philosophy was that of ordinary language philosophy centered primarily at Oxford University.

Wisdom adopted the positions of both G. E. Moore and Wittgenstein, but he rejected the radical critique of metaphysics levelled by the Wittgenstein-inspired Vienna Circle. In contrast to Wittgenstein, Wisdom was not a philosopher of language: he maintained that most significant philosophical problems originate not with language but, in the first instance, as a result of our encounter with problems of the real world. From this standpoint, Wisdom introduced into analytic philosophy the discourse on the meaning of life and on problems of philosophy of religion. Be this as it may, prior to the appearance of Wittgenstein’s Philosophical Investigations (1953), Wisdom’s published works were read as indicators of the directions that Wittgenstein’s thought was taking following the latter’s return to philosophy in 1929.

By the 1960s, Wisdom’s influence had radically diminished. This was due largely to the ascendancy of exact philosophy of language and analytic metaphysics. This development, together with increasing emphasis on the power of scientific knowledge and its techniques, largely overshadowed the exploration of philosophical puzzles, human understanding (“apprehension”), and techniques of deliberation, which were Wisdom’s three chief theoretical concerns.

Table of Contents

  1. Biography
  2. Interpretation, Analysis, and Incomplete Symbols
    1. Interpretation and Analysis
    2. The Task of Analytic Philosophers
  3. Logical Constructions
    1. The Tasks of Philosophical Analysis
    2. Sketching Versus Picturing
    3. Types of Analysis
    4. Ostentation, Instead of Reference
  4. The Metaphysical Turn
    1. Philosophical Perplexity
    2. Philosophical “Statements” as both Misleading and Illuminating
    3. Descriptive Metaphysics
  5. Other Minds
    1. Philosophical Quasi-Doubts and their Therapy
    2. Contemplating Possibilities
    3. The Logic of Philosophical “Statements”
    4. Therapeutic Analysis
    5. On Certainty
  6. What is Philosophy?
    1. Epistemic Anxiety
    2. No Proofs in Philosophy
    3. Philosophy Explores Puzzles
    4. Philosophy Treats Paradoxes
  7. Philosophy of Religion
    1. Epistemic Attitudes
    2. The Logic of God
    3. The Meaning of Life
  8. References and Further Reading
    1. Primary Sources
      1. Books
      2. Papers
    2. Secondary Sources

1. Biography

(Arthur) John Terence Dibben Wisdom was born to the family of a clergyman in Leyton, Essex, on December 9, 1904. He attended the Aldeburgh Lodge School and the Monkton Combe School in Somerset. In 1921, he became a member of Fitzwilliam House, Cambridge, where he read philosophy and attended lectures by G. E. Moore, C. D. Broad, and J. M. E. McTaggart. Wisdom received his Bachelor of Arts in 1924, after which he worked for five years at the National Institute of Industrial Psychology. In 1929, he married the South African singer Molly Iverson. The couple had a son, Thomas, born in 1932, before separating during the Second World War. Between 1929 and 1934, Wisdom was a Lecturer in the Department of Logic and Metaphysics at the University of St. Andrews and a colleague of G. F. Stout. After the publication of his Interpretation and Analysis (1931) and the series of five articles on “Logical Constructions” (1931-1933), Wisdom was named Lecturer in Philosophy at Cambridge and a Fellow of Trinity College. This afforded him the opportunity to acquire firsthand knowledge of Ludwig Wittgenstein’s philosophical work.

Between 1948 and 1950, Wisdom delivered two series of Gifford Lectures on “The Mystery of the Transcendental” and “The Discovery of the Transcendental” that were never published (Ayers 2004). In 1950, Wisdom married Pamela Elspeth Stain, a painter. From 1950 to 1951, he served as president of the Aristotelian Society. In 1952, he was named Professor in Philosophy at Cambridge. Following his retirement from Cambridge in 1968, Wisdom spent four years teaching at the University of Oregon. Wisdom returned to Cambridge in 1972, and six years later was elected Honorary Fellow of Fitzwilliam College. He died in Cambridge on September 12, 1993.

2. Interpretation, Analysis, and Incomplete Symbols

a. Interpretation and Analysis

In his first book in 1931, Wisdom maintains that interpretation and analysis are two kinds of definition. Interpretation is a one-act paraphrase of a word or a phrase, a presentation of its meaning that remains at the same “level,” as when one links a word to its synonyms. By contrast, analysis “unpacks” the meaning at a deeper level (1931, p. 17). St. Augustine effectively captured the difference between interpretation and analysis in his famed reply to the question “What is time?”: “I know well enough what it is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled” (Confessions, Book 11). Wisdom reads Augustine as communicating that he knows the interpretation of “time” but not its analysis. Problems arise because the two forms of definition are often difficult to distinguish in practice since elements of analysis tend to find their way into interpretations, with the result that the two categories sometimes overlap (p. 17).

A central theme in Interpretation and Analysis is Jeremy Bentham’s notion of fictitious entities. According to Bentham:

A fictitious entity is an entity to which, though by the grammatical form of the discourse employed in speaking of it, existence be ascribed, yet in truth and reality existence is not meant to be ascribed. (Bentham 1837, viii. p. 197)

The difference between objects of reality and fictional entities is that the latter are not components of facts. They have, as Bentham put it, only “verbal reality.”

Preserving individual perceptions and corporeal substances in his ontology, Bentham declares all other items “fictitious entities.” Such are the 10 predicaments of Aristotle, but also the color red. Similarly, Wisdom holds that persons, animals, and unicorns are individuals, while events and qualities are not. But concepts like “nations” are both individuals and fictitious entities.

b. The Task of Analytic Philosophers

Following Moore, Wisdom maintains that the business of analytic philosophy is to obtain a clear and precise grasp of a phrase’s meaning. A significant part of Moore’s work consists in trying to find the answer to questions like “What do we mean when we say: ʻThis is a blackboardʼ?” (p. 8). However, following another of his teachers, Broad, Wisdom takes analysis to be only one practice of philosophy. There is also a speculative philosophy, which is fully on par with analytic philosophy. The task of analytic philosophers is to clarify the propositions of speculative philosophy (compare to Broad 1924). Wisdom dedicates to this task a special book, Problems of Mind and Matter (1934a), in which he investigates G. F. Stout’s Mind & Matter (1931), which explores three notions: the “mental,” the “material,” and “psychology.”

Wisdom argues against the claim that language is the subject matter of analytic philosophy. He admits that “one of the best clues to the analysis of facts is the [analysis of the] sentence which expresses it” (1931, p. 64), but he insists that he does not really want to say that every philosophical proposition is bad grammar. In other places, Wisdom is more explicit: “The work of an analytic philosopher is not work on language. Indeed, all his results could be stated in many other systems of symbols” (p. 15) (compare to § 4.2). This point suggests that the findings and formulations of the analytic philosopher might be useful to the special sciences. For example, an analysis of the concept of “rent” can be used in political economy. What analytic philosophers strive for above all is clarity and precision everywhere, not only in philosophy.

3. Logical Constructions

Wisdom discusses his doctrine of logical construction—a term introduced by Bertrand Russell—in a series of five articles that appeared in Mind from 1931 to 1933. The philosophical community for a number of years considered these essays to be “the most wholehearted of all attempts to set out the logical assumptions implicit in philosophical analysisʼ” (Passmore 1966, p. 365).

a. The Tasks of Philosophical Analysis

From what derives the difference between the analytic philosopher and the translator? Wisdom holds that the difference is one of diverse paraphrastic intentions. In the same way in which the statement of the liar does not differ from the statement of the ignorant, the philosopher and the translator often speak the same words, but they intend different things.

That the analytic philosopher’s task closely approximates that of the translator reveals that the philosopher’s aim is not to learn new facts but to acquire a deeper insight into the ultimate structure of the facts. Such analysis is worth doing, in Wisdom’s view, since we may perfectly well know the facts but may possess no knowledge about their essential structure whatsoever (1931-3, p. 169-70) (see § 2.1).

The latter claim is directed, in particular, against the Vienna Circle (compare to Stebbing 1933) inasmuch as, while Wisdom rejects metaphysical entities (for example, sense-data), at the same time he embraces metaphysics as a discipline studying the ultimate meaning, the structure of things.

b. Sketching Versus Picturing

Wisdom rejects the idea of the early Moore that propositions exist. This move appears to follow his reluctance to connect analysis to the world as an ontological entity. Wisdom also rejects Wittgenstein’s statement that “propositions” “picture” facts. This is confirmed by the fact that while “a sentence requires a speaker, a picture… requires an artist” (p. 62). Further justifying this position, he argues that when we write one sentence twice, we write two sentences, while the fact that these sentences “sketch” remains one and the same.

Instead of picturing, Wisdom maintains that language “sketches” facts (p. 56). By the act of “sketching,” one makes each element of a sentence to “name” an element of the fact, while the order of elements in the sentence “shows” the form of the elements of the fact: it shows the “shape” of the fact. Wisdom calls the replacement of the components of facts by elements of the sentence “docketing” (p. 51).

Wisdom assesses sentences on a scale of “good expression” of facts. The sentences that best express a fact feature elements of the same spatial order as the elements of the fact. Importantly enough, the sentences of the ordinary language are not identical with the spatial form of the fact that it is expressing but rather with something from a different logical level that might be derived from spatial form (p. 62). To avoid confusions, Wisdom recommends that when, for example, we report a red patch on this white sheet of paper, we would be more precise if we were to say “this red” instead of “this is red.”

c. Types of Analysis

A fact can be about (can sketch) another fact only if it is of the same order. Wisdom regards a fact to be of the “first order”—that is, its elements qualify as “ultimate elements”—if it is not a fact about a fact: in other words, if it features no element like “community,” or character like “machine,” or any other Benthamite fictitious entities. Wisdom also distinguishes “first derivative” facts: “If one supposes it to be a fact that some object is red, then the first derivative will be the fact that the object is characterized by red” (Urmson 1956, p. 81). The first derivative facts are logical constructions.

Since the ways facts can be about other facts can be of different orders, there are correspondingly different types of analysis. Wisdom discriminates between material, philosophical, and logical analysis (1934b, p. 16). Logical analysis assesses “functors.” Philosophical analysis, by contrast, serves a constructive role, making primary sentences of secondary sentences. Its objective is to render secondary facts ostensive, thereby yielding insight into their structure. Philosophical cognition can be defined as insight into structure, regardless of how one achieves that insight. It employs the method of what Wisdom identifies as “ostentation.”

The scientist undertakes material analyses. Analyses of this sort are even more ostensive than those Wisdom classifies as philosophical. This cannot be a surprise since material analysis is a same-level analysis, philosophical analysis makes a translation into a new level. Despite this clear difference between the two types of analysis, it is a matter of fact that scientists often perform philosophical analysis, while philosophers on their side commonly engage in material analysis, for example, when they attempt to define “good” in naturalistic ethics.

d. Ostentation, Instead of Reference

Philosophers have always made use of the method of “ostentation.” Wisdom sees, for example, Bentham employing it under the guise of “paraphrase,” Russell under the guise of “logical construction” and “incomplete symbol.” Unfortunately, the method has never been analyzed in detail.

Wisdom defines “ostentation” as “a species of substitution” (1933, p. 1) by means of which one more clearly states the facts to which sentences refer. Each meaningful sentence ostensively “locates” facts, albeit with different success. Sentences containing general names, for instance, do not locate facts as successfully as do sentences with individual names.

The importance of the introduction of the notion of ostentation is that with its help, Wisdom avoids resorting to the use of L. S. Stebbing’s “absolute specific sense-qualities” (1933-4, p. 26). While Stebbing believed that the aim of analysis is “to know what precisely there is in the world” (1932-3, p. 65), Wisdom saw the task of analytic philosophy as exploring the ultimate structure of the facts.

4. The Metaphysical Turn

a. Philosophical Perplexity

Between 1934 and 1937, Wisdom regularly attended Wittgenstein’s classes in Cambridge. The impact of this encounter is clearly evident in “Philosophical Perplexity,” where Wisdom proclaims:

I can hardly exaggerate the debt I owe to [Wittgenstein] and how much of the good in this work is his—not only in treatment of this philosophical difficulty and that but in the matter of how to do philosophy. (1936, p. 36 n.)

In the paper, Wisdom underlines his old position that philosophical statements provide no new information. Their point is different from that of the factual propositions. The task of philosophical propositions is:

… the illumination of the ultimate structure of facts, that is the relations between different categories of being or (we must be in the mode) the relations between different sub-languages within a language. (1936, p. 37)

What is new in “Philosophical Perplexity” is the suggested (Wittgensteinian) tolerance toward the opposing claims philosophers make. If, for example, one philosopher maintains that philosophical statements are verbal, and another that they are not verbal, we can affirm that they both are right.

Wisdom pays special attention to the sentences that the neo-positivists dismiss as meaningless. Typical examples of such sentences are: “God exists,” “Humans are immortal,” and “I know what is on in my friend’s mind”—sentences that give rise to traditional philosophical problems. Wisdom insists that it is misleading to call them all “meaningless,” at least because each proposition of this sort exhibits a meaninglessness of different kind (compare to § 5.3). Nonsensical in different respects are propositions such as that two plus three is six and that one can play chess without the queen.

Puzzles of this sort can be solved “by reflecting upon the peculiar manner in which those sentences work,” in other words, by reflecting on their style, not on their subject. Wisdom’s “mnemonic slogan” now is: “It’s not the stuff, it’s the style that stupefies” (p. 38). Foregrounding style as a substantive philosophical concern, Wisdom initiates a move to discriminate between the “content” of a proposition and what we actually want to say with it—its “point.”

b. Philosophical “Statements” as both Misleading and Illuminating

Wisdom maintains that we often cannot say of a philosophical theory why it is false, although we feel that it is theoretically poor. Actually, the philosopher cannot say why a philosophical statement is false, simply because philosophical “statements” are not, properly speaking, statements but rather recommendations for elucidating some matter.

What misleads in philosophical “statements” is, above all, that they have a non-verbal air (compare to § 2.2). Philosophers often maintain, for example, that they can never know what is going on in other minds, as if they are dreaming of a world in which this were possible. This complaint is misleading, argues Wisdom, since it implies likeness that does not exist and conceals likeness that does.

Wisdom further claims that “philosophical theories are illuminating in a corresponding way, namely when they suggest or draw attention to a terminology which reveals likeness and differences concealed by ordinary language” (p. 41). In other words, by struggling with a philosophical puzzle, we can achieve progress alternatively shifting from provocation to resolution (p. 42).

The conclusion Wisdom reaches is that to accept that a theory or a point of view might not only lead one to adopt different theoretical positions but also to acquire a novel cognitive stance of a general kind. Importantly enough, cognitive differences are possible inasmuch as every judgement is also a decision. Even “a man who says that 1 plus 1 makes 2 does not really make a statement,” declares Wisdom, “he registers a decision” (1938, p. 53) (compare to § 5.2).

c. Descriptive Metaphysics

Just as with the propositions of mathematics, and the statements of psychoanalysis, ethics, poetry, and literature, it is difficult to define metaphysical claims. Apparently, metaphysics is closer to logic, understood as a discipline of a priori definitions. This is the conclusion that Moore reached studying Plato and Aristotle and that Russell came to as well in his study of logic and mathematics. Wisdom finds that by contrast with the logician, “the metaphysician looks for the definition of the indefinable” (1938, p. 60). Thus, metaphysics is not a kind of analysis—analysis is a function of logic. Rather, the ends of metaphysics are achieved in a “game of analyses.” When we define metaphysical questions and sentences, we are articulating the goals of play in the game.

To put it otherwise, the metaphysician is not aiming at analysis as such: “What metaphysicians want, or really want, is not definition but description” (p. 65). If we, nevertheless, would like to speak of analysis instead of descriptions in metaphysics, we should stipulate that the metaphysician is striving to analyze the unanalyzable.

5. Other Minds

Over a period of three years, beginning in 1940, Wisdom published a series of eight papers in Mind under the title “Other Minds” (1952a). The publication was the most important philosophical event in Britain during the Second World War, which explains why the opening discussion at the Joint Session of the Aristotelian Society and Mind Association in 1946 was on “Other Minds” at which Wisdom and J. L. Austin presented their positions (compare to Austin 1946).

a. Philosophical Quasi-Doubts and their Therapy

In these papers, Wisdom holds that philosophy is based on ever-recurring doubts. However, when we try to discuss these doubts, they “turn to dust” (1952, p. 6). Why is this? To answer this question, we need to discriminate between natural doubts about some fact of which we have no knowledge, and philosophical doubts. Philosophical doubts are less doubts in the normative sense than concerns over “logical irregularities.”

Wisdom differentiates three kinds of philosophical doubts: (i) Some doubts stem from the infinite corrigibility of statements about people and things, for example, “Smith believes that flowers feel.” (ii) A second sort are “inner-outer doubts.” When assailed by such concerns, we know all the data of a case but nevertheless doubt what is going on “in Smith’s head.” This state of mind figures in circumstances where, for example, we see that a driver stops at red light but do not in fact know whether he sees the red light. (iii) Wisdom’s third class of doubt involves thoughts such as whether a zebra without stripes is still a zebra and whether a man can fulfill a promise by mistake.

Quasi-doubts of these kinds are doubts about predication. They all hinge on the problem of determining whether S is P. Wisdom detects three sources of the problem: (i) Infinity of the criterion of whether S is P. This engenders doubts of the kind evinced by questions such as “Are the taps closed?” and “Is this love?” (ii) A second source is conflict of criteria as to whether S is P. We see this in questions like “Can you play chess without the queen?” and “Are tomatoes fruits or vegetables?” (iii) Wisdom’s third source is hesitation by leap of criteria that determine whether S is P—the “leap” being from the inner to the outer, from the present to the past, from the actual to the potential.

Wisdom takes his position from psychoanalytic therapy, whereby “the treatment is the diagnosis and the diagnosis is the description, the very full description, of the symptoms” (p. 2 n.). The philosophical difficulty is eliminated only when the philosopher himself comprehensively describes his question—not in abstract general terms but narratively, telling stories about them. Wisdom’s conclusion is that ultimately “every philosophical question, when it isn’t half asked, answers itself; when it is fully asked, answers itself” (ibid.). This is the main principle of his therapeutic analysis (compare to § 5.4).

b. Contemplating Possibilities

Wisdom also maintains that instead of speaking of metaphysical doubt, it is more correct to speak of contemplating possibilities (p. 6, 33). When I am pondering a philosophical puzzle “rival images are before me… two alternatives, two possibilities” (p. 14) and, in a process of deliberating on them, I understand the puzzle. Such contemplation aims at judgement, at decision (compare to § 4.2). In fact, “all philosophical doubts are requests for decision” (p. 3 n.), not for information.

As contemplation of possibilities, philosophical knowledge is clearly a priori. According to Wisdom, philosophical knowledge is the most general knowledge, more general than mathematical knowledge. That is why the “ignorance” in philosophy is not bona fide ignorance; the “doubt” in it is not genuine doubt. The philosophical pseudo-ignorance is usually combined with the perfect knowledge of the object. Moreover, observes Wisdom, “to grasp how philosophy though not logic is a priori and though a priori is not logic takes one far towards dissolving its difficulties” (p. 20).

c. The Logic of Philosophical “Statements”

According to Wisdom, the philosophical question is neither a logical proposition nor an empirical warning. It is a question of the form “Aren’t we really all mad?” or an exclamation like “We are all sinners!” Such phrases are requests for notational reform. They are not an appeal for a search of new facts.

Like all conflicts in philosophy, the “conflict between Sceptics and Phenomenalists,” avers Wisdom, “is removed not by proving the one [side] being wrong and the other right, but by investigating certain of the cases of each one’s saying what he does” (p. 56). One can do this by means of “careful description” of the usage of the competing phrases (compare to § 4.3). Wisdom perceives this method as being similar to that of the writers, who blend technique “with the detailed description of the concrete occasion” (p. 57).

Meaningless statements of belief, however, are different in type. This is evident in the contrast between, for example, the statement that in the dead man there is still something alive, and the statement that the clock is moved by a leprechaun, both of which differ typologically from the statement that particular man now exists in a body other than his own. In this connection, Wisdom notes that “there is more difference between the grammar of ʻcurly wolfʼ and ʻpretence wolfʼ than there is between the grammar of ʻcurly wolfʼ and ʻinvisible wolfʼ” (p. 25; compare to p. 68). Moreover, “even within the category of physical objects there are differences in logic” (p. 76 n.), as in how “has legs” relates to “is a chair” differently than to “is a cushion.”

The principle “every sort of statement has its own sort of logic” implies that we cannot decide which among competing metaphysical statements is ultimately the winner (p. 62); there are no final proofs here. The inferences drawn in philosophy are no more than probable; they are true only in “colloquial sense.” As Wisdom explains, we can say “none of these answers will do. There is a step [a decision], and we take it, but goodness knows how [… and this] is not an alternative answer, it is a repetition of the complaint” (ibid.).

d. Therapeutic Analysis

To the uncertainty expressed by the question “How do I know other minds?,” we can reply “By analogy.” This answer, however, as Wisdom points out, is as misleading as it is true; it seems true only initially. In fact, it is just another deceptive “smoother” in that it tranquillizes critical thought, albeit only momentarily. If we say, for instance, that the hippopotamus is a water horse, we must immediately add how this identification misleads.

Wisdom concludes from the foregoing the following thesis of therapeutic analysis:

The whole difficulty [in philosophy] arises like difficulty in a neurotic; the forces are conflicting but nearly equal. The philosopher remains in a state of confused tension unless he makes the [therapeutic] effort necessary to bring them all out by speaking of them and to make them fight it out by speaking of them together. It isn’t that people can’t resolve philosophical difficulties but that they won’t. In philosophy it is not a matter of making sure that one has got hold of the right theory but of making sure that one has got hold of them all. Like psychoanalysis it is not a matter of selecting from all our inclinations some which are right, but of bringing them all to light by mentioning them and in this process creating some which are right for this individual in these circumstances. (p. 124 n.)

e. On Certainty

An argument against the skeptical criticism of the claim “There are invisible leprechauns in the clock” is that we can imagine invisible leprechauns known only by the deity. Apparently, questions like “Are there leprechauns?” are not necessarily meaningless.

Even if we were to see the noumena, this would merely be a visual perception again; thus, as philosophers, we would need to be skeptical about them, too. It turns out that we cannot even imagine true noumena. Wisdom concludes that the skeptic’s statements do not participate in the discourse. In fact:

The sceptic refuses to back anything, saying that everything may lose except Logic which doesn’t. In saying this he appears to back something but he doesn’t. For his own statement can’t lose and doesn’t run. (1952a, p. 102 n.)

Some may claim that we can directly know other minds by telepathy. However, this again is only indirect knowledge—it is not a solution to the problem. To talk, for example, of John seeing literally everything that Smith sees is to speak of one person existing in two bodies. If somehow we all were to have a telepathic connection with Smith’s mind, then his private life would be common and the mind-processes in his head would be physical events.

The notion that we can have knowledge of someone else’s mind is, as Wisdom sees it, absurd. We encounter a logical impossibility here. To say “we can’t know other minds” is in the first instance to acknowledge that this is physiologically impossibly. Once we understand that telepathy, too, cannot be a source of knowing other minds, however, we see that such knowledge is a logical impossibility.

6. What is Philosophy?

a. Epistemic Anxiety

The question “what is philosophy?” plays central role in Wisdom’s works. In a review written in 1943, he maintains that:

… oscillation in deciding between philosophical doctrines goes hopelessly on until one gives up suppressing conflicting voices and lets them all speak their fill. Only then we can modify and reconcile them. (1943, p. 108)

All this provokes in us a feeling of uneasiness, since:

… we are very apt to be dissatisfied with our weighing[;] the weights too often and too much change every reweighing… It is that oscillation which finds expression in [the avowal] “I don’t know what I really want.” (p. 109)

This feeling of epistemic anxiety is most familiar from our experience with moral dilemmas, as on those occasions when we exclaim, “I shouldn’t have done that!” and then, a bit later, we temporize with a remark like, “Well, it isn’t that bad!” Wisdom finds a similar situation when trying to resolve a philosophical issue.

The worst thing, in Wisdom’s conclusion, that we can teach a child is blindly to be driven by a love or hatred that is unchangeable in principle. The pedagogical effort should teach the child to react cautiously and reflectively in different situations. The pupil should be taught to cultivate a broad spectrum of reasoning that he can bring to bear in examining every new development in his environment (compare to Ryle 1979, p. 121). Wisdom explains that the person who best accomplishes this increases the child’s:@

… discrimination not so much of the objects to which he reacts as of his reaction to the objects… Not merely putting something into the child but bringing out the uneasiness which lurks in him. (1952a, p. 110)

b. No Proofs in Philosophy

Wisdom maintains that there cannot be proofs in philosophy—neither in a logical sense nor in an analytic sense. Philosophical proofs are invalid in principle. Indeed, a proof is only possible in complex cases, for example, by algebraic problems, where we have long chains of reasoning. In philosophy, however, the cases we are inclined to consider “proved” are simple. Exactly this is the source of the difficulty: the simpler the case, the more ambiguous are the words of the conclusion. This leads one to contemplate different alternatives and, in the process, to hesitate as to the conclusion. Proofs, however, are free from hesitation per definitionem. There are philosophical questions, not philosophical proofs.

Wisdom maintains that every philosophical question is a request for description of a class of “logical animals”—of a very familiar class of animals. “And because the animals are so familiar there is no question of the answers being wrong descriptions—but only of whether they are happy descriptions or not” (1944b, p. 112).

Entangled philosophical questions introduce new logic. Wisdom understands this to mean that they introduce new ways of seeing things that reveal what is already known in principle but is not before our eyes. Philosophical questions can be likened to the question of a person who is well aware of what a semaphore is but still asks what it is. Obviously this is not a question about facts. Wisdom construes it as a request for a new description, one motivated by the hope that it will eliminate some perplexity. In other words, philosophers exercise deductive reasoning that starts from things that everybody knows (compare to Russell 1914, p. 189ff.).

c. Philosophy Explores Puzzles

In marked disagreement with Wittgenstein, the later Wisdom maintains that “a purely linguistic treatment of philosophical conflicts is often inadequate” (1946a, p. 181). Philosophical puzzles commonly do not, he finds, possess a linguistic etiology (compare to §§ 2.2, 4.2), and they are not different in type from some other unsettling puzzles that confront us in life. The reasonableness employed in philosophical dispute is, says Wisdom, typically of the sort that a woman employs when she decides “which of the two men is the right one for her to marry,” or that a man uses when he must “decide which of two professions is the right one for him to take up” (p. 178).

In fact, the philosopher discusses his problems just as does the businessman, the judge, or the army general does. However, he never approaches his discussions as a preparation for action. The philosopher, declares Wisdom, simply “desires the discussion never to end and dreads its ending.” He is like:

… the man who cannot be sure that he has turned off the tag or the light. He must go again to make sure, and then perhaps he must go again because though he knows the light’s turned off he yet can’t feel sure. (p. 172)

However, in contrast to the neurotic, the philosopher can never resolve his doubts. This is because he does not actually doubt but just pretends to doubt, and he does not pretend merely to others but to himself as well.

Philosophy also resembles logic and mathematics but fields no theories or theorems. Instead, it formulates puzzles, such as those captured in questions like “Can a man do what the other does?” Puzzles of this kind introduce new forms of logic, which the philosopher sifts for hidden characteristic marks of conventional logic. Philosophical puzzles are no less unreal than caricatures; neither do they assert facts. They arise partly from language and partly from our pre-predicative practices.

d. Philosophy Treats Paradoxes

Wisdom’s skeptic claims that we cannot be absolutely sure that, for example, this map represents London. This is true for all statements “about what is so.” When we see a fox head, we can be still not sure that this is a fox’s head. This worry Wisdom dismisses as a product of the logical model of the “man behind the scene [which is…] inappropriate to his logical situation” (1950a, p. 250). What is to be realized when looking at such statements is “how each answer [to a sceptical claim] illuminates what others obscure and obscures what the others illuminate” (p. 254).

It is through a process of asking similar questions and developing answers to them that philosophical problems are resolved. Questions such as “whether the infinite numbers are numbers,” “whether the wild horses are horses,” and “whether a chess game without the queen is a chess game” are all questions of this sort, according to Wisdom, and are requests for judgment (compare to § 7.2). As such discourses reach their terminus, perplexity is replaced by new apprehension, a new “take” on the matter at hand.

Questions of the type “What is this?” are neither inductive nor deductive. Their point differs with different questioners and with different circumstances. Resolving them requires prolonged investigation, which may end in expressions of exasperation, such as “I won’t bother any more with it! I have already thought it over!” Such questions are paradoxical.

Likewise paradoxical, avers Wisdom, are the doctrines of metaphysics, when they are not platitudes. They are “truths which couldn’t but be true” (p. 264), similar to the infinite tautology of absolute skepticism. Usually, they are expressed as paradoxical questions that concern the character of foundations or of knowledge. Metaphysicians approach their questions in terms of general themes, such as things and persons, space and time, good and evil, and so on.

7. Philosophy of Religion

a. Epistemic Attitudes

Wisdom devotes considerable attention to discussing problems of philosophy of religion. His main claim here is that the religious believer and the atheist think about different worlds. “The theist,” he says, “[often] accuses the atheist of blindness and the atheist accuses the theist of seeing what isn’t there” (1944c, p. 158). This difference in attitude determines the difference in seeing different worlds (p. 160).

People with different attitudes see the same facts differently. For example, a married couple may enter a room, and one sense that someone had been there, while the one adamantly deny that there is any clue to substantiate the spouse’s hunch. Most such occurrences are rather a question of feeling than of experience. Wisdom considers it inappropriate in such cases to ask who is right.

Such exercises in reasoning are typically explored in philosophy as well as in religion. However, Wisdom holds that they also have place in some a priori domains of theoretical thinking—in philosophy of mathematics, for example, where two competing parties (say, logicists and constructivists) defend theses, each of them being “right” in their way.

Wisdom’s conclusion, clearly opposing the logic of Gottlob Frege and Russell, is that in such disciplines “the process of argument is not a chain of demonstrative reasoning” (p. 157). Of course, the growth of knowledge in these disciplines is, similarly to that in science, cumulative. However, it starts from several independent premises—not by mechanically iterating the transformation of a set of premises, as in Principia Mathematica.

Wisdom adduces that we can find a solution to a cognitive problem not only by adding new illuminations but also “by talk.” Occasionally, in the process of trying to demonstrate that our opponent is wrong, we become aware that it is we who are mistaken. Often our opponent has unconscious reasons for his attitude, which we should try to make explicit. Such a methodology finds us “connecting and disconnecting” cases, thus “explaining a fallacy in reasoning” (p. 161).

b. The Logic of God

In a 1950 BBC presentation titled “The Logic of God,” Wisdom introduces the example of someone who tries on a new hat and gets the following reaction: “My dear, it’s the Taj Mahal” (1965a). Literally understood, the claim that the hat is a temple is clearly absurd. However, just as absurd is the statement that we can or cannot know other minds. Be this as it may, such claims are not pointless. They simply call, in Wisdom’s view, for a “dialectic process in which they are balanced” (p. 263). Thus, the paradox “We are all mad” should be balanced with its opposite: “We are all sane.” We then arrive at the (quasi-Hegelian) synthesis, “Some of us are mad, but others are not.” Wisdom recommends the same procedure when we address metaphysical problems. Otherwise, we are exposed, he believes, to the threat of the one-sided “road to Solipsism [where] there blows the same wind of loneliness which blows on the road to the house with walls of glass which no one can break” (p. 282).

Wisdom maintains that “sometimes it is worth saying what everybody knows” (1950b, p. 2), in particular, as doing so changes our apprehension of the facts. Such statements do not tell the truth. They reveal it. Indeed, “we sometimes use words neither to give information… nor to express and evoke feelings… but to give greater apprehension of what is before us” (p. 6).

Not all questions have an answer. Among the great unanswerable questions is whether God exists. Wisdom avers that we have only fragmentary evidence for such existence, not proofs. If we want a complete proof here, we should need per impossible to adduce all of God’s characteristics. Similarly, the complete proof of the existence of the rainbow cannot be less complex than all its characteristics.

To substantiate this position, Wisdom refers to his theory of logical models, according to which different kinds of objects have their own logic. For example, the logic of God is much more alien to the logic of electricity, than the logic of milk is to the logic of wine (p. 15). It is more eccentric. A typical characteristic of the logic of God, in contrast to the logic of electricity, is that we have no idea what to expect about its real essence.

There are similar “logics of ignorance.” Thus, the actor may not know exactly how he will act when he assumes the role of his character. He will see that he is getting it wrong only after a first misstep. Conversely, the actor understands that he is on the right track only when his work is complete. Something similar happens when we act in our own character. Euripides, St. Paul, and Sigmund Freud observed how sometimes the agent is not aware that it is not he who performs his deeds. He is governed by his Super-Ego, the logic of which is close (at least for St. Paul) to that of God.

That our knowledge is not only knowledge of facts is attested, Wisdom holds, by the circumstance that, as Freud put it, we do not know even ourselves. We see this in the difficulty we experience when we strive to transcend limited judgments in order to reach some final judgment, or a “divine” judgment, which Wisdom describes as “a judgment which takes everything into account and gives it its correct weight” (1965d, p. 32-3).

c. The Meaning of Life

Wisdom considers the Existentialist movement in philosophy, rather popular on the Continent in the 1950s and 1960s, an evasion, a diversion from the real difficulties of life. He praises it for concentrating on something that only a relatively few philosophers considered worthy of debate in the decades immediately following the Second World War. He charges, however, that the existentialists’ arguments were by and large merely ad rem. It is well known, declares Wisdom, that “one of the best ways of keeping concealed the most horrible is to emphasize the horror of the less horrible and to denigrate the good” (1965c, p. 37).

Against the existentialists, Wisdom insists that despite all the misery in the world, there are situations in which we find complete meaning. He further notes that we can ask “What holds all this up?” but not “What holds up all things?” To be more exact, one cannot answer the question “What is the meaning of all this?” in a single determinate thought or sentence. We find the meaning, on Wisdom’s conception, in many scattered moments of cheerfulness that do not attach to intellectual dishonor, stupidity, or evasion.

Apparently, “What is the meaning of all this?” is not a meaningless question, as the logical positivists maintained. There are many clearly meaningful cases in which one asks “what is the meaning of all this,” as when, for example, the critic tries to grasp the idea of a play. We cannot give only one answer to such questions, though, nor can we supply a fully complete list of the things we believe to be the answer. This, however, does not mean that the words cheat us, as it were, and that such questions cannot be addressed in principle, or that we cannot progress toward an answer. Indeed, opines Wisdom, “the historians, the scientists, the prophets, the dramatists and the poets assist us in our attempts to answer the question of life” (p. 42).

Wisdom concludes that religious issues are also issues of fact (compare to § 6.2). They require new apprehension of facts, in the same way as the court aims at illumination and new apprehension of the facts. To articulate religious propositions is not, according to Wisdom, simply to express an attitude toward life, as the emotivists believe. Nor are such propositions merely matters of intuition or of decision.

8. References and Further Reading

a. Primary Sources

i. Books

  • 1931. Interpretation and Analysis in Relation to Bentham’s Theory of Definition, London: Kegan Paul.
  • 1931-3. Logical Constructions, ed. by J. J. Thomson, New York: Random House, 1969.
  • 1934a. The Problems of Mind and Matter, 2nd ed., Cambridge: Cambridge University Press.
  • 1952a. Other Minds, 2nd ed., Oxford: Blackwell, 1965.
  • 1953a. Philosophy and Psycho-Analysis, Oxford: Blackwell.
  • 1965a. Paradox and Discovery, Oxford: Blackwell.
  • 1991. Proof and Explanation: The Virginia Lectures, ed. by S. F. Barker, Lanham (Maryland): University of America Press.

ii. Papers

  • 1933. “Ostentation,” in (1953a): 1-15.
  • 1934b. “Is Analysis a Useful Method in Philosophy?” in (1953a): 16-35.
  • 1936. “Philosophical Perplexity,” in (1953): 36-50.
  • 1938. “Metaphysics and Verification,” in (1953a): 51-101.
  • 1943. “Critical Notice: C. H. Waddington, and others, Science and Ethics,” in (1953a): 102-111.
  • 1944a. “Moore’s Technique,” in (1953a): 120-148.
  • 1944b. “Philosophy, Anxiety and Novelty,” in (1953a): 112-119.
  • 1944c. “Gods,” in (1953a): 149-168.
  • 1946a. “Philosophy and Psycho-Analysis,” in (1953a): 169-181.
  • 1946b. “Other Minds,” in (1952a): 206-229.
  • 1947. “Bertrand Russell and Modern Philosophy,” in (1953a): 195-209.
  • 1948a. “Note on the New Edition of Professor’s Ayer’s Language, Truth and Logic,” in (1953a): 229-247.
  • 1948b. “Things and Persons,” in (1953a): 217-228.
  • 1950a. “Metaphysics,” in (1952a): 245-65.
  • 1950b. “The Logic of God,” in (1965a): 1-22.
  • 1952b. “Ludwig Wittgenstein, 1934-37,” in (1965a): 87-9.
  • 1953b. “Philosophy, Metaphysics and Psycho-Analysis,” in (1953a): 248-82.
  • 1957. “Paradox and Discovery,” in (1965a): 114-38.
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b. Secondary Sources

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Author Information

Nikolay Milkov
Email: nikolay.milkov@upb.de
University of Paderborn
Germany

Plato: The Academy

greek_vase Plato’s enormous impact on later philosophy, education, and culture can be traced to three interrelated aspects of his philosophical life: his written philosophical dialogues, the teaching and writings of his student Aristotle, and the educational organization he began, “the Academy.” Plato’s Academy took its name from the place where its members congregated, the Akadēmeia, an area outside of the Athens city walls that originally held a sacred grove and later contained a religious precinct and a public gymnasium.

In the fifth century B.C.E., the grounds of the Academy, like those of the Lyceum and the Cynosarges, the two other large gymnasia outside the Athens city walls, became a place for intellectual discussion as well as for exercise and religious activities. This addition to the gymnasia’s purpose was due to the changing currents in Athenian education, politics, and culture, as philosophers and sophists came from other cities to partake in the ferment and energy of Athens. Gymnasia became public places where philosophers could congregate for discussion and where sophists could offer samples of their wisdom to entice students to sign up for private instruction.

This fifth-century use of gymnasia by sophists and philosophers was a precursor to the “school movement” of the fourth century B.C.E., represented by Antisthenes teaching in the Cynosarges, Isocrates near the Lyceum, Plato in the Academy, Aristotle in the Lyceum, Zeno in the Stoa Poikile, and Epicurus in his private garden. Although these organizations contributed to the development of medieval, Renaissance, and contemporary schools, colleges, and universities, it is important to remember their closer kinship to the educational activities of the sophists, Socrates, and others.

Plato began leading and participating in discussions at the Academy’s grounds in the early decades of the fourth century B.C.E. Intellectuals with a variety of interests came to meet with Plato—who gave at least one public lecture—as well as conduct their own research and participate in dicussions on the public grounds of the Academy and in the garden of the property Plato owned nearby. By the mid-370s B.C.E., the Academy was able to attract Xenocrates from Chalcedon (Dillon 2003: 89), and in 367 Aristotle arrived at the Platonic Academy from relatively far-off Stagira.

While the Academy in Plato’s time was unified around Plato’s personality and a specific geographical location, it was different from other schools in that Plato encouraged doctrinal diversity and multiple perspectives within it. A scholarch, or ruler of the school, headed the Academy for several generations after Plato’s death in 347 B.C.E. and often powerfully influenced its character and direction. Though the Roman general Sulla’s destruction of the Academy’s grove and gymnasium in 86 B.C.E. marks the end of the particular institution begun by Plato, philosophers who identified as Platonists and Academics persisted in Athens until at least the sixth century C.E. This event also represents a transition point for the Academy from an educational institution tied to a particular place to an Academic school of thought stretching from Plato to fifth-century C.E. neo-Platonists.

Table of Contents

  1. The Academy Prior to Plato’s Academy: Sacred Grove, Religious Sanctuary, Gymnasium, Public Park
  2. Athenian Education Prior to Plato’s Academy: Old Education, Sophists, Socrates and his Circle
  3. The Academy in Plato’s Time
    1. Location and Funding
    2. Areas of Study, Students, Methods of Instruction
  4. The Academy after Plato
  5. References and Further Reading
    1. Primary Sources
    2. Secondary Sources

1. The Academy Prior to Plato’s Academy: Sacred Grove, Religious Sanctuary, Gymnasium, Public Park

In early times, the area northwest of Athens near the river Cephissus was known as the Akadēmeia or Hekadēmeia and contained a sacred grove, possibly named after a hero called Akademos or Hekademos (Diogenes Laertius, Lives and Opinions of Eminent Philosophers III.7-8, cited hereafter as “Lives”). Plutarch mentions a mythical Akademos as a possible namesake for the Academy, but Plutarch also records that the Academy may have been named after a certain Echedemos (Theseus 32.3-4). While the Academy may have been named after an ancient hero, it is also possible that an ancient hero may have been created to account for the Academy’s name.

The Academy was bordered on the east by Hippios Kolonos and to the south by the Kerameikos district, which was famous for its pottery production.  In the late sixth century B.C.E., the Peisistratid tyrant Hipparchus reportedly constructed a public gymnasium in the area known as the Academy (Suda, Hipparchou teichion). This building project, known for its expense, walled in part of the area known as the Academy. Hipparchus probably developed the gymnasium at the Academy to win favor with residents of the Kerameikos district. Like the other major gymnasia outside the city walls, the Lyceum and the Cynosarges, the Academy’s function as a gymnasium operated in tandem with its function as a religious sanctuary.

After Xerxes led the Persians to burn Athens in 480 B.C.E., Themistocles rebuilt the city wall in 478 B.C.E. (Thucydides 1.90), dividing the Kerameikos into an inner Kerameikos and outer Kerameikos. Some time afterwards, Cimon reportedly rebuilt the Academy as a public park and gymnasium by providing it with a water supply, running tracks, and shaded walks (Plutarch, Cimon 13.8).  On the way to the Academy from Athens, one passed from the inner Kerameikos to the outer Kerameikos through the Dipylon gate in the city’s wall; continuing on the road to the Academy, one passed through a large cemetery. Referring to the area of the outer Kerameikos on the way to the Academy, Thucydides writes, “The dead are laid in the public sepulcher in the most beautiful suburb of the city, in which those who fall in war are always buried, with the exception of those slain at Marathon” (Thucydides 2.34.5, trans. Crawley).  Pausanias, writing in the second century C.E., likewise describes the Academy as a district outside of Athens that has graves, sanctuaries, alters, and a gymnasium (Attica XXIX-XXX).  In addition to the shrines, altars, and gymnasium mentioned by Thucydides and Pausanias, there were also gardens and suburban residences in the nearby area (Baltes 1993: 6).

Due to the improvements initiated by Hipparchus and Cimon, the Academy became a beautiful place to walk, exercise, and conduct religious observances. Aristophanes’ The Clouds, first produced in 423 B.C.E., contrasts the rustic beauty of the Academy and traditional education of the past with the chattering and sophistic values of the Agora. Describing the difference, Aristophanes’ “Better Argument” says,

But you’ll be spending your time in gymnasia, with a gleaming, blooming body, not in outlandish chatter on thorny subjects in the Agora like the present generation, nor in being dragged into court over some sticky, contentious, damnable little dispute; no, you will go down to the Academy, under the sacred olive-trees, wearing a chaplet of green reed, you will start a race together with a good decent companion of your own age, fragrant with green-brier and catkin-shedding poplar and freedom from cares, delighting in the season of spring, when  the plane tree whispers to the elm. (1002-1008, trans. Sommerstein)

While The Clouds illustrates that the grounds of the Academy in the 420s had running tracks, a water source, sacred olive groves, and shady walks with poplar, plane, and elm trees, it is not clear whether the Academy was as free of sophistry as Aristophanes presents it, perhaps ironically, in his comedy. At any rate, the Academy was very soon to become a place for intellectual discussion, and its peaceful environment was also headed for disruption by the Spartan army’s occupation of its grounds during the siege of Athens in 405-4 B.C.E.

2. Athenian Education Prior to Plato’s Academy: Old Education, Sophists, Socrates and his Circle

The Greek word for education, paideia, covers both formal education and informal enculturation. Paideia was traditionally divided into two parts: cultural education (mousikē), which included the areas of the Muses, such as poetry, singing, and the playing of instruments, and physical education (gymnastikē), which included wrestling, athletics, and exercises that could be useful as training for battle. Instruction in cultural and physical education was not paid for by public expenditure in the archaic or classical period in Athens, so it was only available to those who could afford it. Education often took place in public places like gymnasia and palestras. During the classical period, writing and basic arithmetic became a basic part of elementary education as well.  In addition to formal education, attendance at religious festivals, dramatic and poetic competitions, and political debates and discussions formed an important part of Athenians’ education. Broadly, an Athenian man educated in the “Old Education” championed by Aristophanes’ “Better Argument” would be familiar with the poetry of Homer and Hesiod, be able to read, write, and count well enough to manage his personal life and participate in the life of the polis, and be cultured enough to appreciate the city’s comic and tragic festivals.

In the fifth century B.C.E., philosophers and sophists came to Athens from elsewhere, drawn by the city’s growing wealth and climate of intellectual activity. Anaxagoras likely came to Athens sometime between 480 and 460 B.C.E. and associated with Pericles, the important statesman and general (Plato, Phaedrus 270a). Parmenides and Zeno came to Athens in the 450s, and sophist Protagoras from Abdera came to Athens in the 430s and also associated with Pericles. Gorgias the rhetorician from Leontini came to Athens in 427 B.C.E., and he taught rhetoric for a fee to Isocrates, Antisthenes, and many others.

Itinerant teachers like Protagoras and Gorgias both supplemented and destabilized the traditional education provided in Athens, as Aristophanes’ comedy The Clouds, the dialogues of Plato, and other sources document. In order to gain paying students, sophists, rhetoricians, and philosophers would often make presentations in public places like the Agora or in Athens’s three major gymnasia, the Academy, the Cynosarges, and the Lyceum. While the accounts of Xenophon and Plato contradict Aristophanes’ comic portrayal of Socrates as a teacher of rhetoric and natural science, the Platonic dialogues do show Socrates frequenting gymnasia and palestras in search of conversation. In the dialogue Euthyphro, Euthyphro associates Socrates with the Lyceum (2a); in the dialogue Lysis, Socrates narrates how he was walking from the Academy to the Lyceum when he was drawn into a conversation at a new wrestling school (203a-204a). Similarly, the Euthydemus presents a conversation between Socrates and two sophists in search of students in a gymnasium building on the grounds of the Lyceum (271a-272e). While Socrates, unlike the sophists, did not take payment or teach a particular doctrine, he did have a circle of individuals who regularly associated with him for intellectual discussion. While the establishment of philosophical schools by Athenian citizens in the major gymnasia of Athens seems to be a fourth-century phenomenon, the Platonic dialogues indicate that gymnasia were places of intellectual activity and discussion in the last decade of the fifth century B.C.E., if not before.

3. The Academy in Plato’s Time

 As noted in the previous section, the Academy, the Lyceum, and the Cynosarges functioned as places for intellectual discussion as well as exercise and religious activity in the fifth century B.C.E. It is likely that the aristocratic Plato spent some of his youth at these gymnasia, both for exercise and to engage in conversation with Socrates and other philosophers. After Socrates’ death in 399 B.C.E., Plato is thought to have spent time with Cratylus the Heraclitean, Hermogenes the Parmenidean, and then to have gone to nearby Megara with Euclides and other Socratics (Lives III.6). Isocrates, student of Gorgias, began teaching in a private building near the Lyceum around 390 B.C.E., and Antisthenes, who also studied with Gorgias and was a member of Socrates’ circle, held discussions in the Cynosarges around that time as well (Lives VI.13). While the Platonic Academy is often seen as the prototype of a new kind of educational organization, it is important to note that it was just one of many such organizations established in fourth-century Athens.

It is likely that Isocrates and Antisthenes established schools of some sort before Plato. Contemporary scholars often assign a founding date for the Academy between the dates of 387 B.C.E. and 383 B.C.E., depending on these scholars’ assessment of when Plato returned from his first trip to Syracuse. Rather than assign a particular date at which the Academy was founded, as though ancient schools possessed formal articles or charters of incorporation (see Lynch 1972), it is more plausible to note that Plato began associating with a group of fellow philosophers in the Academy in the late 390s and that this group gradually gathered energy and reputation throughout the 380s and 370s up until Plato’s death in 347 B.C.E.

a. Location and Funding

Plato was himself from the deme of Collytus, a wealthy district southwest of the Acropolis and within the city walls built by Themistocles. Collytus was a few miles from the Academy, so Plato’s relocating nearby the Academy would have been an important step in establishing himself there.  While some have emphasized the Academy’s remoteness from the Agora (Rihill 2003:174), the six stades (three quarters of a mile) from the Dipylon gate and three more stades from the Agora would not have constituted much of a barrier to anyone interested in seeing the goings on of the Academy in Plato’s time.

In keeping with the Academy’s customary use as a place of intellectual exchange, Plato used its gymnasium, walks, and buildings as a place for education and inquiry; discussions held in these areas were semi-public and thus open to public engagement and heckling (Epicrates cited in Athenaeus, Sophists at Dinner II.59; Aelian, Historical Miscellany 3.19; Lives VI.40). While some scholars have thought that Plato somehow resided in the sacred precinct and gymnasium of the Academy or purchased property there, this is not possible, for religious sanctuaries and areas set aside for gymnasia were not places where citizens (or anyone else) could set up residency. Rather, as Lynch, Baltes, and Dillon have argued, Plato was able to purchase a property with its own garden nearby the sanctuaries and gymnasium of Academy. While much of the Platonic Academy’s business was conducted on the public grounds of the Academy, it is natural that discussions and possibly shared meals would also occur at Plato’s nearby private residence and garden. Given the proximity of Plato’s private residence to the sanctuary and gymnasium of the Academy and the fact that his nearby property and school were both referred to as “the Academy” (Plutarch, On Exile 603b), there has been confusion about the particulars of the physical plant of the Platonic Academy.

Plato was of aristocratic stock and of at least moderate wealth, so he had the financial means to support his life of philosophical study. Following Socrates’ example and departing from the sophists and Isocrates, Plato did not charge tuition for individuals who associated with him at the Academy (Lives IV.2). Still, students at the Academy had to possess or come up with their own sustenance (Athenaeus, Sophists at Dinner IV.168). In addition to receiving funds from either Dion of Syracuse or Anniceris of Cyrene to purchase property near the Academy (Lives III.20), Diogenes Laertius records that Dion paid for Plato’s costs as choregus or chorus leader—a claim also made in Plutarch’s Dion XVII.2)—and purchased Pythagorean philosophical texts for him, and that Dionysus of Syracuse gave him eighty talents (Lives III.3,9). Part of the purpose of Plato’s trips to Syracuse may have been to participate in political reform, but it is also possible that Plato was seeking patrons for the philosophical activity engaged in at the Academy.

While it is probable that Plato associated with other philosophers, including the Athenian mathematician Theaetetus, in the Academy as early as the late 390s (see Nails 2009: 5-6; Nails 2002: 277; Thesleff 2009: 509-518 with Proclus’s Commentary on the First Book of Euclid’s Elements, Book 2, Chapter IV for more details on Theaetetus’s involvement with the Academy), it is the purchase of the property near the Academy after his trip to see Dion in Syracuse that scholars often refer to when speaking of the founding of the Academy in either 387 B.C.E. or 383 B.C.E. While purchase of this property was important to the development of the Platonic Academy, it is important to remember, as Lynch has shown, that Plato’s Academy was not legally incorporated or a juridical entity.  While the wills of Theophrastus (Lives V.52-53) and Epicurus (Lives X.16-17) make provisions for the continuation of their schools and the future control of school property, the will of Plato does not mention the Academy as such (Lives III.41-43). This indicates that while the Platonic Academy was thriving during Plato’s lifetime, it was not essentially linked to any private property possessed by Plato (compare Dillon 2003: 9; see further Nails 2002: 249-250).

b. Areas of Study, Students, Methods of Instruction

 The structure of the Platonic Academy during Plato’s time was probably emergent and loosely organized. Scholars infer from the varied viewpoints of thinkers like Eudoxus, Speusippus, Xenocrates, Aristotle, and others present in the Academy during Plato’s lifetime that Plato encouraged a diversity of perspectives and discussion of alternative views, and that being a participant in the Academy did not require anything like adherence to Platonic orthodoxy. In this way, Plato reflected Socrates’ willingness to discuss and debate ideas rather than the sophists’ claim to teach students mastery of a particular subject matter.  To get a sense of the topics discussed in the Academy, our primary sources are the Platonic dialogues and our knowledge of the persons present at the Academy.

While it is tempting to talk of teachers and students at the Academy, this language can lead to difficulties. While Plato was clearly the heart of the Academy, it is not clear how, if at all, formal status was accorded to members of the Academy. The Greek terms mathētēs (student, learner, or disciple), sunēthēs (associate or intimate), hetairos (companion), and philos (friend), as well as other terms, seem to have been variously used to describe the persons who attended the Academy (Baltes 1993: 10-11; Saunders 1986: 201).

While the precise function of the Platonic dialogues within the Academy cannot be settled, it is practically certain that they were studied and perhaps read aloud by the Academics in Plato’s time. It is also likely that the dialogues were circulated as a way to attract possible students (Themistius, Orations 23.295). As a cursory survey, dialogues like the Republic, Timaeus, and Theaetetus show Plato’s interest in mathematical speculation; the Republic, Statesman, and the Laws attest to Plato’s interest in political theory; the Cratylus, Gorgias, and Sophist show an interest in language, logic, and sophistry, and many dialogues, including the Parmenides, Sophist, and Republic show an interest in metaphysics and ontology. While Plato’s interests were varied and interconnected, the topics of the dialogues reflect topics that Academics were likely to be engaged with.

The array of topics examined in Plato’s dialogues do parallel some of what we know about the philosophical interests of the individuals at the Academy in Plato’s lifetime. Theaetetus of Athens and Eudoxus of Cnidus were mathematicians, and Phillip of Opus was interested in astronomy and mathematics in addition to serving as Plato’s secretary and editor of the Laws. Aristotle, a wealthy citizen of Stagira, came to the Academy in 367 as a young man and stayed until Plato’s death in 347. Aristotle’s twenty-year long participation in the Platonic Academy shows Plato’s openness in encouraging and supporting philosophers who criticized his views, the Academy’s growing reputation and ability to attract students and researchers, and sheds some light on the organization of the Academy. Aristotle reportedly taught rhetoric at the Academy, and it is certain that he researched rhetorical and sophistical techniques there. It is very probable that Aristotle began writing many of the works of his that we possess today at the Academy (Klein 1985: 173), including possibly parts of the biological works, even though biological research based on empirical data is not a line of inquiry that Plato pursued himself. Aristotle’s multiple references to Platonic dialogues in his own works also suggest how the Platonic dialogues were used by students and researchers at the Academy. While most of the pupils at the Platonic Academy were male, Diogenes Laertius lists two female students, Lastheneia of Mantinea and Axiothea of Philius in his list of Plato’s students (Lives III.46-47).

While the Platonic Academy was a community of philosophers gathered to engage in research and discussion around a wide array of topics and questions, the Academy, or at least the individuals gathered there, had a political dimension. Plutarch’s Reply to Colotes claims that Plato’s companions from the Academy were involved in a wide variety of political activities, including revolution, legislation, and political consulting (1126c-d). The various Epistles ascribed to Plato support this view by attesting to Plato’s involvement in the politics of Syrcause, Atarneus, and Assos. While claims that the Academy was an “Organized School of Political Science” or the “RAND Corporation” of antiquity go too far in ascribing formal structure and organization to the Academy, Plato and the individuals associated with the Academy were involved in the political issues of their time as well as purely theoretical discussions about political philosophy.

As noted above, some of the discussions Plato held were on the public grounds of the Academy, while other discussions were held at his private residence. Aristoxenus records at least one poorly received public lecture by Plato on “the good” (Elements of Harmonics II.30), and a comic fragment from Epicrates records Plato, Speusippus, Menedemus, and several youths engaging in dialectical definition of a pumpkin (Athenaeus, Sophists at Dinner 2.59). While it is difficult to reconstruct how instruction occurred at the Academy, it seems that dialectical conversation, lecture, research, writing, and the reading of the Platonic dialogues were all used by individuals at the Academy as methods of philosophical inquiry and instruction.

Although the establishment of the Academy is an important part of Plato’s legacy, Plato himself is silent about his Academy in all of the dialogues and letters ascribed to him. The word “Academy” occurs only twice in the Platonic corpus, and in both cases it refers to the gymnasium rather than any educational organization. One occurrence, already mentioned, is from the Lysis, and it describes Socrates walking from the Academy to the Lyceum (203a). The other occurrence, in the spurious Axiochus, refers to ephebic and gymnastic training (367a) on the grounds of the Academy and does not refer to anything that has to do with Plato’s Academy.

Plato’s silence about the Academy adds to the difficulty of labeling his Academy with the English word “school.” Diogenes Laertius refers to Plato’s Academy as a “hairesis,” which can be translated as “school” or “sect”  (Lives III.41). The noun “hairesis” comes from the verb “to choose,” and it thereby signifies “a choice of life” as much as “a place of instruction.” The head of the Academy after Plato was called the “scholarch,” but while scholē forms the root of our word “school” and was used to refer to Plato’s Academy (Lives IV.2), it originally had the meaning of “leisure.” The Greek word diatribē can also be translated as “school” from its connotation of spending time together, but no matter what Greek term is used, the activities occurring at the Academy during Plato’s lifetime do not neatly map on to any of our concepts of school, university, or college. Perhaps the clearest term to describe Plato’s Academy comes from Aristophanes’ Clouds, written at least three decades before the Academy was established: phrontistērion (94). This term can be translated as “think tank,” a term that may be as good as any other to conceptualize the Academy’s multiple and evolving activities during Plato’s lifetime.

4. The Academy after Plato

In 347 B.C.E. Plato died at the age of approximately eighty years old. According to Diogenes Laertius, Plato was buried in the Academy (Lives III.41). Unlike the claim that Plato purchased property in the sacred precinct of the Academy, this assertion is possible, for the grounds of the Academy were used for burial, shrines, and memorials. At any rate, Pausanias records that in his own time there was a memorial to Plato not far from the Academy (Attica XXX.3).

Although the entrenchment of the words   “academy” and “academic” in contemporary discourse make the persistence of the Platonic Academy seem inevitable, this is probably not how it appeared to Plato or to members of the Academy after his death (Watts 2007: 122). Rather, the Academy continued to develop its sense of identity and plans for persistence after Plato’s death.

One way to develop a partial picture of the Academy after Plato’s death is to review the succession of Academic scholarchs. The chronological succession of scholarchs after Plato, according to Diogenes Laertius, is as follows:

  • Speusippus of Athens, Plato’s nephew, was elected scholarch after Plato’s death, and he held that position until 339 B.C.E.
  • Xenocrates of Chalcedon was scholarch until 314 B.C.E.
  • Polemo of Athens was scholarch of the Academy until 276 B.C.E.
  • Crates of Athens, a pupil of Polemo, was the next scholarch.
  • Arcesilaus of Pitane was scholarch until approximately 241 B.C.E.
  • Lacydes of Cyrene was scholarch until approximately 216 B.C.E.
  • Telecles and Evander, both of Phocaea, succeed Lacydes as dual scholarchs.
  • Hegesinus of Pergamon succeed the dual scholarchs from Phocaea.
  • Carneades of Cyrene succeeded Hegesinus.
  • Clitomachus of Carthage succeeded Carneades in 129 B.C.E.

While Clitomachus is the last scholarch listed by Diogenes Laertius, Cicero provides us with information about Philo of Larissa, with whom he himself studied (De Natura Deorum I.6,17). Philo was a pupil of Clitomachus and was a head of the Academy (Academica II.17; Sextus Empiricus, Outlines of Phyrrhonism I.220). Antiochus of Ascalon, who also taught Cicero, is sometimes considered a head of the Academy (Sextus Empiricus, Outlines of Phyrrhonism I.220-221), but his philosophical position (I.235) and the fact that his school did not meet on the grounds of the Academy (Cicero, De Finibus V.1) makes Antiochus’s school discontinuous with the Platonic Academy.

The terms “Old Academy,” “Middle Academy,” and “New Academy” are used in somewhat different ways by Cicero, Sextus Empiricus, and Diogenes Laertius to describe the changing viewpoints of the Platonic Academy from Speusippus to Philo of Larissa. What seems clear from the various accounts is that, with Arcesilaus, a skeptical edge entered into Academic thinking that persisted through Carneades and Philo of Larissa.

The Mithridatic War of 88 B.C.E. and Sulla’s destruction of the grounds of the Academy and Lyceum as part of the siege of Athens in 86 B.C.E. (Plutarch, Sulla XII.3) mark the rupture between the geographical precinct of the Academy and the lineage of philosophical instruction stemming from Plato that together constitute the Platonic Academy. The destruction of the gymnasium at the Lyceum also marks the end of Aristotle’s peripatetic school (Lynch 1972: 207).

While the Platonic Academy can be said to end with the siege led by Sulla, philosophers including Cicero, Plutarch of Chaeronea, and Proclus continued to identify themselves as Platonists or Academics. In 176 C.E., the Roman Emperor and Stoic philosopher Marcus Aurelius helped continue the influence of Platonic and Academic thought by establishing Imperial Chairs for the teaching of Platonism, Stoicism, Aristotelianism, and Epicureanism, but the holders of these chairs were not associated with the long-abandoned schools that once met on the grounds of the Lyceum or the Academy.

Sometime in the fourth century C.E., a Platonic school was reestablished in Athens by Plutarch of Athens, though this school did not meet on the grounds of the Academy. After Plutarch, the scholarchs of this Platonic school were Syrianus, Proclus, Marinus, Isidore, and Damascius, the last scholarch of this Academy. In 529 C.E. the Christian Roman Emperor Justinian forbade Pagans from publicly teaching, which, along with the Slavonic invasions of 580 C.E. (Lynch 1972: 167), marks an end of the flourishing of Neo-Platonism in Athens.

The Platonic Academy forms an important part of Plato’s intellectual legacy, and analyzing it can help us better understand Plato’s educational, political, and philosophical concerns. While studying the Academy sheds light on Plato’s thought, its history is also invaluable for studying the reception of Plato’s thought and for gaining insight into one of the crucial sources of today’s academic institutions. Indeed, the continued use of the words  “academy” and “academic” to describe educational organizations and scholars through the twenty first century shows the impact of Plato’s Academy on subsequent education.

Today, the area that contains the sacred precinct and gymnasium that housed Plato’s Academy lies within a neighborhood known as Akadimia Platonos. The ruins of the Academy are accessible by foot, and a small museum, Plato’s Academy Museum, helps to orient visitors to the site.

5. References and Further Reading

a. Primary Sources

  • Aelian, (Claudius Aelianus) (2nd-3rd cn. C.E.). Historical Miscellany. Trans. Nigel G. Wilson. Cambridge, MA: Loeb Classical Library, 1997.
    • Chapter XIX of Book 3 of Aelian’s Historical Miscellany is titled “Of the dissention between Aristotle and Plato.” This chapter records a conflict between Plato and Aristotle that has been used to infer that Plato had a private home where he taught in addition to leading conversations on the grounds of the Academy.
  • Aristophanes (c.448-380 B.C.E.). Clouds. Trans. Alan Sommerstein. Warminster: Aris and Phillips, 1991.
    • While written too early to shed light on Plato, this text is crucial for understanding Athenian education, the sophists, and Socrates. It also contains the passage cited above that describes the grounds of the Academy in the 420s.
  • Aristotle (384-322 B.C.E.).
    • The writings of Aristotle are a valuable resource for learning more about the philosophies of some of the individuals that were part of the early Academy. See for example the references to Speusippus in Metaphysics Zeta, Chapter 2, Lambda, Chapter 7, and Mu, Chapter 7; see also the references Euxodus in Metaphysics Alpha, Chapter 8, Lambda, Chapter 8, and Nicomachean Ethics, Book 10, Chapter 2.
  • Aristoxenus of Tarentum (c.370-300 B.C.E.). The Harmonics of Aristoxenus. Ed. and trans. Henry S. Macran. Oxford: Clarendon Press, 1902.
    • Aristoxenus was a student of Aristotle’s and he is an early source for Plato’s public lecture “On the Good.”
  • Athenaneus of Naucratis (2nd-3rd cn. C.E.). The Deipnosophists. In Seven Volumes. Trans. Charles Burton Gluck. Cambridge, MA: Loeb Classical Library, 1951.
    • This lengthy work is a source of much information about antiquity. Scholars of the Academy are particularly drawn to the fragment from Epicrates preserved by Athenaneus that gives a comic presentation of Platonic dialectic.
  • Cicero, Marcus Tullius (106-43 B.C.E.).
    • Cicero’s many writings, including Academia, De Natura Deorum, De Finibus, and Tusculan Disputions contain information about the Academy.
  • Diogenes Laertius (2nd-3rd cn. C.E.). Lives and Opinions of Eminent Philosophers. Two Volumes. Trans. R. D. Hicks. Cambridge, MA: Loeb Classical Library, 1925.
    • Diogenes is an invaluable resource for the lives of ancient philosophers, although he is writing five hundred or so years after the philosophers he describes.
  • Pausanias. (2nd cn. C.E.). Description of Greece. Four Volumes. Trans. W. H. S. Jones. Cambridge, MA: Loeb Classical Library, 1959.
    • Book I of Pausanias’ work deals with Attica; Chapters XXI-XXX shed light on the history of the Academy and how it appeared to Pausanias several centuries later.
  • Philodemus. (c.110-c.30 B.C.E.). Index Academicorum.
    • Philodemus was an Epicurean philosopher who wrote a work on the Platonic Academy. Some fragments of this work have been discovered. For more information, see Blank (2019), below.
  • Plato. Complete Works. Ed. John Cooper. Indianapolis: Hackett, 1997.
    • While the dialogues and letters of Plato do not mention the Platonic Academy, they are an important resource in understanding Plato’s educational and political commitments and activities as well as the educational environment of Athens in the last few decades of the fifth century.
  • Plutarch of Chaeronea (c.45-125 C.E.). Parallel Lives and Moralia.
    • Plutarch’s works are collected in the Loeb Classical Library under Lives (Eleven Volumes) and Moralia (Fifteen Volumes). Particularly valuable for the student of the Academy are Reply to Colotes and Life of Dion, but many of the works found in Plutarch’s corpus shed light on Plato, the Academy, and Platonism.
  • Proclus (412-485 C.E.). A Commentary on the First Book of Euclid’s Elements. Trans. Glenn R. Morrow. Princeton: Princeton University Press, 1970.
    • Book 2, Chapter IV of Proclus’s commentary gives an account of the development of mathematics that includes helpful information about Plato and other members of the Academy. The “Foreword to the 1992 Edition” of Morrow’s translation by Ian Mueller is also helpful to students of Plato’s Academy.
  • Sextus Empiricus (2nd-3rd cn. C.E.). Outlines of Pyrrhonism. Four Volumes. Trans. R. G. Bury. Cambridge, MA: Loeb Classical Library, 1955.
    • As part of his presentation of skepticism, Sextus articulates how skepticism and Academic philosophy differ in Book I, Chapter XXXIII.
  • Suda.
    • The Suda is a tenth-century C.E. Byzantine Greek encyclopedia. The entries on “To Hipparchou teichion,” “Akademia,” and “Platon” were helpful for this article. An online version of the Suda can be accessed at http://www.stoa.org/sol/
  • Themistius (c.317-388 B.C.E.). The Private Orations of Themistius. Trans. Robert J. Penella. Berkeley: University of California Press, 2000.
    • Themistius was a philosopher and senator in the fourth century C.E. who taught in Constantinople. In his 23rd Oration, “The Sophist” he relays that a Corinthian farmer became Plato’s student after he read the Gorgias; Axiotheia had a similar experience reading the Republic, and Zeno of Citium came to Athens after reading the Apology of Socrates.
  • Thucydides (c.5th cn. B.C.E.). The Peloponnesian War. Ed. Robert B. Strassler. Trans. Richard Crawley. New York: Touchstone, 1998.
    • While Thucydides’ work does not shed light on the Academy, he does describe its environs and other aspects of Athenian history that are important for understanding Plato.

b. Secondary Sources

  • Athanassiadi, Polymnia. Damascius. The Philosophical History. Athens: Apamea Cultural Association, 1999.
  • Baltes, Matthias. “Plato’s School, the Academy,” Hermathena, No. 155 (Winter 1993): 5-26.
    • A very clear and well documented portrait of Plato’s Academy.
  • Blank, David, “Philodemus,” The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.), URL = .
  • Brunt, P. A. “Plato’s Academy and Politics” in Studies in Greek History and Thought. Oxford: Oxford University Press, 1993.
  • Cherniss, Harold. The Riddle of the Early Academy. Berkeley: University of California Press, 1945.
  • Chroust, Anton-Herman. “Plato’s Academy: The First Organizational School of Political Science in Antiquity,” The Review of Politics, Vol. 29, No. 1 (Jan., 1967): 25-40.
  • Dancy, R. M. Two Studies in the Early Academy. Albany: State University of New York Press, 1991.
  • Dillon. John. The Heirs of Plato: A Study of the Old Academy (347-274 BC). Oxford: Clarendon Press, 2003.
    • A study of the Academy with special attention to the philosophies of Plato’s successors.
  • Dillon, John. The Middle Platonists: 80 B.C. to A.D. 220. Ithaca: Cornell University Press, 1996.
  • Glucker, John. Antiochus and the Late Academy. Göttingen: Hypomnemata 56, 1978.
  • Hadot, Pierre. What is Ancient Philosophy? Trans. Michael Chase. Cambridge, MA: Harvard University Press, 2002.
  • Hornblower, Simon and Anthony Spawforth. The Oxford Classical Dictionary. 3rd ed. Oxford: Oxford University Press, 2003.
  • Klein, Jacob. Lectures and Essays. Annapolis: St. John’s College Press, 1985.
  • Lynch, John Patrick. Aristotle’s School: A Study of a Greek Educational Institution. Berkeley: University of California Press, 1972.
    • This work is essential to anyone investigating classical educational institutions.
  • Mintz, Avi. Plato: Images, Aims, and Practices of Education. Cham: Switzerland: Springer, 2018.
  • Nails, Debra. Agora, Academy, and the Conduct of Philosophy. Dordrecht: Kluwer Academic Publishers, 1995.
  • Nails, Debra. The People of Plato: A Prosopography of Plato and Other Socratics. Indianapolis: Hackett Publishing, 2002.
    • This work provides historical context for all of the individuals mentioned in the Platonic dialogues.
  • Nails, Debra. “The Life of Plato of Athens” in A Companion to Plato, edited by Hugh Benson. Malden, MA: Wiley-Blackwell Publishing, 2009.
  • Natali, Carlo. Aristotle: His Life and School. Edited by D. S. Hutchinson. Princeton: Princeton University Press, 2013.
  • Press, Gerald A., ed. The Bloomsbury Companion to Plato. London: Bloomsbury Academic, 2015.
    • A very valuable reference work on Plato. Chapter 1, “Plato’s Life—Historical and Intellectual Context” and Chapter 5, “Later Reception, Interpretation and Influence of Plato and the Dialogues” are particularly valuable for those interested in the history of the Academy.
  • Preus, Anthony. Historical Dictionary of Ancient Greek Philosophy. 2nd edition. Lanham: Rowman & Littlefield Publishers, 2015.
    • This clear and reliable historical dictionary is useful for students of ancient Greek philosophy.
  • Rihill, T. E. “Teaching and Learning in Classical Athens,” Greece & Rome, Vol. 50, No.2 (Oct., 2003): 168-190.
  • Saunders, Trevor J. “‘The Rand Corporation of Antiquity’? Plato’s Academy and Greek Politics” in Studies in Honor of T. B. L. Webster, vol. I, eds. J. H. Betts et al. Bristol: Bristol Classical Press, 1986.
  • Thesleff, Holger. Platonic Patterns: A Collection of Studies. Las Vegas: Parmenides Publishing, 2009.
  • Wareh, Tarik. The Theory and Practice of Life: Isocrates and the Philosophers. Cambridge, MA: Center for Hellenic Studies, 2012.
  • Watts, Edward. “Creating the Academy: Historical Discourse and the Shape of Community in the Old Academy, The Journal of Hellenic Studies, Vol. 127 (2007): 106-122.
    • This article argues that the Old Academy developed in an unplanned fashion and that the Old Academy attempted to craft its identity based on life-style and character as much as doctrine.

Author Information

Lewis Trelawny-Cassity
Email: lcassity@antiochcollege.edu
Antioch College
U. S. A.

James Frederick Ferrier (1808—1864)

James Frederick Ferrier was a mid-nineteenth-century Scottish metaphysician who developed the first post-Hegelian system of idealism in Britain. Unlike the British Idealists in the latter half of the nineteenth century, he was neither a Kantian nor a Hegelian. Instead, he largely develops his idealist metaphysics via his defense of Berkeley and through his rejection of Thomas Reid’s philosophy of common sense. In this way, he is a transitional figure between the philosophy of Enlightenment Scotland and the development of British Idealism in the latter half of the nineteenth century. Ferrier was also the first philosopher in English to refer to the philosophy of knowledge as Epistemology.

The most fully realized version of his metaphysics appears in his Institutes of Metaphysic. For Ferrier, epistemology is primary and must be the starting point for philosophy. His metaphysics depends on the axiom that the minimum unit of cognition involves a synthesis of subject-with-object, which is the absolute in cognition. From here he develops an idealist ontology, which concludes that which really exists is the absolute: some self in union with some object. The central features of his philosophy include the importance of self-consciousness, a rejection of noumena or things-in-themselves, and his theory of ignorance.

Table of Contents

  1. Life and Works
  2. Thought and Writings
    1. Self-consciousness
    2. Reappraisal of Berkeley
    3. Critique of Reid
    4. Idealist Metaphysics
  3. Reception and Influence
  4. References and Further Reading
    1. Primary Sources
    2. Secondary Sources

1. Life and Works

Ferrier was born in Edinburgh, Scotland, in 1808. His father, John Ferrier, was a lawyer known as a Writer to the Signet, and his mother was Margaret Wilson. His family was well connected; his uncle, John Wilson (also known as “Christopher North”), was an author and the Professor of Moral Philosophy at Edinburgh University, and his aunt was the novelist Susan Ferrier. Notable figures such as Sir Walter Scott, James Hogg, William Wordsworth, and Thomas De Quincey were acquainted with Ferrier and his family. He began his education in Ruthwell, Dumfriesshire, where he lived with the family of a Rev. Dr. Duncan. He then went to Edinburgh High School, followed by a period at another school in Greenwich. At the age of seventeen, he attended Edinburgh University for two academic sessions from 1825 to 1827. And, then in 1828 he moved to Oxford to study at Magdalen College for his B.A., which he received in 1831. His student life was unexceptional, and he did not show a particular aptitude for philosophy until later in his life.

He returned to Edinburgh after graduation and began a short-lived career in law. It was at this time that he developed his interest in philosophy. In the early 1830s he became friends with the philosopher Sir William Hamilton, and they remained in close contact until Hamilton’s death in 1856. Indicative of his growing interest in German thought, Ferrier traveled to Germany in 1834 where he spent several months in Heidelberg; his awareness of the German Idealists is apparent from the fact that he returned to Scotland with a photograph and a medallion of Hegel. In 1837 he married his cousin Margaret Wilson who was the daughter of his famous uncle “Christopher North.” By all accounts, they had a happy marriage and went on to have five children.

In the late 1830s, Ferrier started to publish articles in philosophy, and this led to his subsequent academic career. In 1842 he gained his first academic chair, becoming the Professor of Civil History at Edinburgh. In 1844-1845 he acted as Hamilton’s substitute in the Chair of Logic and Metaphysics at Edinburgh during the older philosopher’s illness. Then, in 1845, Ferrier moved his family to St. Andrews where he became the Professor of Moral Philosophy and Political Economy. He unsuccessfully attempted to get two Edinburgh Chairs: Moral Philosophy in 1852 and Logic and Metaphysics in 1856. He was unsuccessful in the first case due to sectarian politics and in the latter instance because his metaphysics were considered to be too far from the Scottish philosophy of his predecessors. For this reason, he remained at St Andrews for the remainder of his career. He died in St Andrews in 1863, and he is buried in St Cuthbert’s Churchyard, which is in the city center of Edinburgh.

Ferrier published several articles on literature and philosophy during his lifetime, and many of these were published in Blackwood’s Magazine. Among his articles, there are a few that are particularly indicative of his philosophical interests and eloquent writing style. These are his seven-part series “An Introduction to a Philosophy of Consciousness” (1838-1839), “Berkeley and Idealism” (1842), and “Reid and the Philosophy of Common Sense” (1847). A selection of his collected works appears in three volumes (originally published by Blackwood and Sons in 1875 and republished by Thoemmes Press in 2001). The first volume contains his most significant work, the Institutes of Metaphysic, which was originally published in 1854; here, Ferrier presents a complete system of metaphysics. The contemporary reaction to this was mixed, and Ferrier believed that certain critics, in an attempt to stifle his self-designated “new Scottish philosophy” in favor of the more traditional, or “old Scottish philosophy,” of his predecessors, deliberately misinterpreted his Institutes. Therefore, he subsequently wrote a scathing defense of the Institutes called Scottish Philosophy: The Old and the New (1856) in which he reiterates his arguments in favor of idealism and attacks his critics. A selection from Scottish Philosophy appears as “Appendix” to “Institutes of Metaphysic” in the first volume of his complete works. The second volume contains his lectures on Greek Philosophy, which he worked on in the later years of his life and was published posthumously. The final volume consists of a selection of his articles.

2. Thought and Writings

a. Self-consciousness

A topic that Ferrier concentrates on throughout his philosophical works is self-consciousness, which he generally refers to as “consciousness.” It is: “that notion of self, and that self-reference, which in man generally, though by no means invariably, accompanies his sensations, passions, emotions, play of reason, or states of mind whatsoever” (Ferrier 2001: vol. 3. 40). His focus on self-consciousness is central to his rejection of the Enlightenment goal to develop a “science of human nature.” Further, it forms the basis of his idealism.

He places upmost importance on self-consciousness because he believes that it is the peculiar and defining characteristic of humanity. He contends that things such as sensation and the capacity for reason are not only shared with other animals but they are given by nature; the human being who is subject to them is akin to “a spoke in an unresting wheel. Nothing connected with him is really his. His actions are not his own” (Ferrier 2001: vol. 3. 36). By contrast, consciousness is the act of will through which a thing becomes a person. One is not born conscious, it must be asserted: “The notion of self … is absolutely genetic or creative. Thinking oneself ‘I’ makes oneself ‘I,’ and it is only by thinking himself ‘I’ that a man can make himself ‘I’; or, in other words, change an unconscious thing into that which is now a conscious self” (Ferrier 2001: vol. 3. 109). Prior to consciousness there is no self or personality; without it the human being is a creature of nature that lives for others. Yet, post-consciousness a person’s acts are her own. It follows that consciousness is the precondition for everything that involves a self. In this way, consciousness is required for freedom, responsibility, morality, religion, and conscience.

Moreover, Ferrier explains in “An Introduction to a Philosophy of Consciousness” that a person’s knowledge of the external world depends on an act of negation in which she distinguishes between the self and the not-self. Thus, one becomes aware of the not-self in conjunction with the self. He describes this principle of idealism as “the fundamental act of humanity” (Ferrier 2001: vol. 3. 177). The concomitance of self and other forms the basis of his metaphysics, and it is a topic that he returns to throughout his published works.

In “An Introduction to a Philosophy of Consciousness” he sets out his concerns with contemporary philosophy and calls for a change of focus. His primary target is the Enlightenment goal to develop a “science of human nature.” In his view, this project is impossible because humanity is essentially different from anything else in the world that can be studied. For instance, in astronomy there is a distinction between the subject and the object; the scientist (the subject) is removed from the celestial objects (the objects) that she studies. Yet, in a “science of human nature” the philosopher is at once both the subject and the object. Now, given that self-consciousness is the defining feature of humanity and thereby central to any account of humanity, a problem arises. If the mind is an object of research, the object is deprived of its characteristic feature, namely self-consciousness, which remains with the subject of the research, leaving nothing but “a wretched association machine” (Ferrier 2001: vol. 3. 195). But, if the mind is considered with self-consciousness, then it cannot be properly considered an object of research because the objectivity is lost in so far as the subject and the object are identical. This leads Ferrier to suggest a change of focus for philosophy; instead of the empirical endeavor of a “science of human nature,” he prefers a more metaphysical approach, which is the development of a “philosophy of consciousness.”

In suggesting a “philosophy of consciousness,” Ferrier conceives philosophy as an extension of what people already do. Philosophy and self-consciousness are different only in degree and not in kind. Philosophy is a systematic and elevated self-consciousness, whereas self-consciousness is unsystematic and informal philosophy. He describes it as follows: “Consciousness is philosophy nascent; philosophy is consciousness in full bloom and blow … thus all conscious men are to a certain extent philosophers, although they may not know it” (Ferrier 2001: vol. 3. 197).

b. Reappraisal of Berkeley

Later in the nineteenth century, the British Idealists such as T. H. Green, F. H. Bradley, and Edward Caird were influenced by Kant and the German Idealists. Ferrier was aware of the German philosophers, but his own idealism does not appear to be directly influenced by them. Nonetheless, he was the first Scottish philosopher to seriously consider them. Thomas de Quincey said that: “he was introduced, as if suddenly stepping into an inheritance, to a German Philosophy refracted through an alien Scottish medium” (The Testimonials of J.F. Ferrier 1852, p.22). His friend and mentor, Hamilton, attempted to synthesize the commonsense philosophy deriving from Reid with the transcendental realism of Kant. Ferrier separates himself from Kant (and by extension also from Hamilton) by rejecting the existence of noumena or thing-in-themselves in the absence of percipient beings. He considers the German Idealists in a more favorable light, and he wrote biographical entries on both Schelling and Hegel for the Imperial Dictionary of Philosophy (see Ferrier 2001: vol. 3. 545-568). He also makes the occasional reference to Fichte, Schelling, and Hegel in his published works; in general, he views them positively, while depicting Hegel as an opaque genius. For instance, he says:

whatever truth there may be in Hegel, it is certain that his meaning cannot be wrung from him by any amount of mere reading, any more than the whisky which is in bread … can be extracted by squeezing a loaf into a tumbler. He requires to be distilled, as all philosophers do, more or less—but Hegel to an extent which is unparalleled. A much less intellectual effort would be required to find out the truth for oneself than to understand his exposition of it. (Ferrier 2001: vol. 1. 96)

Yet, the most important idealist influence for Ferrier was the Irish philosopher Berkeley: “we are disposed to regard [Berkeley] as the greatest metaphysician of his own county (we do not mean Ireland; but England, Scotland, and Ireland) at the very least” (Ferrier 2001: vol. 3. 458). Indeed, Ferrier, along with his contemporary Alexander Campbell Fraser, can be credited with reviving Berkeley’s philosophy in the nineteenth century. Ferrier refers to Berkeley on numerous occasions throughout his published works, and in “Berkeley and Idealism” he provides an argument for idealism that is developed out of his reaction to Berkeley. First, he defends Berkeley from the accusation that he denies the existence of the external world. Second, he expands on an idealist conception of non-existence, which is something that he believes that Berkeley has overlooked.

Berkeley shared Locke’s belief that ideas are the immediate objects of the mind. However, he rejected Locke’s view that ideas represent real things, and that real things are the indirect objects of the mind. Berkeley argued that ideas are the real things and that there is nothing beyond them. Thus, for Berkeley, the mind directly knows reality. His conclusion that ideas are real things led many to conclude that Berkeley denied the existence of material objects (for instance, see Leibniz, Samuel Johnson, and Reid). Yet, Ferrier strongly rejects the widespread belief that Berkeley denies the existence of matter. He argues that Berkeley readily accepts the existence of matter in the ordinary understanding of such; the external world consists of solid extended bodies that are perceived by the senses. However, he allows that Berkeley denies the existence of the world in itself, a world beyond perceivers. Ferrier emphasizes that what Berkeley wants to show is that reality is as it appears to perceivers; it is the immediate object of perceptions. He denies the existence of intermediate entities between the perceiver and reality and instead argues that that which is perceived is that which exists. In connection with this, Ferrier supports another aspect of Berkeley’s epistemology, specifically, his contention that primary and secondary qualities are akin in so far as each depends on perceivers and provide information about reality. Neither primary nor secondary qualities denote anything more objective about reality; reality is that which is perceived and both primary and secondary qualities are perceived.

Berkeley considered his own philosophy to be in line with common sense and Ferrier agrees. According to Ferrier, it is Berkeley rather than Reid who is “the champion of common sense” (Ferrier 2001: vol. 3. 301). Berkeley’s idealism places the mind in direct contact with reality; there are no intermediate entities. And, this, Ferrier suggests, is in line with the experience of ordinary people who do not distinguish between the perceptions of objects and the objects themselves. It is the notion of thing-in-themselves, or of a world that exists independently of perceivers that is at odds with common sense. Berkeley’s idealism, by contrast, is in accordance with common sense.

On the one hand, Ferrier describes Berkeley as “the champion of common sense.” On the other hand, he says that the significance of Berkeley’s philosophy is that he provides the basis for absolute idealism. He says:

[Berkeley] was the first to stamp the indelible impress of his powerful understanding on those principles of our nature, which, since his time, have brightened into imperishable truths in the light of genuine speculation. His genius was the first to swell the current of that mighty stream of tendency towards which all modern meditation flows, the great gulf-stream of Absolute Idealism. (Ferrier 2001: vol. 3. 293)

For Ferrier, common sense and absolute idealism are complementary. According to Ferrier, when “genuine idealism” is “instructed by the unadulterated dictates of common sense” it is indistinguishable from “genuine unperverted realism” (Ferrier 2001: vol. 3. 309).

His admiration for Berkeley is clear and he says: “Among all philosophers, ancient or modern, we are acquainted with none who presents fewer vulnerable points than Bishop Berkeley” (Ferrier 2001: vol. 3. 291). Nevertheless, he acknowledges that there is a weakness in Berkeley’s philosophy, namely, his failure to address non-existence. Something that is levied against idealism is the suggestion that it contains the implication that things flit in and out of existence; for example, the tree exists only in so far as it is perceived, and when it is not perceived, it cannot exist. Ferrier recognizes that Berkeley’s account seems to suggest that the world exists only in so far as it is perceived. He believes that this makes him vulnerable to accusations of subjective idealism. To overcome this, Ferrier broadens Berkeley’s account to include non-existence.

There are two parts to his discussion of non-existence. First, he reiterates the Berkeleian argument that mind-independent objects cannot exist because it is impossible to conceive of them. He says that if a philosopher speaks of the world-as-it-is-in-itself (for instance, the world existing prior to and following the existence of percipient beings), they are obliged to posit an ideal percipient. For example, in order to think of the River Nile existing in a world where there are no percipient beings, one must think about it in terms of its perceivable qualities: size, color, boundaries and so forth. But, in thinking of such things, one is still thinking of the act of perception and not the thing-in-itself. Here, Ferrier returns to “the fundamental act of humanity.” He emphasizes that that which is perceived is inseparable from the act of perception; it is impossible to consider what is seen in isolation from the act of seeing, what is heard in isolation from the act of hearing, and so on.

Second, Ferrier asserts that this argument must be extended to included non-existence as well. Not only is the existence of the world inconceivable without a real or ideal perceiver, but also non-existence similarly requires such a perceiver. In order to conceive nothing, that is silence, colorlessness, tastelessness, and so forth, the philosopher must refer to her perceptual framework. He develops Berkeley’s view that existence is percipi by insisting that non-existence is also percipi. Using Kantian language, he argues that “no phenomena, not even … the phenomenon of the absence of phenomena, are thus independent or irrespective” (Ferrier 2001: vol. 3. 315). Ferrier contends that it is not only matter that depends upon perceivers but also the non-existence of matter. He says:

[U]niversal colourlessness, universal silence, universal impalpability, universal tastelessness, and so forth, are just as much phenomena requiring, in thought, the presence of an ideal percipient endowed with sight and hearing and taste and touch, as their more positive opposites were phenomena requiring such a percipient. (Ferrier 2001: vol. 3. 311)

In this way, non-existence is just as much a known concept as existence. In order to conceive of either the existence or the non-existence of the world, a percipient being, whether real or ideal, is required. By supplementing Berkeley’s theory in this manner, he believes it becomes invulnerable to accusations of subjective idealism; one cannot say that the world will cease to exist in the absence of percipient beings because percipient beings are required to conceive of the world ceasing to exist.

c. Critique of Reid

Although he died more than a decade before Ferrier was born, Thomas Reid’s influence on Scottish philosophy remained strong during Ferrier’s youth and career. Hamilton is famous for his annotated edition of Reid’s works, and while Ferrier professes admiration for Hamilton’s scholarship, he wholeheartedly rejects the focus of his intellect. In Ferrier’s view, Reid produced a form of realism that not only failed to overcome the representative theory of perception but also resulted in its own form of representationism. Additionally, for Ferrier, Reid’s commonsense philosophy is inadequate and anti-philosophical. Instead, he calls for a new Scottish philosophy that is more systematic and rational; that is, an idealist metaphysics.

Reid was a Berkeleyan in his youth, but Hume’s skepticism led him to reassess his philosophical assumptions, which, in turn, led him to reject the theory of ideas. A version of the theory of ideas can be found in a range of philosophers from Descartes to Hume. In general, this theory posits that ideas are the immediate objects of one’s mind. This epistemological belief allows for a variety of metaphysical positions, including: Locke’s realism, Berkeley’s idealism, and Hume’s skepticism. Reid recognized that Hume’s astute reasoning was the logical development of the theory of ideas. At the same time, he could not accept Hume’s conclusions that we must be skeptical about things such as the continued existence of objects or the continuation of one’s personal identity. Thus, Reid examined the foundations of this theory: the existence of ideas. He realized that he had no experience of ideas and concluded that they are philosophical constructs, which are at odds with common sense. According to Reid, all persons share a priori commonsense principles upon which all reasoning depends. For instance, the belief in the existence of the external world, the principle of causality, and the belief that one is the same person she was yesterday and will be tomorrow, all count among Reid’s principles of common sense. The aspect of Reid’s theory that is most important for Ferrier is his philosophy of perception. Reid holds that we perceive objects directly and not via intermediate entities such as ideas. In his view, all persons have a commonsense belief in the existence of the external world that is irresistible and prior to reasoning. In this way, Reid was said to remove representationism from the theory of perception; the objects of knowledge are the things themselves rather than representative intermediaries such as ideas. Ferrier, however, argues that Reid failed to disprove representationism and that Reid’s theory of perception retains a form of representationism.

A discussion of the perception of matter is central to Ferrier’s philosophical writings, and it is this issue that he believes demonstrates the central difference between Berkeley and the commonsense school. One of his main talking points is representationism. On this topic, he dismissively says that “Berkeley thus accomplished the very task which, fifty or sixty years afterwards, Reid laboured at in vain” (Ferrier 2001: vol. 1. 490). Ferrier believes that Reid and others have misunderstood Berkeley by mistaking him for a representationist. Yet, Ferrier believes that idealism—both his own and Berkeley’s—is the only type of philosophy that can overcome representationism. He criticizes Reid’s theory of perception throughout his published works, and his argument against him is best expressed in his article “Reid and the Philosophy of Common Sense.” Here, he refutes Reid’s realist account of perception and develops his own idealist theory.

Ferrier divides philosophical accounts of perception into two schools: the metaphysical school and the psychological school. His idealist metaphysics is an example of the former and Reid’s commonsense philosophy is an example of the latter. Both schools accept that the perception of matter occurs, yet, they disagree about what this entails. Ferrier considers “the perception of matter” to be a whole, indivisible unit:

In the estimation of metaphysic, the perception of matter is the absolutely elementary in cognition, the ne plus ultra of thought. Reason cannot get beyond, or behind it. It has no pedigree. It admits of no analysis. It is not a relation constituted by the coalescence of an objective and a subjective element. It is not a state or a modification of the human mind. It is not an effect which can be distinguished from its cause. It is not brought about by the presence of antecedent realities. It is positively the FIRST, with no forerunner. The perception-of-matter is one mental word, of which the verbal words are mere syllables. (Ferrier 2001: vol. 3. 410, 411)

On the other hand, there is the psychological school’s approach to the perception of matter, which considers the relation between two component parts: the subjective perception and the objective matter. And, in Ferrier’s view, this approach leads to representationism.

Representationists make a distinction between an immediate and a remote object of the mind. For instance, Locke argues that we know things in the world via our ideas; things are the indirect objects of our minds, whereas ideas are the immediate object of our minds. What Ferrier believes is that Reid and other “psychologists” similarly set up a remote and an immediate object of the mind in their accounts of perception. He argues that the psychological school holds that there is the material world which exists regardless of whether it is perceived or not and that there are percipient beings who know the material world via their perceptions of it. It follows that in this account of the perception of matter there is both an objective aspect (the external world) and a subjective aspect (the subject’s perception of that world). He observes that this creates both an immediate and a remote object of knowledge; the subject knows her perception of the world immediately, whereas she knows the world remotely and only via her perception of it. He says:

When a philosopher divides, or imagines that he divides, the perception of matter into two things, perception and matter; holding the former to be a state of his own mind, and the latter to be no such state; he does, in that analysis, and without saying one other word, avow himself to be a thoroughgoing representationist. For his analysis declares that, in perception, the mind has an immediate or proximate, and a mediate or remote object. Its perception of matter is the proximate object, the object of its consciousness; matter itself, the material existence, is the remote object—the object of its belief. (Ferrier 2001: vol. 3. 415)

Therefore, Ferrier suggests that in avoiding representationism, Reid and others are paradoxically guilty of the very thing that they are attempting to dispel. In order to truly avoid representationism Ferrier insists on an idealist account of perception. Again he returns to “the fundamental act of humanity.” In his view, the “perception of matter” is a composite that cannot be broken down into its constituent parts; subjects and objects are always presented at once and can never be separated.

While Ferrier’s critique of Reid’s analysis if the perception of matter is astute, at other times, he makes derogatory remarks about his predecessor in an ad hominem manner. For instance, he says that when Reid is considered alongside philosophers such as Berkeley or Hume, he is akin to a “whale in a field of clover” (Ferrier 2001: vol. 1. 495). Remarks such as these have more to do with the dominance of commonsense philosophy during his lifetime and the ways in which it hampered his own career than with a thoughtful analysis of Reid’s ideas. Yet, despite his dismissal of Reid and the philosophy of common sense, Ferrier, nevertheless, wants to retain the language of “common sense.” Indeed, he believes that his own idealism is an example of an enlightened system of common sense.

d. Idealist Metaphysics

One of Ferrier’s criticisms with the philosophy of common sense is that he believes it formalizes the inadequacies of ordinary thinking.

Common sense … is the problem of philosophy, and is plainly not to be solved by being set aside, but just as little is it to be solved by being taken for granted, or in other words, by being allowed to remain in the primary forms in which it is presented to our notice. (Ferrier 2001: vol. 3. 64)

By contrast, he thinks that philosophy should fulfill a corrective purpose; he says: “philosophy exists only to correct the inadvertencies of man’s ordinary thinking” (Ferrier 2001: vol. 1. 32). A rational consideration of the laws of thought is required to separate unrefined opinions from the “genuine principles of common sense.” This is exactly what he tries to achieve in his major work the Institutes of Metaphysic; here, he attempts to systematically reveal the laws of thought via reason.

The Institutes is arranged into three main books, which follow on from one another: the Epistemology, the Agnoiology or theory of ignorance, and finally the Ontology. Together, they comprise his idealist metaphysics. Unusually, for a philosophical work, the Institutes is written in a deductive style. Ferrier’s metaphysics are deduced from an axiomatic, self-evident principle. In the introduction to his Institutes he asserts that: “From this single proposition the whole system is deduced in a series of demonstrations, each of which professes to be as strict as any demonstration in Euclid, while the whole of them taken together constitute one great demonstration” (Ferrier 2001: vol. 1. 30). His “Epistemology” consists of twenty-two propositions, the “Agnoiology” has eight propositions, and he concludes with the eleven propositions that form his “Ontology.” Each proposition involves a demonstration and a subsequent discussion in which he posits a counter-proposition that he disproves.

While Ferrier’s own philosophy is largely unknown to contemporary epistemologists, it is noteworthy that he was the first philosopher in English to call the philosophy of knowledge “epistemology.” His own epistemology is central to his philosophy as is evident from the fact that it forms the largest part of his metaphysics. It is also the common focus that appears in all of his published works. In his 1841 article “The Crisis of Modern Speculation,” he says: “Before we can be entitled to speak of what is, we must ascertain what we can think” (Ferrier 2001: vol. 3. 272). And, this is a principle that he follows in the Institutes by grounding his metaphysics in his epistemology. For Ferrier, it is important to secure of the laws of thought before making any positive statements about reality. Thus, “Proposition I” or “the primary law or condition of all knowledge” is the axiom from which the rest of Ferrier’s system follows. It asserts that: “Along with whatever any intelligence knows, it must, as the ground or condition of knowledge, have some cognisance of itself” (Ferrier 2001: vol. 1. 79).

The first proposition asserts that self-consciousness is the necessary concomitant of all knowledge; in knowing anything (for example, “that Tuesday follows Monday,” or “that one is reading Ferrier’s metaphysics”), at the same time, a person knows herself. In this way, Ferrier’s Institutes are the natural development of his work on consciousness; self-consciousness, as the peculiar feature of humanity, shapes his entire metaphysics. From this starting point, the main deductive conclusion that follows is that the minimum unit of cognition requires some self in union with some object. This forms Ferrier’s conception of the absolute; for Ferrier, a synthesis of subject-with-object is the absolute in knowledge.

If that which can be known must be a synthesis of subject-with-object, then, this is a union, which cannot be broken down into its constituent parts. As such, there can be no mere objects or matter per se. He says:

Everything which I, or any intelligence, can apprehend, is steeped primordially in me … Whether the object be what we call a thing or what we call a thought, it is equally impossible for any effort of thinking to grasp it as an intelligible thing or as an intelligible thought, when placed out of all connection with the ego. This is a necessary truth of all reason—an inviolable law of all knowledge. (Ferrier 2001: vol. 1. 120)

Hence, in perception, there can be no objects as they are, independent of knowers (typically known as things-in-themselves or noumena). For Ferrier, things-in-themselves are not objects of knowledge; they are unthinkable and as such they are the contradictory and unknowable by any mind, including by a supreme knower. In rejecting things-in-themselves, he has in mind Reid but also Hamilton and Kant as well as any philosophers who hold that there is a noumenal world. In his idealist epistemology, the notion of a thing-in-itself contradicts the laws of thought; one cannot conceive of a thing-in-itself because the synthesis of subject-with-object is the minimum unit of cognition, which cannot be broken down. Similarly, subjects-in-themselves are unknowable by all minds, including that of a supreme knower. In this way, the ego or self in itself is unknowable. While the self is the constant concomitant of all knowledge, there must also be an object that it is conjoined with. Ferrier calls the self the universal in all knowledge and the object is the particular in all knowledge.

Once he has established what can be known, he wants to reveal what cannot be known. Thus, in his Agnoiology he considers what, if anything, is a possible object of ignorance. This is one of the most unique and interesting features of Ferrier’s philosophy because the philosophy of ignorance has been given limited attention in the history of philosophy. His definition of ignorance is: not knowing that which could be known. In his view, ignorance involves a deficit or a privation of knowledge; it is a failure by the knower, to know something that could be known. In some cases, this might be a result of one’s limited constitution; for instance, a finite knower has more limited abilities for cognition than a supreme knower and there are some things that a finite knower could never know but are nevertheless the object of knowledge for some knower. In other cases, this might be a failure of will or effort; for instance, one might not know the time of day at a given moment, although that is something that could be rectified. By contrast, there are things that could never be known by any knower, including a supreme knower. This is what Ferrier designates the contradictory. For instance, no one, including a supreme knower, could know that 2 + 2 = 5 because this violates the laws of reason. For Ferrier, not knowing the contradictory is not ignorance but rather evidence of the strength of reason. Thus, “Proposition III” of his “Agnoiology” or “the law of all ignorance” asserts that: “We can only be ignorant of what can possibly be known; in other words, there can be an ignorance only of that of which there can be a knowledge” (Ferrier 2001: vol. 1. 412).

Given that in his “Epistemology” he has already concluded that the object of knowledge must be a synthesis of subject-with-object, the central conclusion of the “Agnoiology” is that that which we are ignorant of is a synthesis of subject-with-object, or in other words, the absolute in cognition. That which is the object of knowledge is some synthesis of subject-with-object. That which is the object of ignorance is some synthesis of subject-with-object. Thus, the possible objects of knowledge and ignorance are one and the same: the absolute in cognition. It follows that matter per se and the ego per se are neither the objects of knowledge nor ignorance. He returns to his contention that his idealism is in line with common sense when he says:

Novel, and somewhat startling, as this doctrine may seem, it will be found, on reflection, to be the only one that is consistent with the dictates of an enlightened common sense … If we are ignorant at all (and who will question our ignorance?) we must be ignorant of something; and this something is not nothing, nor is it the contradictory. (Ferrier 2001: vol. 1. 434)

Once Ferrier has established that the absolute must be the object of knowledge and ignorance, he moves to the question of being and considers what is. His “Ontology” directly follows from his “Epistemology” and the “Agnoiology.” In the opening proposition of this section he sets out the possibilities for that which is, which he refers to as “Absolute Existence.” It must be that which is (1) an object of knowledge, (2) that which is an object of ignorance, or (3) that which is neither an object of knowledge nor an object of ignorance. That which we can neither know nor be ignorant of is the contradictory and as such cannot be that which absolutely exists; Ferrier argues that this is a conclusion that even skeptics must allow for. He says:

No form of scepticism has ever questioned the fact that something absolutely exists, or has ever maintained that this something was the nonsensical. The sceptic, even when he carries his opinions to an extreme, merely doubts or denies our competency to find out and declare what absolutely exists. (Ferrier 2001: vol. 1. 466)

Therefore, that which exists must be the object of knowledge or ignorance, or, in other words, it is the absolute: a synthesis of subject-with-object.

The influence of Berkeley again becomes apparent in the development of his idealist ontology because he concludes the Institutes with the proposition that there is only one necessary absolute existence, namely, a supreme mind in synthesis with the universe. He says: “All absolute existences are contingent except one; in other words, there is One, but only one, Absolute Existence which is strictly necessary; and that existence is a supreme and infinite, and everlasting Mind in synthesis with all things” (Ferrier 2001: vol. 1. 522).  Grounding Ferrier’s metaphysics is the notion that God is both the supreme knower and the only necessary knower. Every other knower is finite and contingent; therefore, the existence of reality cannot depend on them. Ferrier argues that reason dictates that there must be a supreme mind to prevent the universe from being contradictory. This is because objects per se are contradictory. Therefore, the universe, which constitutes the objective part of knowledge, must be in conjunction with some subject in order to provide it with existence.

3. Reception and Influence

Ferrier was arguably the best Scottish philosopher of his generation. However, his contemporaries did not uniformly welcome his idealist metaphysics, believing the Institutes to be too far removed from the philosophy of his predecessors. Commonsense philosophy was dominant in the Scottish universities in the decades following Reid’s death. Subsequent generations of philosophers from Dugald Stewart to Hamilton defended some version of commonsense philosophy, which led nineteenth-century writers such as Ferrier, Andrew Seth Pringle-Pattison, and James McCosh to speak of a tradition of “Scottish philosophy.” In the history of Scottish philosophy, the role of the universities was of considerable importance, and acquiring a key university Chair often signified the status of the philosopher at the time. Many important philosophers held such academic chairs; for instance, both Adam Smith and Thomas Reid held the Chair of Moral Philosophy at Glasgow, Dugald Stewart was the Chair of Moral Philosophy at Edinburgh, and Sir William Hamilton was the Chair of Logic and Metaphysics at Edinburgh. A notable exception to this list is David Hume who unsuccessfully tried to acquire Chairs of philosophy at both Edinburgh and Glasgow. In many respects, Ferrier was the obvious candidate to succeed Hamilton in the esteemed Chair of Logic and Metaphysics at Edinburgh. Although Hamilton was best known for his editions of Reid’s works, he tried to combine Reid with Kant, while placing a greater emphasis on metaphysics than there had been before. Ferrier developed this tendency towards metaphysics even further with his idealism and his rejection of Reid’s commonsense philosophy. Additionally, Ferrier had taught in place of Hamilton during his mentor’s illness during the forties, and he was highly esteemed by Hamilton and others for his philosophical acuity. Nevertheless, Ferrier was unsuccessful in his attempt to acquire the Chair of Logic and Metaphysics in 1856, losing out to the lesser-known Alexander Campbell Fraser.

He reacted angrily to his defeat and it led him to produce his polemical work Scottish Philosophy: The Old and the New, which is a defense of his philosophical system as well as a scathing attack on his opponents. Ferrier’s animosity is not directed at Fraser; instead, he targets those who campaigned against him as well as Edinburgh’s Town Council who were responsible for appointing Hamilton’s successor. Here, he employs extraordinary rhetoric to argue that there is a distinction between old and new Scottish philosophy. In his analysis, his idealist metaphysics represents a “new Scottish philosophy,” whereas adherence to Reid and Hamilton is equivalent to perpetuating the “old Scottish philosophy.” In the campaign against Ferrier, his idealism was portrayed as being insufficiently Scottish. He replies that his philosophy is quintessentially Scottish even though it differs from Reid and Hamilton in certain respects. He says: “Philosophy is not traditional. As a mere inheritance it carries no benefit to either man or boy. The more it is a received dogmatic, the less it is a quickening process” (Ferrier 1856: 9). To discredit Ferrier his philosophy was compared to both Hegel and Spinoza with associations of pantheism and atheism mixed with nationalism and xenophobia. Ferrier denies the accusation that his philosophy is Hegelian and points out that claims to the contrary are simply propaganda. Moreover, he responds to suggestions that his philosophy is similar to Spinoza’s by wholeheartedly demonstrating his antipathy toward those who campaigned against him: “all the outcry which has been raised against Spinoza has its origin in nothing but ignorance, hypocrisy, and cant” (Ferrier 1856: 14). Ferrier was educated in the Scottish tradition, and the work he created was in direct reaction to it. The difference between Ferrier’s Institutes of Metaphysic and Reid’s philosophy of common sense is substantial. However, the difference between Ferrier’s thought and Hamilton’s is less dramatic.

Ironically, some decades later, the association with Hegel did not carry a negative connation. Alexander Campbell Fraser went on to teach several of the British Idealists of the latter part of the nineteenth century, and Edward Caird, an avowed Hegelian, was the Professor of Moral Philosophy in Glasgow for several years. The idealist R. B. Haldane summed up this change in attitude when he said: “The Time-Spirit is fond of revenges” (Haldane 1899: 9). In retrospect, Ferrier’s idealism appeared a few decades too early to be received by a receptive audience.

4. References and Further Reading

a. Primary Sources

  • Ferrier, James Frederick, Philosophical Works of James Frederick Ferrier, 3 vols: i. Institutes of Metaphysic, ii. Lectures on Greek Philosophy, iii. Philosophical Remains, Bristol: Thoemmes Press, 2001.
  • Ferrier, James Frederick, Scottish Philosophy: The Old and the New, Edinburgh: Sutherland and Knox, 1856.

b. Secondary Sources

  • Boucher, David, “Introduction” in The Scottish Idealists: Selected Philosophical Writings, Exeter: Imprint Academic, 2004.
  • Broadie, Alexander, A History of Scottish Philosophy, Edinburgh: Edinburgh University Press, 2009.
  • Cairns, Revd. J, An Examination of Professor Ferrier’s “Theory of Knowing and Being,” Edinburgh: Thomas Constable and Co, 1856.
  • Davie, George, Ferrier and the Blackout of the Scottish Enlightenment. Edinburgh: Edinburgh Review, 2003.
  • Davie, George, The Democratic Intellect: Scotland and Her Universities in the Nineteenth Century. Edinburgh: Edinburgh University Press, 1961.
  • Davie, George, The Scotch Metaphysics A Century of Enlightenment in Scotland. London: Routledge, 2001.
  • Ferreira, Phillip, “James Frederick Ferrier” in A. C. Grayling, Naomi Goulder, and Andrew Pyle (eds.), Continuum Encyclopedia of British Philosophy, London: Thoemmes Continuum, 2006, ii. 1085-1087.
  • Fraser, Alexander Campbell, “Ferrier’s Theory of Knowing and Being” in Essays in Philosophy. Edinburgh: W.P. Kennedy, 1856.
  • Graham, Graham (ed.), Scottish Philosophy in the Nineteenth and Twentieth Centuries, Oxford: Oxford University Press, 2015.
  • Graham, Graham, “The Nineteenth-Century Aftermath” in Broadie, Alexander ed. The Cambridge Companion to the Scottish Enlightenment, Cambridge: Cambridge University Press, 2003.
  • Haldane, E. S., James Frederick Ferrier. Edinburgh and London: Oliphant Anderson & Ferrier, 1899.
  • Haldane, John, “Introduction” in Ferrier, James Frederick, Philosophical Works of James Frederick Ferrier, Bristol: Thoemmes Press, i. Institutes of Metaphysic, 2001.
  • Jaffro, Laurent, “Reid said the business, but Berkeley did it.” Ferrier interprète de l’immatérialisme in Revue philosophique de la France et de l’étranger 135: 1, pp.135-149, 2010.
  • Keefe, Jenny, “James Ferrier and the Theory of Ignorance” in The Monist, Volume 90, No.2, pp.297-309, 2007.
  • Keefe, Jenny, “The Return to Berkeley” in British Journal for the History of Philosophy, Volume 15, Issue 1, pp.101-113, 2007.
  • Lushington, E. L., “Introductory Notice” in Ferrier, James Frederick, Philosophical Works of James Frederick Ferrier, Bristol: Thoemmes Press, ii. Lectures on Greek Philosophy, 2001.
  • Mander, W. J., British Idealism: A History, Oxford: Oxford University Press, 2011.
  • Mander, W. J. and Panagakou, S., British Idealism and the Concept of the Self, London: Palgrave Macmillan, 2016.
  • Mander, W. J. (ed.), The Oxford Handbook of British Philosophy in the Nineteenth Century, Oxford: Oxford University Press, 2014.
  • Mayo, Bernard, “The Moral and the Physical Order: A Reappraisal of James Frederick Ferrier,” Inaugural Lecture, University of St Andrews, 1969.
  • McCosh, James, The Scottish Philosophy, New York: Robert Carter and Brothers, 1875.
  • McDermid, Douglas, “Ferrier and the Myth of Scottish Common Sense Realism” in Journal of Scottish Philosophy, Volume 11, Issue 1, pp.87-107, 2013.
  • McDermid, Douglas, The Rise and Fall of Scottish Common Sense Realism, Oxford: Oxford University Press, 2018.
  • Muirhead, J. H., The Platonic Tradition in Anglo-Saxon Philosophy, London: George Allen & Unwin, 1931.
  • Segerstedt, Torgny T., The Problem of Knowledge in Scottish Philosophy (Reid-Stewart-Hamilton-Ferrier). Lund: Gleerup, 1931.
  • Seth, Andrew, Scottish Philosophy: A Comparison of the Scottish and German Answers to Hume, Edinburgh and London: William Blackwood and Sons, 1885.
  • Sorley, W. R., A History of English Philosophy, Cambridge: Cambridge University Press, 1920.
  • Thomson, Arthur, Ferrier of St Andrews: An Academic Tragedy, Edinburgh: Scottish Academic Press, 1985.
  • The Testimonials of J.F. Ferrier, Candidate for the Chair of Moral Philosophy in the University of Edinburgh, Second Series, 1852.

 

Author Information

Jenny Keefe
Email: keefe@uwp.edu
University of Wisconsin–Parkside
U. S. A.

Eduard Hanslick (1825–1904)

Eduard Hanslick was a Prague-born Austrian aesthetic theorist, music critic, and the first professor of aesthetics and history of music at the University of Vienna, who is commonly considered the founder of musical formalism in aesthetics. His seminal treatise Vom Musikalisch-Schönen (On the Musically Beautiful) of 1854 is one of the most significant contributions to musical aesthetics ever written, as is evident from the ten editions the book went through during Hanslick’s lifetime, with many editions to follow. Hanslick’s classic treatise has been translated into English as early as 1891. On the Musically Beautiful, or OMB, posits an aesthetic approach to music derived solely from its specific material features that helped to shape the fields of aesthetics and musicology up to our own day. Hanslick’s scientific and objectivist orientation, his critical attitude towards metaphysics, and his theory of emotion—strikingly reminiscent of modern cognitive concepts—guarantee his continued relevance for current debates.

OMB is notorious primarily for its ostensible repudiation of any pertinent connection between music and affect states. Hanslick’s concept of music, according to this view, is based solely on the formal aspects of pure music that does not arouse, express, represent, or allude to human emotion in any way relevant to its artistic essence: The content of music, Hanslick (in)famously proclaimed, consists entirely of “sonically moved forms.”

This article provides an introduction to Hanslick’s biography, his early music reviews, which differ considerably from the eventual opinions he is commonly associated with, and portrays the key arguments of Hanslick’s aesthetic approach as presented in OMB, including a reconstruction of the complex genesis of this book. The concluding paragraphs encompass an overview of several crucial sources of Hanslick’s viewpoint, seemingly oscillating between German idealism and Austrian positivism, as well as a concise history of Hanslick’s reception in analytical philosophy of music, which continues to struggle with the issues posed by Hanslick’s cognitive concept of emotion and has drafted numerous strategies to circumvent Hanslick’s skeptical outcome.

Table of Contents

  1. Biography
  2. Early Works and Critical Writings
  3. Vom Musikalisch-Schönen / On the Musically Beautiful
    1. Genesis and Conceptual Organization of OMB
    2. Purpose, Methods, and General Outlook of OMB
    3. Arousal, Expression, and the Cognitive Concept of Emotion
    4. The Musically Beautiful and Music’s Relation to History
    5. Listening, Music’s Relation to Nature, and Music’s Content
    6. Conclusion: The Curious Nature of Hanslick’s Formalism
  4. The Intellectual Background of Hanslick’s Aesthetics
    1. Hanslick and German Idealism
    2. Hanslick and Austrian Realism
    3. Editorial Problems and Eclectic Origins of OMB
  5. The Reception of Hanslick’s Aesthetics and Its Relevance to Current Discourse
    1. A General Outline of Hanslick’s Reception by Austro-German Discourse
    2. Hanslick’s Reception by Analytical Aesthetics and the Direct Impact of OMB
    3. Bypassing Hanslick’s Cognitivist Arguments: Kivy, Davies, and Moods
  6. References and Further Reading
    1. Primary Sources
    2. Secondary Sources

1. Biography

Eduard Hanslick, who Germanized his surname by inserting a “c” upon his move to Vienna in 1846, was born in Prague on September 11, 1825 as the son of Josef Adolf (1785–1859) and Karoline Hanslik (1796–1843), daughter of the Jewish court factor Salomon Abraham Kisch (1768–1840). According to Hanslick’s memoirs, his father was responsible for his education and thus may have sparked his interest in aesthetics, as Josef Adolf edited the two volumes of Johann Heinrich Dambeck’s Vorlesungen über Ästhetik (Lectures on Aesthetics, 182223) and filled in as Dambeck’s substitute in 1816­–17, teaching aesthetics at Prague’s Charles University. Hanslick, who also took lessons with the renowned composer Václav Tomášek (1774–1850), completed his philosophical elementary studies—a three-year course in general education mandatory for all prospective university attendees—between 1840 and 1843, enrolled in law at Prague, and attained his doctoral degree in Vienna in 1849 (on Hanslick’s early days, see Grey 2002, 828–29; Grey 2011, 360–61; Hanslick 2018, xv–xvi). Hanslick’s background in law had significant influence on his philosophical methodology as his standard for evidence and his emphasis on “proximate causes” (Hanslick 1986, 32)—which limit the chain of “admissible causes-in-fact” and enable Hanslick’s strong focus on “the music itself” instead of the listener, performer, or composer (Pryer 2013, 55)—are clearly derived from juridical training. After a short-lived employment as a fiscal civil servant in Klagenfurt (Carinthia) in 1850–52, during which Hanslick prepared for an academic profession (Wilfing 2018, 91n), he returned to Vienna to work at the ministry of finances and was subsequently transferred to the ministry of education in 1854.

This move proved crucial for Hanslick’s future career, as Count Thun-Hohenstein (1811–88), who led the education department from 1849 to 1860, had been charged with the overall reform of Austrian education following the 1848–49 revolution, and Hanslick thus came into direct contact with Thun’s agenda and the demands of the science policies of the Hapsburg Monarchy. The initial traces of the book he would become famous for also fall within this time frame, with OMB completed in 1854. In 1856, this book was acknowledged retroactively as a philosophical habilitation, thereby granting Hanslick an unsalaried professorship at the University of Vienna that turned into a salaried position in 1861, and ultimately a full post in 1870. Hanslick retained this post until he retired in 1895, and his successor Guido Adler (1855–1941) was appointed as professor of theory and history of music, a designation diverging markedly from Hanslick’s emphasis on aesthetics. Hanslick was established profoundly in the cultural and musical scenery of Vienna: he consulted in awarding public music grants and judged musical contests, was an official Austrian delegate at international conferences and world fairs, and he became the first chair of Denkmäler der Tonkunst in Österreich (Monuments of Musical Art in Austria) from 1893 to 1897, a society editing musical pieces of historic bearing on Austria until today. In addition to his academic activities, Hanslick experienced a widely successful career as a music critic (see the next section), which lasted until 1895, when Hanslick retired from his music editor post at Neue Freie Presse. Despite his retirement, Hanslick continued to publish criticism in this very journal until his death in 1904, with the last text to appear on April 7, two months before his passing—an event noted as far as the Musical Times and the  New York Times (McColl 1995).

2. Early Works and Critical Writings

Except for his aesthetic treatise, Hanslick is renowned primarily for his activities as a music critic. As philosophical commentators usually concern themselves exclusively with OMB, the present section will briefly sketch Hanslick’s relevance in 19th-century musical discourse and will also indicate the diversity of his critical position. Today, Hanslick is known best for his skeptical attitude towards the New German School—a vague label for a loose group that is thought to comprise composers such as Hector Berlioz (1803–69), Franz Liszt (1811–86), and Richard Wagner (1813–83), but does also refer to influential journalists such as Franz Brendel (1811–68), editor-in-chief of Neue Zeitschrift für Musik. Hanslick’s career as a music critic started early on as an occasional contributor to Beiblätter zu Ost und West (Prague 1844) and—upon his move to Vienna in 1846—the Wiener Allgemeine Musik-Zeitung, ultimately transferring to the imperial Wiener Zeitung in 1848, prior to his music editor posts at Die Presse (1855–64) and its liberal offshoot Neue Freie Presse (1864–95). At that time, Hanslick proved to be an advocate of composers he would eventually disapprove of, such as Berlioz, who was called the “most magnificent phenomenon in… musical poetry,” and Wagner, who was proclaimed the “greatest dramatic talent among living composers” (Hanslick 1993, 40, 59; for the latter review, see Hanslick 1950, 33–45). Hanslick, who was acquainted personally with important composers of his era—he met Wagner as early as 1845 and acted as a local guide for Berlioz in 1846 (Payzant 1991 and 2002, 63–71)—at that time professed a romantic outlook (Yoshida 2001, 181–84) and deemed “pure” music a “language of the emotions” and the “revelation of the innermost world of ideas” (Hanslick 1993, 98, 115). For readers of an aesthetic theorist commonly associated with the “repudiation” of emotive musical meaning (Budd 1980) and the proponent of a classicist conception of music that does not refer to anything beyond itself, Hanslick’s 1848 essay on “Censorship and Art-Criticism” must seem particularly surprising. In this text, he condemns the “inadequate perspective that saw in music merely a symmetrical succession of pleasing tones.” Truly artful music, he continues, represents “more than music”; it is a “reflection of the philosophical, religious, and political world-views” of its time (Hanslick 1993, 157).

In the early 1850s, however, Hanslick’s outlook on music shifted considerably and eventually developed into a more “formalist” viewpoint that inverted his previously positive appraisal of Wanger’s operas. Although an exact date or a conclusive inducement for his “volte-face” (Payzant 1991, 107) is hard to determine definitively, the classicist writings of the Prague music critic Bernhard Gutt (1812–49), from whom he adopted multiple quotations (Payzant 1989), the failed political upheaval of 1848–49, and the resulting execution of his cherished colleague Alfred Julius Becher (1803–48) seem to be crucial reasons for Hanslick’s change of opinion (Bonds 2014, 153–54; Landerer and Wilfing 2018, sec. 2). Whereas Hanslick regarded “pure” music as an exhaustive repository for intellectual reflection that exerts tangible impact on the world of politics and religion in 1848, he from this time on develops a more formalistic conception of musical artworks that emphasizes their essentially autonomous nature. In making this move, Hanslick took part in the general erosion of Hegelian criticism, the political direction of which lost most of its appeal in the aftermath of 1848 (Pederson 1996), and entirely detached music and its aesthetic qualities from its involvement with worldly politics. Whereas the political activities of other critics ceased while they retained crucial elements of Hegelian aesthetics, such as emotivism or its focus on concrete content, Hanslick’s reversal was virtually complete. This turn is observable particularly in respect to the debate about external musical meaning that Hanslick declared the pivotal feature of art in 1848. A few years later, prior to the initial edition of OMB in 1854, he had reversed his attitude entirely by stating that “if an orchestral composition requires external means of conceptual understanding [that is, a literary program] in order to please… then its musical value already appears to be in question” (Hanslick 1994, 293). Hanslick’s notion of music’s nature thus shifted from a romantic position emphasizing conceptual meaning to an appraisal of internal musical meaning oriented towards formal issues such as the inherent potential of the main theme or the clarity of melodic figures (Payzant 2002, 88–91, 96–98, 117–19).

Although Hanslick therefore adopted a critical attitude towards the New German School in later years and took issue with its poetization of “pure” music (Larkin 2013), certain matters have to be kept in mind that challenge the widespread assumption of Hanslick being a “stodgy, pedantic spokesperson for ‘conservative’ musical causes” (Gooley 2011, 289). Hanslick’s criticism of Wagner and his followers generally concerned the musical aspects of their works and deplored an absence of motivic-thematic manipulation or an overly rigorous devotion to a literary program that supposedly interfered with the “organic” unfolding of melody. His general valuation of these works, however, often proves to be astoundingly differentiated (on Hanslick’s appraisal of Wagner, see Grey 1995, 1–50; Pederson 2013, 176–77; Bonds 2014, 237–46). Although Hanslick assessed Der Ring des Nibelungen in 1876 to be “a distortion, a perversion of basic musical laws,” he was at the same time able to realize that Wagner’s tetralogy represents “a remarkable development in cultural history” (Hanslick 1950, 139, 129). It is beyond serious debate that Hanslick preferred Beethoven (1770–1827), Brahms (1833–97), and Mozart (1756–91) to Mahler (1860–1911), Strauss (1864–1949), or the Wagner “school.” Hanslick, however, did not panegyrize his preferred musicians as he did not condemn his “opponents” without reservation. Although Hanslick bemoaned Wagner’s musical system, his continuous modulations, and the dubious semantic qualities of the Leitmotiv—which he called “musical uniforms”—he nonetheless appreciated his “genius for theatrical effect” (Hanslick 1950, 121, 151) and stressed the musical virtues of specific sections of Wagner’s operas. As he clarified in 1889: “Only a fool or dedicated factionist” would answer the question of Wagner’s qualities “with two words: ‘I idolize him!’ or ‘I abhor him!’” (Hanslick 1889, 56). Furthermore, Hanslick critically (and sometimes financially) supported more modernistic composers such as Bedřich Smetana (1824–84) or Antonín Dvořák (1841–1904) as long as their general artistic principles conformed to his aesthetic approach to a certain degree (Brodbeck 2007 and 2009; Larkin 2013).

3. Vom Musikalisch-Schönen / On the Musically Beautiful

a. Genesis and Conceptual Organization of OMB

From July 1853 to March 1854, Hanslick pre-published several chapters of OMB as stand-alone articles that deal with the subjective impression and (physiological) perception of music, as well as with the complex relations between music and nature. His three-piece essay “On the Subjective Impression of Music and its Position in Aesthetics” (Hanslick 1853) was eventually transformed into chapters 4 and 5 of the finalized manuscript, whereas “Music in its Relations to Nature” (Hanslick 1854)—itself based on a public lecture of 1851—turned into chapter 6, with both texts running through hardly any significant alterations. Scholarship on the actual genesis of OMB is rather sparse, as Hanslick’s private records were lost during the Second World War (Wilfing 2018, sec. 1), and has not yet reached a consensus regarding the chronological development of Hanslick’s momentous monograph. Whereas Geoffrey Payzant surmised that Hanslick’s articles were taken from the final version of OMB (Payzant 1985, 180), recent research points to the logical order of Hanslick’s argument that runs counter to the familiar sequence of published chapters in OMB and assumes that these three chapters (4–6) were indeed written prior to the more famous chapters 1 to 3, therefore presenting the nucleus of OMB (Landerer and Wilfing 2018, sec. 4; Hanslick 2018, xvii–xix). According to this view, Hanslick first lays the foundation for his aesthetic approach by clarifying an idea of tone (chapter 6) and the way in which tones are received from the standpoint of physiology and psychology (chapters 4 and 5). This analysis is followed by Hanslick’s concept of emotion, how emotions are predicated upon these physiological and psychological responses, and what role emotions play in musical aesthetics (chapters 1–2). Finally, following Hanslick’s hypothesis that emotion does not form a substantial component of objectivist aesthetics, he presents his positive thesis (chapter 3) and closes his argument with concluding comments that summarize his key findings and widen the conceptual framework of OMB (chapter 7).

b. Purpose, Methods, and General Outlook of OMB

Hanslick did not write any other academic works apart from OMB and the Geschichte des Concertwesens in Wien (History of Concert in Vienna, 1869) and focused his literary output almost entirely on reviews. Why did he decide to publish an aesthetic treatise at the age of 29? The reason given by Hanslick himself is to provide a critique of aesthetic emotivism that dominated mid-century discourse and to challenge the “advocates of the music of the future,” who supposedly endangered the “independent significance of music” (Hanslick 2018, lxxxv). By directly accusing Liszt and Wagner of belittling the inherent qualities of “pure” music, Hanslick contributed significantly to the view that OMB has to be read as a book directed against Wagner—a view that was conducive for the longevity of Hanslick’s treatise through the discussions surrounding the New German School. Even though there is some truth to this claim, scholars contest that Wagner’s music could be actually regarded as the prime spark for the production of OMB (Grey 2003, 169; Brodbeck 2014, 50), not least of all since Wagner’s later works that Hanslick specifically disapproved of were not yet written and Wagner’s name rarely appears in the initial edition of Hanslick’s treatise (several quotes from Wagner’s theoretical writings are belatedly included in the sixth edition of 1881). Wagner’s music—even though it was a useful target in order to remain relevant—thus does not seem to be the crucial reason for writing OMB, as the conceptual framework of Hanslick’s argument would have been very much the same “had the figure of Wagner not been there” (Bujić 1988, 8). A more tangible motive seems to be Hanslick’s very early aspiration towards an academic profession in order to leave behind his rather tedious employment as a public servant. We know from letters written around 1851 that Hanslick noticed the absence of musical aesthetics and musicology from the Viennese university curriculum and saw the opportunity to carve a niche for his unique talent. In light of Hanslick’s academic ambitions, it comes as no surprise that OMB does not start with a theoretical definition of art, music, or beauty. On the contrary, Hanslick’s examination commences with an exhaustive definition of musical aesthetics as a scientific discipline.

Whereas romantic aesthetic theorists had occupied themselves with music’s relation to affect states, feelings, and emotions, scientific aesthetics should focus on the object itself instead of its (historical) production or (arbitrary) reception. If musical aesthetics is to become scientific, Hanslick proclaims in a sentence that strikingly anticipates Edmund Husserl’s (1859–1938) phenomenology (Wilfing 2016, 24–25), it has to “approach the natural scientific method at least as far as trying to penetrate to the things themselves” (Hanslick 2018, 1). Furthermore, the specified aesthetics of music should detach itself from any theoretical dependency on a general concept of artistic beauty that is employed to categorize “pure” music ex post facto. German idealism typically contrived an aesthetic approach firmly rooted in an overarching philosophical framework. Art, regardless of the specific medium, thus must satisfy certain epistemic principles and ethical criteria derived from this general system in order to be classified as beautiful. Idealist aesthetics therefore typically identified universal conditions of artistic beauty that were binding equally for a poem, a tragedy, a painting, a sculpture, or a piece of music (Wilfing 2018, sec. 3.3). For Hanslick, this system-bound approach was completely misguided as he is concerned exclusively with musical beauty, the “musically-beautiful,” so that it is even hard to see how his notion of specific musical beauty is related to any general concept of beauty (Bonds 2014, 190). For him, the “laws of beauty of each art are inseparable from the characteristics of its material, of its technique” (Hanslick 2018, 2). For this reason alone, Payzant’s rendition of Vom Musikalisch-Schönen as On the Musically Beautiful captures Hanslick’s ideas much better than Cohen’s The Beautiful in Music that suggests an aesthetic approach contrary to Hanslick’s intentions: he did not propose an abstract principle of artistic beauty, administered retroactively to “pure” music, but was interested principally in beauty solely and explicitly manifest in the art of tones (Hamilton 2007, 81; Bonds 2014, 190).

c. Arousal, Expression, and the Cognitive Concept of Emotion

To this end, Hanslick develops two central theses: a positive one, explored in chapter 3, that attempts to show that musical beauty is dependent completely on the inherent qualities of music itself, and a negative one, defined in chapters 1–2, that challenges the familiar concept that music is supposed to represent feelings and that its emotive content forms the basis of aesthetic judgment. Both ideas share common ground in Hanslick’s objective approach: as the musical artwork and its material features represent the core of Hanslick’s aesthetics, the “subjective impression” of music, its emotive impact, is relegated to a secondary aftereffect of musical material. We must thus “stick to the rule that in aesthetic investigations primarily the beautiful object, and not the perceiving subject, is to be researched” (Hanslick 2018, 2–3). Hanslick specifically addresses two ways in which music is thought to be related to affect states: (1) The idea that music’s purpose is to arouse emotion and (2) that emotions represent the content of musical artworks (an assumption employed frequently to compensate for the lack of notional meaning in music alone). The first stance is countered by the classical argument of beauty having no purpose and “content of its own other than itself.” Beauty may very well arouse pleasant feelings in the perceiving individual, but to do so is not at all constitutive for the musically beautiful that exists apart from the listener’s cognition and remains beautiful “even if it is neither viewed nor contemplated. The beautiful is thus namely merely for the pleasure of the viewing subject, but not by means of the subject” (Hanslick 2018, 4). In an argument that anticipates Edmund Gurney’s (1847–88) renowned distinction between impressive music and expressive music (Gurney 1880, 314), Hanslick moreover maintains that music’s beauty and its emotive impact do not correlate inevitably. Thus, a beautiful composition may not arouse any specific feelings, whilst the strong emotive impact of another musical piece does not necessarily substantiate its aesthetic qualities (Hanslick 2018, 31–33; Robert Yanal 2006 dubs this idea the “third thesis” of OMB). In general, emotive arousal—for the most part depending on individual experience, musical edification, historical discourse, and so on—cannot provide a reasonable foundation for scientific aesthetics as it exhibits “neither the necessity nor the exclusivity nor the consistency” required to establish an aesthetic principle (Hanslick 2018, 9).

In chapter 2 of OMB, Hanslick presents his key argument against emotion forming the content of “pure” music by introducing his cognitive concept of emotion—a concept that brought his treatise to the forefront of analytical aesthetics. There was widespread consensus amongst idealist systems of art that art must have some sort of content. As “pure” music lacks tangible meaning, romantic theorists invoked the opposite of conceptual definiteness as the obvious candidate for music’s content: emotion (love, fear, anger, and the like). This claim, Hanslick maintains, represents the weak spot of musical emotivism. Emotion by no means forms the conceptless counterpart to literary meaning. On the contrary, emotions are “dependent on physiological and pathological conditions” and are invoked by “mental images, judgments, in short by the entire range of intelligible and rational thought” (Hanslick 2018, 15). The analytical philosopher Peter Kivy (1990, chap. 8) popularized this view with a practical example: If I assume that uncle Charlie is cheating during a card game, the anger I experience is contingent on the object of my emotion, Charlie. However, in order to be angry, a complex structure of cognitive parameters has to be in place. I must consider cheating an immoral or indecent behavior—a belief built upon some sort of ethical system—that is performed purposely by Charlie. As soon as I spot that Charlie is not deceitful wittingly and has played the wrong cards by accident, my anger is likely to evaporate, as its conceptual foundation disappears. Emotion, in short, needs an intentional object to be an emotion—an object that “pure” music is unable to provide. As music lacks the “cognitive mechanism” necessary to portray the objects of concrete emotions, the depiction of a specific feeling “does not at all lie within music’s own capabilities” (Hanslick 2018, 15–16). However, music alone can express the dynamic features of emotions via its own musical impetus and is thus able to portray “one aspect of feeling, not feeling itself” (Hanslick 2018, 18). Thus, even though music alone cannot express love, fear, or anger in a direct manner, its dynamic structure can reproduce the associated movement of concrete emotions or actual events (Hanslick 2018, 30), but not in ways that allow for definite meaning, as the dynamic character of love or anger could both be violent, desperate, or passionate in specific instances.

Hanslick’s exact stance on the relation of emotion and “pure” music represents a major point of contention in current research. Several scholars hold that Hanslick severed any relevant bonds between music and affect states, so that music itself “has nothing to do with emotion” (Zangwill 2004, 29) and emotions in turn have “nothing to do with musical beauty” (Lippman 1992, 299). Other scholars point to the preface of Hanslick’s treatise, in which he states that for him the value of beauty is based on “the direct evidence of feeling” and that his protest only pertains to the “mistaken intrusion of feelings in the domain of science” (Hanslick 2018, lxxxiv). In chapter 1, Hanslick makes the same move when it comes to musical arousal: he does not want to “underestimate” the “strong feelings that music awakens from their slumber,” but merely refutes the “unscientific assessment of these facts for aesthetic principles” (Hanslick 2018, 9). For Payzant, Hanslick accepts music’s capacity to arouse, express, or portray emotion; he only “says that to do so is not the defining purpose of music” (Hanslick 1986, xvi). Stephen Davies and Peter Kivy, who in 1980 concurrently established a concept of musical emotion based chiefly on the dynamic features of musical structure that readily suggest the outward features of expressive behavior (Trivedi 2011), regarded Hanslick as a historical precursor to their shared model of enhanced formalism. The crucial disparity between enhanced formalism and Hanslick’s aesthetics, both authors hold, is that they conceive of expressive properties as objective musical properties, whereas Hanslick was reluctant to take this step (Davies 1994, 204; Kivy 2009, 64). Based on numerous passages of OMB that suggest music’s ability to be “itself intellectually stimulating and soulful” and that show how music alone “absorbs” its creator’s feelings (Hanslick 2018, 45–46, 65), this view has been called into question. As Hanslick locates emotive meaning in music’s kinetic features that replicate the dynamic properties of affective conditions, his stance might come close to enhanced formalism (Cook 2001, 175). In view of Hanslick’s account of musical emotion as “silhouettes” (Hanslick 2018, 27) that open a certain variety of possible meaning whilst precluding capricious readings of music, he seems to regard musical elements as indefinitely expressive (Srećković 2014, 131)—an approach that anticipates Susanne K. Langer’s (1895–1985) theory of music as an “unconsummated symbol” (Wilfing 2016, 26–29).

d. The Musically Beautiful and Music’s Relation to History

Hanslick’s arguments regarding the complex relations between emotions and music, the indeterminate expressivity of musical gestures, as well as their debatable relevance for scientific aesthetics, however, merely apply to “pure” music. As vocal music forms an amalgam of music and poetry, the emotions aroused by it cannot be ascribed to any of its codependent components in arbitrary isolation. Thus, “pure” music—instrumental compositions without a literary program, title, or text—forms the basis of Hanslick’s aesthetics (Hanslick 2018, 23–26). This lopsided approach has led scholars to assume that Hanslick regarded vocal music as an impure blending of “absolute” art forms, whilst considering instrumental music to be the ideal form of music (Alperson 2004, 260; Gracyk, chap. 1). By contrast, other scholars stressed Hanslick’s statement that any leaning towards a specific subclass of music proves to be an “unscientific procedure” (Hanslick 2018, 24), and thus read Hanslick’s favoritism as a methodological consideration without normative implications (Bonds 2014, 12; Grey 2014, 44). For Hanslick, musical beauty is never based on the literary meaning or the emotive features of music but is rather found “solely in the tones and their artistic connection”: “The content of music,” as he famously proclaims, “is sonically moved forms” (Hanslick 2018, 40–41). The purport of Hanslick’s notorious sentence has evoked a wide array of possible readings. Although the “forms” he speaks about have been interpreted occasionally to refer to large-scale forms (concerto, sonata, rondo, and so on) and have thus been translated in the singular (Dahlhaus 1989, 130; Karnes 2008, 30), it seems likely that this term actually denotes musical elements and their structural conjunction (Wilfing 2018, sec. 3.3). In contrast, sonically or “tonally” (tönend), as Payzant renders this term (Hanslick 1986, 29), is an unclear concept that has been explained divisively. Whereas Payzant takes this term to refer to “tone” as part of the diatonic musical scale (2002, 44–46), Landerer and Rothfarb translate tönend as “sonically” and therefore emphasize its auditory features. Much of the question whether Hanslick perceived “pure” music to be captured entirely in the score itself (Subotnik 1991, 279; Alperson 2004, 266) or to require an auditory experience to be appreciated aesthetically (Bujić 1988, 10; Hamilton 2007, 82) hinges on the problematic translation of tönend.

Hanslick, however, willingly concedes that an assertive definition of the musically beautiful is virtually impossible to achieve because “pure” music cannot express concrete meaning. Any account of music’s content thereby amounts to “dry technical specifications” or “poetic fictions” (Hanslick 2018, 43). Music, in each case, must be understood musically and can be grasped only from within, as no verbal report can suffice. If we want to specify the content of a given theme for another person, “we have to play the theme itself for him” (Hanslick 2018, 113). Although Hanslick is unable to provide an exhaustive definition of musical beauty, he guards against potential fallacies: For him, the musically beautiful represents more than symmetry, regularity, proportion (Hanslick 2018, 57–59), or a pleasant sequence of tones, as these images neglect the crucial aspect of beauty: Geist (mind or intellect). The forms music consists of are “not empty but rather filled, not mere borders in a vacuum but rather intellect shaping itself from within” (Hanslick 2018, 43). Consequently, the act of composition is an “operation of the intellect in material of intellectual capacity” and the musically beautiful is produced primarily by the “intellectual power and individuality” of the composer’s imagination that has been absorbed by musical structure as a tonal idea that “pleases us in itself” (Hanslick 2018, 45–46). “Pure” music, Hanslick contends, has its own logic based on purely musical factors, the effect of which is governed by certain natural laws that have to be discovered, examined, and elucidated by aesthetic analysis (Hanslick 2018, 47–50). At this point, the tentative character of Hanslick’s approach becomes apparent, as he does not give any substantial indication as to how this goal could be realized beyond the idea that we must observe the efficacy of musical elements that are then reduced to general aesthetic categories that in turn lead to an ultimate principle. Although Hanslick cannot provide a conclusive treatment for scientific aesthetics, the pivotal insight of OMB seems clear: musical beauty depends on musical material and not on any concept or emotion. Thus, Hanslick wonders whether the divergent aesthetic qualities of musical artworks might hinge on the gradation or accuracy of emotional expression and answers in the negative: A piece shows more aesthetic qualities than another simply because it contains “more beautiful tone forms” (Hanslick 2018, 51).

Here, Hanslick mentions one of the few concrete examples of musical beauty by declaring creativity, originality, and spontaneity to be essential features of musical prowess. This view is notable because Hanslick’s notion of how musical beauty relates to history is one of the most divisive aspects of OMB. Hanslick’s emphasis on the intrinsic qualities of “pure” music, ruling out the various settings of creation, listening, or performance for aesthetic concerns, has led scholars to assume that Hanslick treats beauty ahistorically (Burford 2006, 172–73; Karnes 2008, 50–52; Bonds 2014, 176–77). This view is often based on Hanslick’s assurance that his concept of beauty applies to classicism as well as romanticism and thereby pertains to “every style in the same way, even in the most opposed ones” (Hanslick 2018, 55). Hanslick moreover advocates a categorical separation between historical reasoning and aesthetic judgment: whereas the historian’s exploration of the broader context of a given piece is undeniably warranted, aesthetic inquiry hears “only what the artwork itself articulates.” In regard to this hierarchy between the aesthetic relevance of artwork and context, Hanslick somewhat anticipates the New Criticism of 20th-century literary studies principally associated with Monroe C. Beardsley and William K. Wimsatt (Appelqvist 2010–11, 77–78). However, this idea is undermined immediately by Hanslick’s remarks on the indisputable connection of artworks to “the ideas and events of the time that produced them.” As music is created by an intellect, it stands in inextricable interrelation with concurrent productions of art and the “poetic, social, scientific conditions” of its time and place (Hanslick 2018, 55–56). For Hanslick, the aesthetic qualities of musical elements (particular cadences, intervallic progressions, modulations, and so on) are subject to historic decline and “wear out in fifty, even thirty years.” Eternal musical beauty is “little more than a nice turn of phrase” and we may say of compositions that “rank high above the norm of their time that they were once beautiful” (Hanslick 2018, 51, 58n). This theoretical contradiction prompted scholars to discern between Hanslick’s principle of scientific aesthetics, which is established ahistorically, and his concept of music itself and particular instances of the musically beautiful, which are subject to change (Landerer and Zangwill 2016, 490–92; Wilfing 2016, 17–18).

e. Listening, Music’s Relation to Nature, and Music’s Content

Although Hanslick openly rejects the listener’s relevance for the constitution of the musically beautiful that exists apart from the listener’s perception, the subjective impression of music forms the topic of chapters 4 and 5 of OMB. Hanslick is not at all interested in establishing a purely intellectual apprehension of musical structure. Beauty is rooted in (physical) sensation and engages the faculty of imagination as an intermediary between sensation, intellect, and feeling: listening to music in a purely rational fashion, Hanslick contends, is as far removed from aesthetic appraisal as mere affective arousal. The musical artwork acts as an “effective median between two animated forces,” the composer and the listener. The aesthetic exaltation of the composer’s imagination yields a theme shaped by the composer’s individuality, which is subsequently elaborated according to the artistic talents of its creator (Hanslick 2018, 63–64). The composer’s personality molds music’s “infinite capacity for expression” through his “consistent preference for certain keys, rhythms, [and] transitions” that transform the composer’s sensibility into a part of objective musical structure, which in turn is open to the listener’s perception (Hanslick 2018, 65). The listener’s judgment about the concrete meaning of a given piece is therefore affected heavily by performance, which allows the artist to release directly the emotion apparently perceived in music (Hanslick 2018, 67–69). For Hanslick, the genuine affective reaction of the listener, especially powerful in the case of music, is beyond dispute, but the ways in which it is constituted varies considerably. If the listener’s approach to “pure” music involves the attentive tracking of compositional development and therefore transcends emotional indulgence, the approach is aesthetical (Hanslick 2018, 88–90). If the emotive impact of music is received passively, however, the listener’s attitude is regarded as “pathological”—a term that carries medical connotations but derives chiefly from the Greek notion of “pathos,” thereby denoting purely passive experience (Hanslick 2018, 81–88). For Hanslick, this mode of listening originates from the physical aspects of sound and its direct effect on the human nervous system and thus lacks the necessary component of Geist to be considered aesthetical. It actually belongs to physiological, psychological, or medical research and is not subject to aesthetic inquiry (Hanslick 2018, 71–80).

Hanslick’s analysis of the complex interplay between composer, artwork, and listener is followed by an investigation of music’s relation to nature, arguably the oldest chapter of OMB. In general, artworks present a twofold relation to nature: first, through their physical material (sound, paint, stone); second, through the content nature affords to art. In the case of “pure” music, considered a cultural artefact, the physical material provided by nature merely amounts to “material for material” (wood, hide, hair) that is used to create actual musical material (tones, intervals, scales), already a product of culture (Hanslick 2018, 95). Nature thus merely offers physical material for acoustic material that in turn provides material for the creative activity of the individual composer, which builds upon the collective repository of music history. As musical content consists entirely of musical features, the origins of which are not natural, Hanslick moreover postulates that nature cannot provide content for “pure” music and thus does not have any relation to musical artworks. Whereas sculptors, painters, and writers are able to draw inspiration from human actions or nature itself, music finds no preceding prototype beyond the history of “artificial” musical material and is thus only akin to architecture. In blatant contrast to mimetic concepts of art, Hanslick thus holds that “the composer cannot transform anything, he has to newly create everything” (Hanslick 2018, 103). At this point, Hanslick once more illustrates the historical evolution of musical material, emerging gradually as a creation of intellect, by noting how certain modern intervals “had to be achieved individually” over multiple centuries. Music itself, in each of its various aspects, is created entirely by intellectual ingenuity and represents a “consequence of the endlessly disseminated musical culture.” Hanslick therefore overtly advises to “beware of the confusion as though this (present) tone system itself necessarily lies in nature” (Hanslick 2018, 95–97). As Hanslick’s concept of scientific aesthetics is based on material features of musical structure, this view has significant implications for his entire stance: since musical material will constantly undergo extension, any alteration pertaining to crucial aspects of musical technique will also affect the basics of aesthetic research (Hanslick 2018, 98–99).

Finally, Hanslick revisits the question of musical content in order to differentiate meticulously between distinct concepts of content usually lumped together indiscriminately. Content is defined as that “what something contains, holds within itself.” In the case of music, “content” denotes the tones and forms a piece of music is made of. This term is not to be confused with “subject matter” that typically indicates abstract literary content of which music has none: “music speaks not merely through tones, it speaks only tones” (Hanslick 2018, 108–109). In music, the concepts of content and form—musical material and its artistic design—mutually determine each other and are ultimately inseparable: “With music, there is no content opposed to form, because it has no form outside of the content” (Hanslick 2018, 111–12). A separation between musical content and its form does merely pertain to cases in which form is applied to large-scale structures, which is not the standard meaning of this term in OMB. Only then can the theme be called content, whereas the overall structure, the “architectonic of the joined individual components and groups of which the piece of music consists,” acts as form. The theme, which “develops in an organically, clearly organized, gradual manner, like luxuriant blossoms from a single bud,” constitutes the irreducible aesthetic “essence” of a piece of music. As everything in a specific musical structure is a “spontaneous consequence” of the initial theme, the multitude of prospects in which a theme could be developed determines its aesthetic substance or Gehalt: “whatever does not reside in the theme (overtly or covertly) cannot subsequently be organically developed” (Hanslick 2018, 113–14). Even though music does thus not present subject matter along the lines of literary meaning, “pure” music, animated by “thoughts and feelings,” does clearly exhibit intellectual “substance.” Generally speaking, “pure” music has content: purely musical content manifest in the distinct musical features of the theme, which Hanslick describes poetically as “spark of divine fire.” Musical content, Hanslick emphasizes in conclusion, purely derives from the “definite beautiful tone configuration” of a given piece as the “spontaneous creation of the intellect out of material of intellectual capacity” (Hanslick 2018, 114–16).

f. Conclusion: The Curious Nature of Hanslick’s Formalism

Hanslick’s aesthetics is frequently considered the “classical definition of formalistic aesthetics in music” (Yoshida 2001, 179) and the “inaugural text in the founding of musical formalism as a position in the philosophy of art” (Kivy 2009, 53). What is meant by musical formalism and which exact version of musical formalism Hanslick is supposed to represent, however, is one of the divisive questions of Hanslick scholarship and of the philosophy of music at large. The conceptual significance of the term ‘form’ and its relevance for Hanslick’s theory seem to be overrated in principle. Philosophical commentators typically overlook that Hanslick’s definition of beauty in music—the focal point of OMB—does not rely upon any idea of form and that this term is indeed absent from Hanslick’s description of music’s artistic quality: by specific musical beauty, Hanslick designates a “beauty that is independent and not in need of an external content, something that resides solely in the tones and their artistic connection” (Hanslick 2018, 40). Furthermore, Hanslick’s infamous statement of “sonically moved forms” did not correspond to music itself, as is surmised regularly, but much more narrowly to music’s content that is thereby equated with form, and vice versa. Even the more pointed version in the second edition of OMB, which states that forms are “solely and exclusively the content and subject of music” did not identify form with music itself but rather claims the identity of the content and forms of music (Hanslick 2018, 41). Thus, these forms are not without content or thought of as empty but rather are imbued by intellect (Geist) “shaping itself from within” (Hanslick 2018, 43), thereby linking beauty to mental activity (Bowman 1991, 47; Paddison 2002, 335; Burford 2006, 179). Hanslick therefore opposes one of the central claims of formalist aesthetics that usually stresses the primacy of formal features over some kind of content (Fisher 1993, 250; Kivy 2002, 67; Beard and Gloag 2005, 65). In music, he states, “we see content and form, material and design, image and idea fused in an obscure, indivisible unity,” which means that “there is no content opposed to form” as music “has no form outside of the content” (Hanslick 2018, 111–12). By stating that form and content are one, Hanslick is “almost alone among formalists” (Payzant 2002, 83) and OMB thus even “reads more like a traditional criticism of formalism” (Hamilton 2007, 88).

Whether Hanslick’s aesthetics is to be regarded as formalist, however, depends entirely on the definition of formalism espoused by scholars. The special variety of Hanslick’s approach is clarified by one of the customary definitions of formalist aesthetics, the conception of formalism as common denominator argument (Carroll 1999, chap. 3 and 2001). In this case, formalism is understood as a universal definition of art, such as in Clive Bell’s (1881–1964) formalist manifesto Art, which posits a circular concept (Gardner 1996, 238; Carroll 2001, 95; Stecker 2003, 141) of “aesthetic emotion” elicited by “significant form” that “distinguishes works of art from all other classes of objects” and thereby defines the fine arts as such (Bell 1914, 13). Formalists, as Dziemidok (1993, 192) states, “strive to determine general criteria of valuation universally applicable to all art forms” and thus miss the “values unique” to each artistic medium by commencing with “universalistic assumptions.” As we have seen in sec. 3.b, this definition of formalism contradicts Hanslick’s insistence on the idea that the criteria of the musically beautiful apply solely to music itself and not to the other art forms. Further concepts of general aesthetic formalism prove to be similarly debatable: Small (1998, 135), for example, describes formalist theories as denying that “emotions have anything to do with the proper appreciation of music” (form versus emotion/content), while Mothersill (1984, 222) emphasizes formalism’s conviction that “elements which suggest or establish a link between the artwork and the world should be disregarded” (form versus context). In view of OMB, both ideas seem somewhat applicable but at the same time miss something important about Hanslick’s viewpoint: whereas aesthetic analysis—conceived as an objectivist scientific approach—is indeed distinct from historical concerns and the stimulation, expression, or portrayal of definite emotion, music itself affects emotion and is connected intimately to concurrent productions of art and the “poetic, social, scientific conditions” of its time and place (Hanslick 2018, 9, 55; cf. Wilfing 2016, 15–18). In general, any detailed appraisal of Hanslick’s formalism does hinge upon the individual definition of aesthetic formalism and ‘form’ itself—a term that is as ambiguous as it is persistent (Tatarkiewicz 1973, 216), which might be of limited efficacy in describing Hanslick’s argument and must thus be employed carefully (Nattiez 1990, 109; Bowman 1991, 53; Payzant 2002, 58).

4. The Intellectual Background of Hanslick’s Aesthetics

a. Hanslick and German Idealism

Historical research on OMB is dominated primarily by questions of intellectual dependency: Who influenced Hanslick’s aesthetic approach and which philosophical movement stimulated the main ideas of his aesthetic approach (Landerer and Wilfing 2018)? Numerous candidates have been invoked as precursors to Hanslick’s “formalism,” ranging from idealist theorists—Kant (1724–1804), Herder (1744–1803), Hegel (1770–1831), Schelling (1775–1854), Vischer (1807–87)—and German poetry—Lessing (1729–81), Goethe (1749–1832), Schiller (1759–1805), or the German literary romantics—to the Austrian context of Hanslick’s aesthetics and “minor” figures such as Michaelis (1770–1834), Novalis (1772–1801), or Nägeli (1773–1836). Generally speaking, current scholarship situates Hanslick’s argument in the (ultimately antithetic) traditions of German idealism and Austrian realism. The most prominent contender as the crucial source of OMB, emphasized particularly in analytical philosophy (Gracyk, chap. 1; Appelqvist 2010–11, 76; Davies 2011b, 297), is Kant’s Kritik der Urteilskraft (Critique of the Power of Judgment, 1790). As OMB is typically regarded as the classical definition of formalistic aesthetics in music and Kant’s Kritik is widely thought to be the origin of general aesthetic formalism, this link appears entirely natural (Ginsborg 2011, 334). Their respective definition of aesthetic intuition as disinterested contemplation, standing apart from rational thought and affect states, as well as their general concept of beauty, which is not subject to an external purpose or definite concepts, establish Hanslick’s awareness of Kant’s theory. Whether Hanslick, who did not receive any formal training in philosophy, ever read Kant or whether he adopted certain notions from post-Kantian aesthetic discourse (Dambeck, Michaelis, Nägeli, and so forth) is open to debate. Although Hanslick’s reliance on Kant’s theory is frequently accepted as fact, this view is complicated by at least three issues: (1) Kant’s notion of music as a servant of poetry and as a language of affect states was criticized vigorously by Hanslick. (2) Hanslick’s concept of specific musical beauty directly opposes Kant’s idealist attitude, which stipulates an abstract principle of beauty, administered retroactively to each art form. (3) The objectivist approach of Hanslick’s aesthetics contradicts Kant’s transcendental methodology, the crucial premise of his entire system (Bonds 2014, 188–89; Wilfing 2018, sec. 3.3).

While Kant is mentioned only once in OMB as one of those “eminent people” who did reject any literary content when it came to music (Hanslick 2018, 107), a different contender as the pivotal source of Hanslick’s aesthetics is referred to on multiple occasions: Hegel. Although a large share of Hanslick’s comments on Hegel are intended as criticism—he accuses Hegelian theories of an “underevaluation” of sensuousness in favor of ideas, for example (Hanslick 2018, 42)—various quotes and his early music reviews confirm that Hanslick was familiar with Hegel’s aesthetic positions. The theoretical importance of Hegel’s Vorlesungen über die Ästhetik (Lectures on Aesthetics, 1835–38) for the basic tenets of Hanslick’s approach have been investigated particularly by Carl Dahlhaus, who supported his viewpoint by drawing attention to Hanslick’s persistent utilization of the term Geist, which also permeates Hegel’s philosophy. Dahlhaus, however, did not regard Hanslick’s treatise as an uncritical extension of Hegel’s theory of art as the corporeal incarnation of the idea, in which music itself is only form, whereas thoughts and feelings are the content (Dahlhaus 1989, 110). For him, Hanslick’s theory inverts Hegel’s system by making the idea purely musical and thereby turning “form” into a concept of the interior, not the exterior (Burford 2006, 170; Bonds 2012, 8). Although Hanslick’s definition of composing as “intellect shaping itself from within” is probably situated in a general setting of Hegelian reasoning, the whole extent of Hanslick’s awareness of Hegel’s writings is unknown, as no related records survive. The situation is different, however, if we turn to Hegelian aesthetic theorists: We know that he read parts of Vischer’s Aesthetik oder Wissenschaft des Schönen (Aesthetics or Science of Beauty, 1846–57), for example, which might have been the most likely source for his Hegelian leanings (Titus 2008). Hanslick candidly criticized Hegelian aesthetics for its historical orientation, which seemingly confused historical research with aesthetic analysis, but he nonetheless emphasized the historical evolution of musical material and the arbitrary appraisal of specific artworks. The idea that artistic material does not merely consist of physical elements (sound, paint, stone), but moreover comprises the entire historical evolution of each art form—the historical interplay between material and mind—was a central concept of Vischer’s theory, linking Hanslick’s approach to Hegelian aesthetics.

b. Hanslick and Austrian Realism

As an Austrian theorist raised in Prague who spent most of his career in Vienna, the delineated relevance of German idealism for the basic tenets of OMB has to be supplemented by an analysis of Hanslick’s Austrian contexts. In the 19th century, Austrian science policies were strongly opposed to philosophical “speculation” that was held responsible for the societal upheaval in the wake of 1789 and 1848. These events caused several reforms of the Austrian school system, the primary purpose of which should be to foster the restoration endeavors of the Habsburg leadership by confining education to propaedeutic instructions compatible with Catholic dogmas and state norms. This political strategy resulted in the preservation of Leibnizian philosophy, the flourishing of positivistic scholarship, and the inhibition of German idealism in favor of methods perceived as decidedly scientific. One intellectual, who consciously modernized the Leibnizian framework engrained in the academic landscape of Austria, was the Prague priest and philosopher Bernard Bolzano (1781–1848). Although Bolzano was forced to resign owing to an unfounded accusation of Kantianism in 1819, the general precepts of his writings prospered in Habsburg territories by way of his scientific successor and Hanslick’s close friend Robert Zimmermann (1824–98), who attained a tenured position at the University of Vienna in 1861. Bolzano published his aesthetic doctrines in Über den Begriff des Schönen (On the Notion of Beauty, 1843) and Über die Eintheilung der schönen Künste (On the Classification of the Fine Arts, 1849). In similar fashion to Hanslick, he defined aesthetic perception as disinterested contemplation, construed musical listening as an intentional monitoring of compositional development, and dismissed emotivist models whilst insisting on particular aesthetics for each art form. Bolzano’s most significant contribution to Hanslick’s aesthetics, however, was his drastically objectivist approach isolated entirely from psychological explanations that might derive from Bolzano’s theory of science. Here, Bolzano outlines his Platonic concept of a “truth as such,” which states something as is, no matter whether this fact has been or ever will be uttered or thought by anyone. The radically objective condition of Hanslick’s concept of musical beauty, which remains beauty “even if it is neither viewed nor contemplated,” matches Bolzano’s Platonic mindset (Bonds 2014, 162; Wilfing 2018, sec. 2).

Another important precursor to Hanslick’s aesthetics, who is significant particularly due to his influence on Austrian science policies in general, is Johann Friedrich Herbart (1776–1841). As Herbart declared natural science the operational benchmark for philosophy and demanded a separation between philosophy, religion, and politics, his approach blended perfectly with the positivistic endeavors of Habsburg authorities and thereby became the semi-official philosophy of Austria. This gradual process was completed by the school reform of 1849, the leading figures of which closely adhered to Herbartian teachings (Landerer and Wilfing 2018, sec. 4), including Zimmermann, Hanslick’s former teacher Franz Exner (1802–53) and his old associate Joseph von Helfert (1820–1910). Hanslick, who attained a position at the ministry of education in 1854, recognized the importance of employing Herbartian principles in OMB, which should set the stage for his academic profession (Payzant 2002, 131). It thus comes as no surprise that Hanslick declared himself a follower of Herbart in his successful habilitation petition of 1856. As recent studies demonstrated convincingly, however, this personal testimony is probably nothing more than an allusion provoked by careerist concerns (Karnes 2008, 31–34; Bonds 2014, 159; Landerer and Zangwill 2016, 90–91). An immediate reference to Herbart is totally absent from earlier editions of OMB, where he is belatedly included in the third edition of 1865 and the sixth edition of 1881 (Hanslick 1986, 77, 85). In spite of this lack of quotes and in view of Herbart’s bearing on Austrian science policies, it is difficult to imagine that Hanslick was completely unfamiliar with Herbart’s ideas prior to the initial edition of 1854. In regard to Hanslick’s argument, Herbartian teachings seem to be important specifically for his formalist approach, for his theory of autonomous instrumental music, for his refutation of emotivist aesthetics, for his emphasis on elemental components of “pure” music and their mutual relations, and for his appreciation of technical musical analysis (Bujić 1988, 7–8; Bonds 2014, 158–62; Wilfing 2018, sec. 2). Generally speaking, the writings of Bolzano and Herbart were similar in various respects—a fact that lead to the frequent blending of their work in post-1848 Austria. Specific features of OMB, however, are decidedly Herbartian, such as Hanslick’s concept of emotion deriving from Herbart’s cognitivist reductionism that regards feelings as a subclass of Vorstellungen or presentations (Landerer and Wilfing 2018, 49n).

c. Editorial Problems and Eclectic Origins of OMB

The Austrian contexts of Hanslick’s aesthetics were supremely important for the contentual alterations following the initial edition of OMB (Landerer and Wilfing 2018, sec. 4). The most striking example of these severe changes, owing to the scientific landscape of contemporary Austria, is the removed final paragraph of Hanslick’s classic treatise. OMB originally concluded in idealist fashion, linking the musically beautiful with “all other great and beautiful ideas.” As “pure” music ultimately represents a sounding portrayal of the motions of the cosmos, it eventually transcends its conceptual limitations, “allowing us to feel… the infinite in works of human talent.” The vital traits of musical structure (harmony, rhythm, sound), Hanslick proclaims, permeate the universe so that one can “find anew in music the entire universe” (Bonds 2012, 4; cf. Hanslick 2018, 120). This original ending of OMB evidently betrayed remnants of German idealism and therefore countered Austrian science policies. This discrepancy was pointed out to Hanslick by the foremost Herbartian philosopher of his time and place: Zimmermann. In an extensive review, published in 1854, he commended the positivistic orientation of Hanslick’s argument that apparently conformed to Herbartian aesthetics, but at the same time criticized the idealist notions present in OMB. According to Zimmermann, the idea that the musically beautiful is completely autonomous epitomized the crucial insight of Hanslick’s argument. For him, this advantage of Hanslick’s aesthetics was compromised by his concession to an aesthetics dependent on speculative metaphysics (Bonds 2012, 5–6). As this public review outlined the Herbartian sentiments of Habsburg authorities responsible for his future career, Hanslick deleted the closing remarks as well as additional passages evocative of his former idealist stances (Landerer and Zangwill 2016; Sousa 2017). It is for this reason that the historical reception of OMB in anglophone scholarship was impacted markedly by Hanslick’s alterations: whereas German-language discourse is based mostly on the initial edition of OMB, its translations utilized editions 7 (Cohen), 8 (Payzant), and 10 (Rothfarb and Landerer) that read more formalistic and positivistic than earlier versions. As the deleted ending of OMB was translated for the first time as late as 1988 (Bujić 1988, 39) and was not discussed seriously by anglophone academics prior to Bonds’s studies, one can get the impression that scholarship in German and English addresses quite different books (Payzant 2002, 44).

A relevant outcome of current research into Hanslick’s intellectual background, however, is the emerging realization that Hanslick’s aesthetics draws upon a wide array of assorted aesthetic discourses integrated into OMB. It is no contradiction that Hanslick’s emphasis on structural relations between musical elements is derived from Herbartian aesthetics, whilst his concurrent refutation of psychological considerations—supremely important for Herbartian aesthetics—appears to be closer to Bolzano. The same applies to Hanslick’s Vischerian concept of historical evolution, overtly opposing the ahistorical orientation of Herbartian aesthetics, and his anti-Hegelian insistence on a categorial distinction between the methods of historical and aesthetic research derived from Herbartian philosophy (Edgar 1999, 443–44; Landerer and Zangwill 2017, 93–94). Hanslick’s textual strategy frequently resembles a virtual collage as in a passage reworded for the second edition of 1858: Hanslick defends that beauty remains beauty “even when it arouses no emotions, indeed when it is neither perceived nor contemplated. Beauty is thus only for the pleasure of a perceiving subject, not generated through that subject” (Bonds 2014, 189; cf. Hanslick 2018, 4). The first part of Hanslick’s quotation is adopted directly from Zimmermann’s review and might even have an immediate antecedent in Bolzano, the former teacher of Zimmermann. Bolzano makes a similar objectivistic statement in On the Notion of Beauty by stating that beauty would remain beauty “even if there existed only one human being in the entire world or no one at all.” The first part of the second sentence, however, alludes to Vischer’s Aesthetics and his concept of Anschauung (perception), thereby directly linking the opposing approaches of Herbartianism and Hegelianism. Hanslick purposely disregards Zimmermann’s ensuing assertion that beauty is based on constant relations between aesthetic properties and thus does not change over time as he acknowledged the historical condition of music and beauty (Landerer and Wilfing 2018, sec. 3). Generally speaking, Hanslick’s argument comprises a multitude of diverse sources—which at times are blatantly antithetic—and his intellectual background is therefore difficult to reconstruct thoroughly. His “eclectic” approach, however, ensured the remarkable durability of Hanslick’s aesthetics, which was not bound by the rise and fall of isolated academic traditions (Bujić 1988, 8).

5. The Reception of Hanslick’s Aesthetics and Its Relevance to Current Discourse

a. A General Outline of Hanslick’s Reception by Austro-German Discourse

The historical reception of Hanslick’s aesthetics, stretching from Viennese Modernism, the beginnings of musicology, and numerous composers to significant philosophers such as Friedrich Nietzsche (1884–1900), Theodor W. Adorno (1903–69), Langer, and analytical aesthetics in general, for the most part represents “terra incognita” (Deaville 2013, 25). Scholarship on Hanslick’s reception is typically restricted to incidental references to conceptual similarities between Hanslick and certain later authors. OMB is mentioned by Karl Popper (1902–94), for example, and probably affected his objective aesthetic approach, his wariness regarding psychological argumentation, and his rejection of emotivism. Ludwig Wittgenstein’s (1889–1951) late work is similarly evocative of Hanslick’s approach, as he declares musical meaning to be purely musical and repudiates the idea that “pure” music could be translated adequately into other modes of expression (Ahonen 2005, 520–23; Szabados 2006, 651–53). Adorno’s adoption of Hanslick’s dynamism (Goehr 2008, 20; Paddison 2010, 131–34) and his distinction between different attitudes towards musical listening betray Hanslick’s impact as much as Adorno’s concept of the historical evolution of musical material (Edgar 1999, 441–44; Paddison 2002, 336), firmly rooted in Hegelian aesthetics. Hanslick’s influence on Nietzsche is particularly remarkable as it spans from his earliest writings to his late work. His vigorous criticism of Wagner in Der Fall Wagner (The Case of Wagner, 1888) and Nietzsche contra Wagner (1889) is inspired evidently by Hanslick’s writings, replicated virtually verbatim on numerous occasions. OMB similarly influenced young Nietzsche, who studied Hanslick’s treatise as early as 1865 and employed Hanslick’s argument in fragment 12[1] of 1871 on the relation between language and “pure” music. Here, Nietzsche verbalizes doctrines that are far more indicative of his eventual refutation of Wagner’s oeuvre than his Geburt der Tragödie (Birth of Tragedy, 1872), written at the same time, might suggest. Scholars have thus assumed a rather brief period of unwavering enthusiasm for the Bayreuth composer (Prange 2011). No philosophical movement, however, has addressed Hanslick’s aesthetics as fruitfully as analytical philosophy, particularly so due to its strong focus on the expressive capabilities of “pure” music.

b. Hanslick’s Reception by Analytical Aesthetics and the Direct Impact of OMB

The crucial feature of analytical philosophy is its methodic scientism as the foundation for all philosophy and all knowledge acquisition in general. Current research into the key attributes of analytical aesthetics regularly highlights its tendency to detach the targets of analysis from various contexts in order to establish the possibility of objective observation (Roholt 2017, 50–51). Hanslick’s positivist approach targeted towards scientific objectivity, his strong appeal to natural science as a guideline for objective aesthetics, and his procedural dissociation of musical artworks from external contexts that are not relevant for aesthetic purposes concurs with this provisional description of analytical philosophy of music. Historically, Hanslick’s aesthetics was perceived as an important corrective to the “fantastic nonsense” and “sentimental speculations” of idealist theories (Lang 1941, 978; Epperson 1967, 109–10) and therefore contributed to the anti-idealist movement of analytical philosophy aimed against Hegelians such as Francis Bradley (1846–1924), Bernard Bosanquet (1848–1923), or John McTaggart (1866–1925). Early analytical aesthetics of the 1950s and 1960s, which initially needed to cast off its widespread reputation of conducting unscientific guesswork, was concerned principally with abstract problems and attempted to determine an exhaustive definition of art, the quality and quantity of aesthetic properties, and the peculiarity of aesthetic perception (Goehr 1993; Lamarque 2000). Even though this focal point of anglophone philosophy left no room for OMB and its emphasis on musical artworks, Hanslick’s treatise gained traction the moment aesthetics redirected its inquiry towards more concrete subjects. Works on issues related to music, increasing strikingly in the 1980s (Lamarque 2000, 14; Davies 2003, 489), proceeded from influential publications by Budd, Davies, and Kivy (all 1980) that featured Hanslick’s aesthetics markedly and set the scene for ensuing decades of anglophone philosophy of music (Davies 2011b, 294). Each of their texts is focused on problems of musical expression and drew from Hanslick’s cognitive concept of emotion, resembling the approach developed by Stanley Schachter and Jerome Singer in the 1960s. Thus, the development of aesthetics concerned with specific objects and the establishment of cognitivist psychology coincide with and form the basis of Hanslick’s fruitful reception by analytical aesthetics.

Hanslick’s theories, the impact of which has even been compared to David Hume’s (1711–76) historic critique of speculative philosophy (Hanslick 1957, vii), shaped the general position on musical meaning in anglophone philosophy. Even though hardly any current approach concurs entirely with Hanslick’s aesthetics (Zangwill 2004 is a prominent exception), his momentous formulation of certain issues continues to dominate aesthetic discourse (Maus 1992, 273; Davies 2003, 492; Hamilton 2007, 82). This fact is exemplified particularly by authors who discard OMB and its cognitivist orientation, but nonetheless acknowledge that his views are permeating anglophone philosophy (Madell 2002, 1–9). His cognitive hypothesis, however, was not the only argument espoused by analytical academics, who also drew from more specific aspects of OMB. Hanslick’s rejection of basic forms of musical expression, treating affective features as a direct result of the composer’s emotional condition (Hanslick 2018, 63–65), for example, is basically accepted by modern research (Kivy 1980, 14–15; Davies 1986, 148; Naar, chap. 3b). Hanslick justifies this view with the theoretical redundancy of an aesthetic approach that traces the cause of emotional expression to a source located outside of art. Musical expression is successful principally in virtue of the expressive properties of music chosen to indicate a specific feeling and cannot be explained by reference to the artist’s affect states, already absorbed by his creation (Kivy 2009, 250; Davies 2011a, 23; Gracyk 2013, 78–79). Another argument aimed against arousal theories that has been discussed frequently by anglophone philosophers, and that was coined mainly by Budd (1985, 125), is the “heresy of the separable experience” (Ridley 1995, 38–49; Scruton 1997, 145–46; Madell 2002, 32, 57, 99). If musical expression is dependent on the response of the listener, music might become nothing more than a random medium of transference, which could be replaced by objects causing an identical response, and loses sight of the individuality of the composition (Hanslick 2018, 91–92). Hanslick proposes that causal theories cannot explain the unique quality of musical artworks as they tend to regard music as a device for affective arousal that could just as well be realized by a warm bath, a cigar, chloroform (Hanslick 2018, 83), or by a drug causing feelings (Kivy 1989, 218, 222, 242; Matravers 1998, 169–85; Robinson 2005, 351, 393, 397).

c. Bypassing Hanslick’s Cognitivist Arguments: Kivy, Davies, and Moods

As we have seen, important objections directed against current theories of musical arousal and expression propounded by anglophone philosophers stem from Hanslick’s aesthetics and extend beyond the cognitivist hypothesis of OMB. His cognitivism is therefore frequently considered the strongest argument that emotivist aesthetics has substantial weaknesses (Kivy 1989, 157; Davies 1994, 209). Hanslick’s (implicit) concept of indeterminate expressivity (Wilfing 2016, 26–29) suggests that emotion is an inherent property of musical structure—an idea that laid the ground for the enhanced formalism of Davies and Kivy, which is based on the similarity perceived between musical motions and the outward features of human emotion. Enhanced formalism does not hold that music refers beyond itself to occurrent emotions but considers expression an objective property of musical structure: music itself is the owner of the emotion it expresses (Davies 1980, 68; Kivy 1980, 64–66). Hanslick, however, had good reasons to abandon enhanced formalism as the theoretical foundation of scientific aesthetics—reasons that paved the way for another argument crucial to analytical aesthetics: the argument from disagreement (Gardner 1996, 245–46; Sharpe 2004, 19–20). While Davies (1994, 213–15) and Kivy (1990, 175–77) fully agree that “pure” music cannot express Platonic attitudes (emotions such as pride or shame that involve complex concepts), they hold that it is able to portray definite emotional properties of a lower order. Hanslick’s attitude is even more skeptical: As the dynamic character of affect states is only one moment of emotion, not emotion itself, music can merely allude to a certain variety of affect states, not to any sentiment in particular, and any survey among an audience regarding the emotion ascribed to a piece would thus yield varied results (Hanslick 2018, 23). As enhanced formalism is based on the semblance perceived between musical motion and emotive behavior, Davies and Kivy needed to dismiss Hanslick’s claim about considerable disagreement by gradually retreating to more and more general emotions, which serve as umbrella concepts for specific emotions (Kivy 1980, 46–48; Davies 1994, 246–52). Other scholars pointed to Hanslick’s metaphor of expressive silhouettes and construed his argument in terms of indeterminate expressivity along the lines of Rorschach’s inkblot testing, thereby updating Hanslick’s argument for modern debates (Ahonen 2007, 93).

Generally speaking, OMB introduced numerous important arguments to analytical aesthetics that remain the subjects of current research, such as the famous paradox of negative emotion, which Hanslick directed against theories of musical arousal. If every death march or every somber adagio, Hanslick declares, had the power to elicit grief in the listener, nobody would bother with such works (Hanslick 2018, 90–91). Solutions to Hanslick’s question vary from the rejection of emotive arousal (Kivy 1989, 234–59) and accounts of the way negative emotions have beneficial pedagogic effects (Levinson 1982; Davies 1994, 307–20; Ridley 1995, chap. 7) to revised arousal theories that hold that emotional reactions to music rarely mirror the feeling depicted by a given piece (thus, a somber adagio could arouse compassion instead of sorrow; Matravers 1991 and 1998, chap. 8). Finally, Hanslick’s cognitivist formalism has contributed to a noticeable reframing of the general approach to emotive musical meaning. Matravers, for example, asserted that a piece of music would depict a specific emotion if it arouses a feeling, the physiological components of which would correspond to the emotion depicted (Matravers 1998, 149). As music cannot portray the cognitive elements of genuine emotions, Hanslick’s argument is bypassed by an appeal to feeling as the somatic feature of emotion, which music is able to prompt directly (Matravers 1991, 328). Ridley, who endorses Hanslick’s cognitive objection to common arousal theories, shares this idea by considering “objectless passions” as feelings, the gestural character of which is evoked by the dynamic qualities of music (Ridley 1995). Thus, OMB and its cognitivist orientation occasioned a shift from issues of emotional expression to issues of music’s relation to non-cognitive affect states—a shift also made clear by an increased discussion on music and moods (Radford 1991; Carroll 2003; Sizer 2007). Although OMB has thus come under attack in anglophone philosophy, the constant rebuttal of Hanslick’s aesthetics at the same time illustrates the degree to which his approach is ingrained in analytical philosophy in regard to questions of musical meaning. The lion’s share of theorists continues to consider Hanslick’s cognitive argument to be accurate in principle and adjusts their models of expressivity accordingly. Hanslick’s influence on current debates thus goes beyond the assenting reception of OMB and thereby remains equally present in modern theories intentionally sidestepping the key argument of Hanslick’s approach.

6. References and Further Reading

a. Primary Sources

  • Hanslick, Eduard. 1950. Music Criticisms, 1846–1899. Translated by Henry Pleasants. Harmondsworth: Penguin Books.
  • Hanslick, Eduard. 1957. The Beautiful in Music: A Contribution to the Revisal of Musical Aesthetics. Edited by Morris Weitz. Translated by Gustav Cohen. Indianapolis: Bobbs-Merrill.
  • Hanslick, Eduard. 1986. On the Musically Beautiful: A Contribution Towards the Revision of the Aesthetics of Music. Translated by Geoffrey Payzant. Indianapolis: Hackett.
  • Hanslick, Eduard. 1993. Sämtliche Schriften: Historisch-kritische Ausgabe. Vol. 1, Aufsätze und Rezensionen 1844–1848. Edited by Dietmar Strauß. Vienna: Böhlau.
  • Hanslick, Eduard. 1994. Sämtliche Schriften: Historisch-kritische Ausgabe. Vol. 2, Aufsätze und Rezensionen 1849–1854. Edited by Dietmar Strauß. Vienna: Böhlau.
  • Hanslick, Eduard. 2018. On the Musically Beautiful: A New Translation. Translated by Lee Rothfarb and Christoph Landerer. Oxford: Oxford University Press.

b. Secondary Sources

  • Ahonen, Hanne. 2005. “Wittgenstein and the Conditions of Musical Communication.” Philosophy 80: 513–29.
  • Ahonen, Hanne. 2007. “Wittgenstein and the Conditions of Musical Communication.” PhD diss., University of Columbia.
  • Alperson, Philip. 1984. “On Musical Improvisation.” Journal of Aesthetics and Art Criticism 43, no. 1: 17–29.
  • Alperson, Philip. 2004. “The Philosophy of Music: Formalism and Beyond.” In The Blackwell Guide to Aesthetics, edited by Peter Kivy, 254–75. Malden: Blackwell.
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Research for this article was supported financially by the Austrian Science Fund (FWF, project number P30554-G30).

Author Information

Alexander Wilfing
Email: alexander.wilfing@oeaw.ac.at
Austrian Academy of Sciences
Austria

and

Christoph Landerer
Email: chlanderer@gmail.com
Austria

The Semantic Theory of Truth

The semantic theory of truth (STT, hereafter) was developed by Alfred Tarski in the 1930s. The theory has two separate, although interconnected, aspects. First, it is a formal mathematical theory of truth as a central concept of model theory, one of the most important branches of mathematical logic. Second, it is also a philosophical doctrine which elaborates the notion of truth investigated by philosophers since antiquity. In this respect, STT is one of the most influential ideas in contemporary analytic philosophy. This article discusses both aspects.

The STT is designed to define truth without circularity and to satisfy certain minimal conditions that must be met by any adequate theory of truth.

STT as a formal construction is explicated via set theory and the concept of satisfaction. The prevailing philosophical interpretation of STT considers it to be a version of the correspondence theory of truth that goes back to Aristotle. This theory is presented here in its modern shape, that is, as associated with first-order logic. Tarski’s original account used the elementary theory of classes (a theory similar to the simple theory of types).

One of Tarski’s most important results was to show that a theory of truth for set theory cannot be given within set theory itself, and that any truth definition for a formal language L must be given in a language which is essentially stronger than L.

Table of Contents

  1. Historical Introduction
  2. Outline of STT
  3. Informal Presentation of STT
  4. Formal Presentation of STT
  5. Philosophical Comments
  6. Final Remarks
  7. References and Further Reading

1. Historical Introduction

Alfred Tarski (1901–1983) was a Polish mathematician, logician and philosopher. He lived in the U.S.A. from 1939 onward and became an American citizen in 1945. He was a member of the Polish Mathematical School, the Warsaw School of Logic and the Lvov-Warsaw Philosophical School. These schools flourished in the interwar period (1918-1939).

While investigating problems associated with the definability of real numbers, Tarski came to the conclusion that the concept of satisfaction informally used in mathematics can help in defining the concept of truth. In 1930, he delivered two lectures (one in Warsaw. the second in Lvov) devoted to the concept of truth. In 1931, he began to work on a monograph on this topic. It was published in 1933 (see Tarski 1933) as Pojęcie prawdy w językach nauk dedukcyjnych (The Concept of Truth in Languages of Deductive Sciences). This book was well-received in Poland.

Due to Tarski’s contacts with the Vienna Circle, his semantic ideas became known abroad. The German translation (Der Wahrheitsbegriff in den formalisierten Sprachen) of Tarski’s Polish book appeared in 1935 (see Tarski 1935). In the same year, Tarski lectured at the Paris Congress for Scientific Philosophy; his lectures on the foundations and semantics and on the concept of logical consequence were applauded; (see Tarski 1936 and Tarski 1936a). His popular paper on the concept of truth appeared in Philosophy and Phenomenological Research in 1944 (see Tarski 1944). The English translation based on the German version of the book on truth (see Tarski 1956a) was included in Tarski’s famous collection Logic, Semantics, Metamathematics (1956). The last Tarski’s essay on truth (rather more popular than formal), namely “Truth and Proof”, was published in 1969 (see Tarski 1969). Since all Tarski’s writings on truth present principally the same ideas, this article does not refer to his particular works, except in some places.

2. Outline of STT

The Semantic theory of Truth (STT) has many ingredients. The most important are as follows:

  • (A) Truth as a property of sentences;
  • (B) Relations between truth and meaning;
  • (C) Diagnosis of semantic paradoxes;
  • (D) Resolution of semantic paradoxes;
  • (E) Relativization to languages;
  • (F) T-scheme (A is true if and only if A);
  • (G) The principle BI of bivalence;
  • (H) Material and formal adequacy of a truth-definition;
  • (I) Conditions imposed on a metalanguage in order to obtain a proper  truth-definition;
  • (J) The relation between language and metalanguage;
  • (K) The truth-definition itself;
  • (L) Maximality of the set of truths in a given language;
  • (M) The undefinability theorem.

These points are gradually elaborated in the next remarks, with capital letters referring back to the above list.

(A)–(B). For Tarski, sentences are truth-bearers. However, sentences are always equipped with meanings. Tarski avoided explaining what the meaning of an expression is. On the other hand, he explicitly said that the problem of defining truth is meaningless for purely informal languages. Roughly speaking, the semantic truth-definition (SDT, for brevity) is formulated for formalized languages.

(C)–(D). The Liar Paradox is a serious problem for any truth-definition. The ancient version attributed to Epimenides runs as follows. A Cretan says “I am lying now”. If he is actually lying, his sentence is true, but if he is not lying, the sentence in question is false.  Contradiction! For the modern version, consider the sentence

(S) The sentence denoted by (S) is false.

Observe that (S) = ((S) is false). Since, (S) and ‘(S) is true’ are equivalent, we obtain a contradiction expressed by

(LP) (S) is true if and only if (S) false.

What are sources of the Liar Paradox (LP)? First, it employs the sentence (S) which asserts its own falsity. Such a situation is called a self-referential use of a semantic concept; the semantic concept in this case is falsehood. Second, the Paradox uses a rule that a sentence, let us say A, is true if and only if A (which Tarski called the T-scheme). Third, we apply, classical logic, in particular, the law of bivalence, that is, (BI).

This diagnosis, which was proposed by Stanisław Leśniewski (Tarski’s teacher in Warsaw) and adopted by Tarski, offers three ways out of the Paradox. First, one could eliminate self-referentiality from the language. Second, reject the T-scheme. Third, change logic, in particular, reject (BI). The third strategy is popular in the twenty-first century, and it uses the techniques of many-valued logic, logic with truth-value gaps, or paraconsistent logic. These solutions will not be commented upon in this article. Anyway, Tarski considered them to be too complex and too narrow because they require the rejection of what should be retained. The T-scheme, according to him, is so intuitive that it cannot be rejected. Thus, the proper solution is to eliminate self-referentiality, he said.

(E)–(F). How to eliminate self-referentiality? The main idea is that the concept of truth should be relativized to a language. More specifically, we deal with the context ‘the sentence A is true in a language L’. However, this move is still insufficient, because if self-referentiality is to be banished, the adjective ‘true’ must belong to another language. This new language is called the metalanguage and is abbreviated by the symbol ML (we assume that L is a corresponding language). The simplest and the most popular situation is that L is an object-language (used to speak about the world) and ML forms its metalanguage, suitable for speaking about L. Here is an example. Assume that German is our object-language, but English serves as the associate metalanguage. We write in L ‘Schnee ist weiss’, but in ML we write ‘The German sentence “Schnee ist weiss” means that snow is white’. We see that ML must contain resources for speaking about expressions belonging to L. In order to indicate that we are speaking about L-expressions, we use quotation marks, but many other devices can be employed. For instance, we can use italics and write that the sentence Schnee is weiss means that snow is white. The most important observation is that expressions like ‘Schnee ist weiss’ and Schnee ist weiss are (metalinguistic) names in ML of the corresponding German sentence that is in L. The standard way of capturing the reported distinction is to say that expressions are used in L, but mentioned in ML.

The above conventions function as the part of STT. A simple example is

(1) ‘Schnee ist weiss’ in German is true if and only if snow is white.

The interaction of two languages in (1) consists in the fact that the name of the german sentence is on left, and its English translation is on the right. If the same language functions as both L and ML, one should speak about self-translation. According to the foregoing explanations we can generalize (1) into

(TS) ‘A’ is true in L if and only A*,

where the symbol A* refers to a translation of the sentences denoted by the name ‘A’. It is the general form of the T-scheme. (For additional discussion of the T-scheme, see the Liar Paradox.) Note that we cannot replace (TS) by

(2) For any A, ‘A’ is true if and only if A,

because the letter A is not free in the expression ‘A’. Quotes can be regarded as a name-forming operator. Anyway, concrete biconditionals (T-sentences, T-equivalences) arising from (TS) play the crucial role in STT. Roughly speaking, they capture the following intuition: a sentence saying so and so is true if so and so.

All explanations given above are formulated in ordinary English. It is easy to see several inconveniences of this approach. For instance, we should multiply quotes, when we pass from using to mentioning, for instance to write ‘‘A’’, when ‘A’ is mentioned. To simplify the issue, we replace some occurrences of quotes by such expressions as ‘name’, ‘sentence’, and so forth. Also, the concept of translation as applied to ordinary languages is not precise. The most important thing is that ordinary languages contain their own metalanguages, that is they are (to use Tarski’s way of speaking), semantically closed. This circumstance causes semantic paradoxes; the Liar is only one of them, but we will not consider others.

Tarski was very sceptical about the possibility of successfully providing a coherent truth-definition for ordinary language. Hence, he worked with a formal language. Such a language must have a well-defined alphabet (the set of elementary expressions), a well-defined set of formulas and a logical basis. If L is a formalized language, its ML is only partially formal, usually a part of ordinary mathematics. The following example illustrates the issue. Let ‘P(a)’ be the considered formula. It is an atomic formula of first-order language and says that a is P (the object a has a property P). The truth conditions of this sentence should be formulated by

(3) ‘P(a)’ is true if and only if a is a member of the set P,

where the non-italics letter P refers to the set that is denoted by the italicized predicate letter P. When (3) is expressed more formally in set theory, the binary relation “is a member of” is usually represented by the Greek letter epsilon, namely . In this example, the language of set theory serves as the metalanguage ML. To finish this part, note that Tarski liberalized his early negative attitude to ordinary speech. In his later works, he introduced the concept of languages having specified structure (see Tarski 1944). They are not semantically closed formalized languages, but are well-described by specification of their units, complex expression and the underlying logic.

3. Informal Presentation of STT

 

As noted earlier, Tarski considered the concept of satisfaction (more precisely, the satisfaction relation) as basic for defining truth. In particular, truth is to be defined as a special case of satisfaction. Assume that L is given – it is a first-order formal language. Open formulas are defined as containing free variables. By contrast, closed formulas have no free variables – for instance, P(a) or xPx. Open formulas are satisfied or not, depending upon how the free variables are interpreted in a given domain D, but sentences are true or false. Take the formula ‘x is a city’. Let D consist of cities and rivers. Our formula is satisfied by London, but not by Thames (we assume that the name ‘Thames’ refers to the river Thames). Furthermore, the sentence ‘London is a city’ is true in D, but the sentence ‘Thames is a city’ is false in D. Roughly speaking, satisfaction converts open formulas into true sentences, but non-satisfaction into false ones. Moreover, these considerations show that an instance of the T-scheme, namely the equivalence ‘the sentence ‘London is a city’ is true if and only if London is a city’ correctly displays the main ordinary intuition associated with the predicate ‘is true’.

The above explanations do not provide a definition of truth. Consider now two collections of ideas:

(A) (General case): open formulas,
satisfaction by some objects from D;
non-satisfaction by some objects from D;

(Special case): closed formulas (sentences), satisfaction by ?;
non-satisfaction by ?

Inspecting the formulas ‘x is a city’ and ‘London is a city’ leads to the conclusion that although satisfaction depends on valuation (valuation given by a valuation function consists in attributing denotations from D to expressions of L) of free variables, truth and falsehood do not. The reason is very simple and even trivial, namely that sentences have no free variables. Consequently, truth and falsehood should (even must) be independent of how the valuation function acts with respect to terms that are free variables. On the other hand, logical values are determined by valuations of constants (individual names, such as ‘London’) and predicates (such as ‘is a city’) as well as by the understanding of logical constants (propositional connectives, quantifiers and identity).

The last observation motivates the following formulation of SDT assuming that the domain of interpretation D is fixed:

(3) (a) ‘A’ is true if and only if ‘A’ is satisfied by any object in D;

(b) ‘A’ is false if and only if ‘A’ is satisfied by no object in D.

Using ‘London is a city’ as an example we have that this sentence is true if and only if it is satisfied by any object from D (this formulation will be commented upon below). Now, (A) can be corrected by dropping question-marks as

(B) Open formulas: satisfaction by some objects from D, but not others;

sentences: satisfaction by all objects from D (truth);

open formulas: non-satisfaction by some objects from D;

sentences: satisfaction by no objects from D (falsity).

The formal version of (B) is formulated in the next section.

The definition of sentences as open formulas without free variables looks at first sight like an artificial mathematical trick, but such constructions frequently occur in mathematical practice as useful simplifications. For example, the straight line can be considered as a special case of a curve, or Euclidean space as a special instance of Riemannian space, and so forth. Consequently, (B) can be charged with being a result of a purely formal game, completely alien to ordinary and philosophical intuitions. Tarski did not conceal that his explanations pertaining to truth employ mathematical concepts and techniques that are perhaps fairly obvious for practising mathematicians, but that are not convincing as tools of a reasonable philosophical analysis. This article does not do that. However, one can also try to argue that this definition fulfills some intuitive constraints. For instance, it entails that no sentence is true and false at the same time (the metalogical principle of contradiction). On the other hand, if A is an open formula, it is not the case that either A is satisfied or ¬A is satisfied. The formulas P(x) and ¬P(x) can serve as an example – both can be satisfied, for instance, ‘x is a city’ and ‘x is not a city’ can be satisfied though not by the same city. This example shows that generally speaking satisfaction of open formulas has some other properties than truth attributed to sentences, although, both concepts are related in many ways. By definition, every sentence is satisfied by all objects or by no object. Assume that the formula xP(x) is true and, thereby, satisfied by every object. Its negation, the formula x¬P(x), is satisfied by no object. This assertion implies the metalogical principle of the excluded middle. Thus, we reach (BI) (the principle of bivalence).

Let us try to come up with a philosophical paraphrase of the statement that if truth and falsehood are independent of valuations of free variables, then having logical values by sentences depends on how things are in considered universes, in our example, in D. It is time to introduce (informally, but it suffices) the concept of model. Models are algebraic structures consisting of a universe U (that is, a set of objects; some items can be distinguished and named by special names – individual constants) and relations, defined on U (other elements of model are omitted). If X is a set of sentences and M is its model, then all sentences belonging to X are true in M. Perhaps we could say that if truth and falsehood are indeed free of such valuations, then whether sentences have definite logical values is how things are in a relevant model.

Two additional remarks are in order. First, satisfaction by all objects cannot be regarded as equivalent to being a logical tautology. Satisfaction is always relative to a chosen (fixed) universe. In particular, all conclusions made in this section assume that the stock of predicates – such as ‘is a city’ is established in advance and its elements have a definite meaning that stems from a specific interpretation. If A is a logical tautology this means that A is true (now in the outlined sense) in all models Second, truth and falsehood relativizes truth (and falsehood) not only to L, but also to M. To sum up, SDT considers truth as relativized to an interpretation of L via M. In fact, SDT defines the set of true sentences in a given L. This literally means that the definition in question is extensional, that is, determines the scope of the predicate ‘is true’. However, taking into account that every definition of a given set X as a reference of a predicate P, directly or indirectly, deals with the content of P, SDT offers an understanding of the property expressed by P.

To be satisfactory SDT must conform to so-called conditions of adequacy. More specifically, this definition must be (a) formally correct, and (b) materially correct Condition (a) means that the definition does not lead to paradoxes and it is not circular. These requirements involve the interplay of L and ML functioning as insurance against semantic inconsistencies. Moreover, SDT does not appeal to the concept of truth for ML. Condition (b) is formulated as the Convention T (CT, for brevity) stating that (a) a formally correct truth-definition should logically entail all instances of T-scheme available in L; (b) Tr L (the set of true sentences of L is a subset of the entire L). CT shows that the T-scheme is not a required T-definition. On the other hand, Tarski underlined that every particular T-sentence provides a partial definition of truth for a given sentence. One could possibly form the conjunction of all T-equivalences as the definition, but this formula would to be infinite in length (thus, this maneuver is limited to finite languages). Moreover, the T-scheme does not imply (BI).

A standard objection against STT points out that it stratified the concept of truth. It is because we have the entire hierarchy of languages Lo (the object language), L1 ( = MLo), L2 (= ML1), L3 (M L2), …. Denote this hierarchy by the symbol HL. It is infinite and, moreover, there is no universal metalanguage allowing a truth-definition for the entire HL. Such a language would be semantically closed and, thereby, inconsistent. STT generates the hierarchy ‘truth in L0’, ‘truth in L1’ ‘truth in L2’, …, contrary to the ordinary use of ‘is true’ which is not stratified. Thus, SDT must be separately performed at every level of HL. Two observations are in order in this context. Firstly, we have that Tr(Ln) Tr(Ln+1), for every n, due to the fact that every Ln is translated into its metalanguage Ln+1. Consequently, HL is cumulative, that is, Tr(Ln+1) includes all truths of Ln. Secondly, taking first-order logic as the foundation and the Hilbert thesis (every theory can be formalized in the first-order language), we define ‘true in the first order L’ in ML. This second language is partially informal. In fact, SDT for first-order languages requires tools from weak-second order logic (but it is too formal issue to be explained in this survey). Thus, the stratification objection (originally formulated for Tarski’s construction via a simple theory of types) can be easily discarded and we can stay with one concept of truth. The price is that the concept of truth cannot be used for sentences formulated in ML.

4. Formal Presentation of STT

The earlier explanations concerned the simplest case, namely satisfaction of monadic open formulas, that is, of the form P(x). What about the formula (a) ‘x is a larger city than y’, which expresses the relation of being a larger city? We can say that the sequence <London, Manchester> satisfies (a), but not the sequence <Manchester, London>. (This article assumes the reader knows logical notations and elementary set-theoretical concepts, particularly the concept of sequence.) Since formulas can have arbitrary length, we need a generalization of this procedure in order to have a uniform way of dealing with all cases. This was Tarski’s motivation for introducing the concept of satisfaction by means of infinite sequences of objects. Since formulas are of arbitrary but always finite length, infinite sequences have a sufficient number of members to cover the satisfaction of all possible cases of particular formulas. This intuition is articulated by

(4) A is satisfied by an infinite sequence s = <s1, s2, s3,…>, where sn (n 1) refers to the nth term of s.

The definition of satisfaction (SAT; the symbol I refers to an interpretation) is as follows (This article simplifies indexing, and it restricts terms to individual variables and individual constants; the knowledge of this logical notation is assumed):

(5) (a) ‘Pj (t1, …., tk )’ SAT(s, I) ⇔ <ℑ (‘t1’), …, ℑ(‘tk’)> Rj (=I(‘Pj’);

(b) ‘¬A SAT(s, I) ⇔ ‘A SAT(s, I);

(c) ‘A B SAT(s, I) ⇔ ‘A SAT(s, I) and ‘B SAT(s,I);

(d) ‘A B SAT(s, I) ⇔ ‘A SAT(s, I) or ‘B SAT(s, I);

(e) ‘A B SAT(s, I) ⇔ ‘¬A SAT(s, I) ‘B SAT(s, I);

(f) ‘A B SAT(s, I) ⇔ ‘AB SAT(s, I) and ‘BA SAT(s, I);

(g) ‘xiA(xi)’ SAT(s, I) ⇔ ‘A(xi)’ SAT(s’, I), for every sequence s’, which differs from the sequence s at most at the ith place;

(h) ‘xiA(xi)’ SAT(s, I) ⇔ ‘A(xi)’ SAT(s’, I), for some sequence s’, which  differs from the sequence s at most at the ith place.

The first clause establishes the satisfaction-conditions for atomic formulas that refer to relations (sets can be considered as one-placed relation). Conditions (b)–(f) repeat the semantic definitions of propositional connectives, (g) and (h) concern quantifiers and say that an (open) universal formula is satisfied by every sequence, but an existential formula by some sequence (‘differs at most at most ith place’ is a technical phrase to capture the intended meaning). The reference to an interpretation ℑ indicates its role in correlation of expressions and their references, for instance predicates and relations. Since I is always associated with a model M, the expression ‘A SAT(s, I) can be replaced by the phrase ‘A SAT(s, M) (a formula A is satisfied by a sequence s in a model M). If s is an infinite sequence and A has n free variables, only n terms of s are relevant to A’s being satisfied or not. Another formal possibility to define the satisfaction relation consists in introducing sequences of a sufficient finite length.

What about sentences? Consider the example with London and Manchester. The formula (*) ‘x1 is a larger city than x2’ is satisfied by every ordered pair <s1, s2> such that s1 = I(x1) and s2 = I(x1) are cities, and s1 is larger than s2. In particular, the pair <London, Manchester> satisfies (3). Note that the sequence <s1, s2> can be enlarged by adding an arbitrary number of terms in order to have an infinite sequence <s1, s2, s3, …, sk, …>, but this operation is irrelevant to satisfaction or lack thereof. Informally speaking, if a sequence <s1, s2> satisfies (or not) the formula (*), the same applies to the sequence <s1, s2, s3, …, sk, …>, because the terms s1, s2 are the only one that are significant for the satisfaction business in question. Now substitute Manchester. That gives (**) ‘x1 is a larger city than Chicago’. This formula is satisfied by the sequence < s1> such that s1 = I(x1), is a city and s1 being larger than Chicago, in particular by the object <London>. Enlarging the sequence <London> by adding an arbitrary number of terms does not change the situation. Every sequence of the form <London, s2, s3, …, sk, …> satisfies the formula (**). Finally, consider (***) ‘London is a larger city than Manchester’, which is just a sentence, not an open formula. Since it has no free variables, its satisfaction does not depend on valuations of free variables. Hence, every infinite sequence of the form <s1, s2, s3, …, sk, …> satisfies (***). In other words, we can replace sk by an arbitrary object and this step has no relevance for the satisfaction of (***). It is satisfied, because London is a larger city than Manchester. Another way to the same result consists in using a theorem of first-order logic ‘if A is a sentence, xi A A. Assume that a sequence s satisfies (***). By clause (5g), formula A is also satisfied by every sequence s’ which differs from s at most at the ith place. Since A has no free variables, the ith place can be arbitrarily chosen from terms of s’. This means, that every sequence satisfies A. This reasoning implies that if a sentence A is satisfied by at least one sequence, it is also satisfied by any other sequence. Conversely, if a sentence is not satisfied by at least one infinite sequence, it is also not satisfied by any other infinite sequence.

Accordingly, the following statements are obtained

(6) A sentence is satisfied by all sequences if and only if it is satisfied by at least one sequence.

(7) A sentence is not satisfied by all sequences if and only if it is satisfied by no sequence.

Both assertions lead to

(8) If A is a sentence it is satisfied by all sequences or is satisfied by no sequence.

(6) and (7) lead to the following definition:

(SDT) (a) ‘A’ is true in M if and only if ‘A’ is satisfied by every infinite sequence of objects M (equivalently: by at least one such sequence);

(b) ‘A’ is false in M if and only if ‘A’ is not satisfied by some infinite sequence of objects from M (or by no sequence).

However, we can also prove that if a sentence is satisfied by any infinite sequence of objects (or by one such sequence), it is also satisfied by the empty sequence of objects. Thus, SDT can also be formulated by saying that the sentence A is true if and only if it is satisfied by the empty sequence of objects (the notion of the empty sentence is a generalization of the usual definition of sequence. This definition is model-theoretic and explicitly appeared in (Tarski, Vaught 1957). Tarski’s original treatment assumed that satisfaction and truth refer to the one domain in which expressions are interpreted. One can eventually say that the concept of model was implicitly involved in Tarski 1933.

Let us look at the consequences of SDT in the above formulation. Since it assumes resources to meet (LP) and similar paradoxes, its consistency against semantic antinomies is guaranteed. Since SDT does not use the concept of truth, it is not circular. On the other hand, we must suppose that out metatheory (weak second-order arithmetic) is correct in an intuitive sense. According to Tarski, SDT is formulated in the morphology (syntax) of ML. Due to the understanding of logic around 1930, it covered set theory or the theory of logical types. Thus, Tarski was justified in his view that the correctness of metatheory is reduced to that of pure logic.

Today, the situation is more complicated. One can say that SDT proceeds as a typical mathematical construction based on a portion of set theory. Although some philosophers – for instance, Husserl and his followers – will probably be dissatisfied by this situation vis-a-vis their claim that philosophical constructions have to be free of presuppositions, the defenders of SDT (and similar constructions) can reply that (a) conformity to mathematical practice is more important than established a priori metaphilosophical postulates, and that (b) an informal understanding of ML is inevitable for logical constructions pertaining to L. Since ML exceeds L in expressive means, we have also a good articulation of the claim that ML must be richer than L in order for truth for the latter to be defined in the latter. SDT satisfies CT and implies (BI).

The set Tr(L) has various metamathematical properties. It is consistent, forms a deductive system, which is maximal (no sentence can be added without losing consistency), compact (Tr(L) is consistent if and only if its every finite subset is consistent) and syntactically complete (for any A, A Tr(L) or ¬A Tr(L). On the other hand, sets of truths are not always finitarily axiomatizable, In other words, it is not so that for any Tr(L), there exists a finite set X Tr(L), such that Cn(X) = Tr(L) (the symbol Cn refers to the consequence operation). SDT leads to a very elegant account of logical consequence (see Tarski 1936a). We say that the sentence A belong to the set of consequences of the set X if and only if every model of X is also a model of A. In symbols, A CnX if and only for every M, if M is a model of X (every sentence from X is true in M), then A is true in M.

STT, claiming that ‘is true in L’ is defined in ML, raises the question whether we can define truth inside L. The Tarski Undefinability Theorem (TUT) says that if a consistent theory T contains the arithmetic of natural numbers, the set of T-truths is not definable in T. In other words, the truth-predicate is not definable in languages sufficiently rich for expressing the arithmetic of natural numbers. So, TUT is a limitative theorem. Gödel’s first incompleteness theorem (GFT) is perhaps the most famous example of a limitative theorem. If states that if AR (the formal arithmetic of natural numbers) is consistent, it is also incomplete, that is, there are arithmetical sentences A and ¬A, such that they are not provable in AR.

The informal proof of GFT proceeds in the following way. Consider the sentence (i) ‘the sentence (i) is not provable’. If (i) is true, it is unprovable, but if it is false, it is unprovable as well, because logic cannot lead to false consequences (we tacitly assume that axioms of AR are true). Using the law of excluded middle, we obtain that there exists a true but unprovable theorem.

The above reasoning is semantic. The formal proof of GFT is purely syntactic and uses arithmetization that is, translation of metamathematical concepts and theorems into the language of AR.

Assume that STTL is a correct (consistent) truth-theory for L formulated in this language and that a formula A L mentions itself and says ‘A does not define truth’. If A Tr(L), truth is undefinable by A. Now, A is not a theorem of STTL, that is ¬(STTLA) (or A Cn(STTL). This assertion is justified by the reductio argument. Assume that STTLA. Hence, (¬A Cn( STTL). Hence, ¬A can be either false or independent of STTL. The first-case is impossible, because it would mean that STTL defines truth for L. Thus, the second possibility remains, namely that STTL does not define truth for L. Assume that A is false. This means that STTL defines truth of L. However, it is impossible, because A would be a false theorem of STTL, but we assumed that this theory is materially correct and so contains not falsehoods. Thus, we proved that STTL does not define the truth- predicate for L (the informal version of Tarski’ undefinability theorem (TUT)). A more technical version of this theorem says that there is no formula Tr(A) LAR such that for any A LAR, AR ├ A ⇔ Tr(‘A’). The proof of TUT in this formulation uses the fixed-point lemma (FPL), which says that if A(x) LAR and A(x) has one free variable, then B LAR (AR ├ B A(‘B’). The proof is remarkably brief. Assume that there is a formula mentioned in the first part of (TUT). By (FPL), there exists a sentence A such that AR ├ A ¬T(‘L’). By our assumption, we obtain AR ├ T(L) ⇔ ¬T(L), but it conflicts with consistency of AR.

Formulations and proofs of GFT and TUT essentially appeal to self-referentiality. However, the former theorem does not demonstrate that the sentence ‘I am not provable’ is paradoxical, but only that it is independent of AR. The situation in the context of TUT is radically different. In particular, the second part of the informal proof of this theorem shows that adding the formula A (in the indicated meaning) results in the contradiction. The formal proof TUT via FPL confirms this assertion. In fact, FPL can be considered as a metalogical (metamathematical) pointing out of what is wrong with the Liar Paradox. This outcome is important because shows that paradoxes related to self-reference are not curiosities but that they have deep connections with general mathematical results. Finally, one should see a fundamental difference between GFT and TUT. Although both have similar informal formulations appealing to the concept of truth, the forms can be replaced by its syntactic version, the latter not. In the language of recursion, the set of provable sentences of AR is not recursive (a set is recursive if and only if it is computable; it implies that the complement of recursive set is recursive as well), but recursively enumerable (a set is recursively enumerable provided that it can be enumerated by natural numbers; it does not implies that is, complement can be enumerated as well), but the set of arithmetical truths does not fulfils the condition of recursive enumerability. Thus, semantic cannot be reduced to syntax. This fact is particularly important in metamathematics, because doing formal semantics for theories sufficient for expressing AR require infinitistic methods, but syntax of such systems is finitary.

5. Philosophical Comments

Tarski explicitly asserted that he considered STT as an answer to one of the central problems of epistemology. This claim motivates several philosophical comments about the truth-theory. However, we enter here risky territory, because philosophy is full of conflicts and polemics. Limiting attention to analytic philosophy, STT has (had) radical critics such as Otto Neurath and Hilary Putnam, radical defenders such as Rudolf Carnap and Karl Popper, sceptics maintaining that it is philosophically sterile, and an army of more or less followers trying to improve or reinterpret it such as Donald Davison, Hartry Field, Paul Horwich and Saul Kripke. At least three important contemporary philosophers radically changed their views under Tarski’s influence, namely Kazimierz Ajdukiewicz (who rejected radical conventionalism), Carnap (who changed his early view that logical syntax is the core of philosophy and defended semantics as the foundation of philosophical analysis) and Popper (who adopted scientific realism as the most proper philosophy of science).

The above brief survey focused on positive as well as negative influences of Tarski’s ideas. Both indicate that STT is a contemporary philosophical tool, at least in the camp of analytic philosophy. (Continental philosophy is ignored here, although a longer treatment should also refer to this tradition.)

Without pretence to completeness, here are the problems which should be touched upon by any philosophically reasonable truth-theory in philosophy. Being philosophically reasonably does not mean correct, but rather deserving attention in the world of philosophy).

  1. What are the bearers of truth?
  2. What are the initial intuitions associated with a given truth-definition?
  3. How to define truth, and what about the consequences of SDT?
  4. Is the division of truth-bearers stable, that is, do at least some truth-bearers sometimes change their truth-values (briefly: is truth relative or absolute)?
  5. What is a truth-criterion and what is the relationship between truth-criteria and truth-definition?
  6. What is the relation of a particular truth-theory to its rivals?
  7. How can a given truth-theory be defended against various objections?
  8. What is the relation of truth to other philosophical problems?

So, there is much for a theory of truth to accomplish. This article tries to show how the STT of truth is related to these questions, or at least to some of them.

(1) STT assumes that truth-bearers are sentences in the syntactic sense. Yet there are several more concrete possibilities. Sentences? Propositions? Statements? Judgments? These entities can be either linguistic units or objects expressed by linguistic utterances. By contrast, concepts are not truth-bearers, contrary to what Hegelians say. To have a convenient label, we can say that, according to STT, entities qualified as true or false are of the propositional syntactic category. This way of speaking has nothing to do with the question of the ontological nature of propositions, for instance, as abstract objects. Tarski himself chose meaningful sentences as entities on which truth is predicated.

(2) Tarski always stressed that his definition follows the intuitions of Aristotle. Tarski was influenced by the Stagirite himself as well as his Polish teachers, particularly Tadeusz Kotarbiński. Tarski, like most Polish philosophers, uses the label ‘classical truth definition’ as referring to Aristotelian ideas. At the beginning, Tarski identified the classical and correspondence theory of truth, but later he expressed greater reservations with respect to explanations via expressions, such as “agreement” or “correspondence” than to Aristotle’s original formulation. It is not controversial that a T-equivalence says of a true sentence that it states how things are.

What about SDT? We have two options, first, having some justifications in Tarski’s explanations that satisfaction by all sequences of objects is a mathematical trick, and, second, that the official definition corresponds to some ordinary intuitions. The second option is based on some facts, for instance, that SDT entails T-sentences and  BI. Anyway, SDT suggests that truth depends on the domain (model) and how it is. This definition does not appeal to terms such as ‘agreement’ (of a truth-bearer and the world, fact, state of affairs, and so forth.), ‘picturing of the world by minds, thought, and so forth.’, ‘structural similarity’, and so forth. One can propose to distinguish the strong correspondence theory, as in the famous formulation veritas est adequatio rei et intellectus, and the weak (semantic) correspondence. Presumably STT might be interpreted as a weak correspondence theory.

(3) Tarski decided to define truth by a single formula (the definition satisfaction is recursive). He considered introducing truth by axioms, but he rejected this possibility for philosophical reasons. More specifically, he was afraid of being criticized by philosophers from the Vienna Circle for advocating physicalism (see Tarski 1936). This motivation is presently completely historical. Today, the axiomatization of the concept of truth is commonly applied.

TUT has some intriguing consequences for philosophy. Assume what is natural and philosophically tempting, namely that the collection TRUTH of all truths is infinite. By TUT, TRUTH is not definable by resources conceptually available within it. The only admissible way out within set theory consists in considering TRUTH to be too big a set (Zermelo-Fraenkel system), a class as distinct from sets (Bernays-Gödel-von Neumann) or a category. All these outcomes are formally correct, but lead to not quite pleasant consequences, at least for philosophers who like to say something about the set of all truths. However, set theory and TUT seriously limit such theoretical ambitions. On the other hand, this fact gives a precise meaning for the assertion that truth is transcendental in the sense of the medieval theory of transcendentalia (verum omnia genera transcendit).

(4) The classical concept of truth is commonly considered as absolute, that is, if A is true then it is true eternally (for ever) and sempiternally (since ever). On the other hand, SDT indexes truth by L and M. Does this deprive truth of its absolute character? This question is connected with such issues as bivalence, logical determinism and many-valued logic. Without entering into details concerning this fairly complex stock of ideas, it might be suggested that one can model-theoretically prove that truth is eternal if and only if it is sempiternal. Thus, the classical theory of truth in the semantic setting can be considered as associated with the absolute concept of truth. Even if this conclusion encounters reservations, the possibility of analysing the absolutism/relativism controversy within the philosophical theory of truth via SDT is a remarkable fact.

(5) Clearly, SDT is a-criterial. This means that the definition in question does not generate any truth-criterion, although it says what truth is. If mathematics is taken into account, proof can be regarded as a measure of truth. However, there arises a problem. Let the symbol Pr denote the provability operator. By the Löb theorem, we have PrAA, a theorem very similar to TrAA. But, due to the first incompleteness theorem, the formula A ⇒ PrA cannot be consistently added to the provability logic. Hence, there is no counterpart of the T-scheme with Pr instead Tr, that is, the scheme PrA A. So, we must conclude that proof is not a complete truth-criterion even in mathematics. This fact can motivate various ways out, for instance, modifying the concept of proof (every true mathematical assertion can be proved in a formal system; this assertion does not contradict the incompleteness theorem) or replacing truth by proof, eventually with additional constraints, for instance, that proofs must be constructive. However, such proposals are restricted to mathematics. Another suggestion is that truth-criteria consist of procedures which justify satisfaction of open formulas by some objects.

(6) Tarski grew up in the tradition of division of truth-theories into the classical theory and so-called non-classical theories, namely the evidence theory (A is true if A is evident), the coherence theory (A is true if it can be embedded in a coherent system without destroying its coherence), the common agreement theory (A is true if specialists agree about its correctness) and the utilitarian theory (A is true if A is useful). The non-classical theories are criteria, because they appeal to procedures assuring that something is true. Tarski himself mentioned the last definition and the coherence account. In general, he considered non-classical theories as lacking precision and he did not discuss them as serious alternatives for STT.

Another issue involving the relation between various truth-theories concerns substantial and minimalist accounts. The latter approach (the redundancy theory, the deflationary theory, and so forth.) reduces the truth-definition to the T-scheme. Under this view, STT is a minimalist theory. Tarski himself discussed this question. His counterexample was the sentence ‘All consequences of true sentences are true.’ It is not justified by the T-scheme, and it does not justify asserting that all consequences of true sentences are true. There are much more complicated examples, for instance, the sentence ‘There exist true but not provable sentences’, which looks not to be subject to a minimalist translation. If so, STT is essentially richer than any minimalist theory of truth.

(7) Consider three objections stated by Franz Brentano against the classical theory, and consider trying to show that STT meets them successfully. First, the concept of correspondence is obscure and cannot be satisfactorily explained. More precisely, in order to establish what a truth-bearer corresponds to in reality, one must compare the former with the latter. But it is impossible, due to relata of such a comparison. However, this objection applies to the strong notion of correspondence, not to its weak form. The second objection is more serious. Assume that we define truth by a definition D. Yet D is a sentence. In order to have a good definition D must be true. Now, the definition is either circular (if it uses itself) or falls into the regressum ad infinitum, because in order to formulate D, we must appeal to D’ related to D, and so forth. Third, the concept of correspondence does not explain the truth of negative sentences. The answers to these objections depend on the relation of L to ML. These relations do not entail that SDT is circular or leads to an infinite regress. The problem of negative sentences has a simple solution in STT because they are true (or false) under the same definition as positive ones.

(8) Tarski underlined that one can accept STT without being committed to strong ontological or epistemological views such as idealism or realism. In other words, STT is independent of such philosophical assumptions or consequences. Independently of Tarski’s intentions, it is easy to give an example of a philosophical problem closely related to STT, namely the semantic realism / semantic anti-realism debate. Generally speaking, (semantic) realists, such as Donald Davidson, use STT; but (semantic) anti-realists (such as Michael Dummett) reject this account of truth. This controversy concerns the mutual relation of the condition of truth and condition of assertibility. The realist says that the meaning of a sentence (MS) is given by its truth-conditions (TC), but the anti-realist says the meaning is given by assertibility-conditions (AC). Thus, we have two equalities:

(i) MS = TC (realism);

(ii) MS = AC (anti-realism).

However, (i) and (ii) are still too vague. In fact, (i) and (ii) should be transformed into

(iii) MS = TC  TC ⇒ AC;

(iv) MS = AC TC = AC.

The antirealist says that truth-conditions exceed assertibility-conditions, but the antirealist identifies truth-conditions with the assertibility conditions. How does STT work here? It justifies (iii), but it refutes (iv). If, as many anti-realists claim, the conditions of assertibility are governed by intuitionistic logic, it does not generate sufficient and necessary conditions for asserting any mathematical sentence. The point is that the incompleteness theorem constructively holds for Heyting arithmetic (Peano arithmetic based on intuitionistic logic). If so, the anti-realist cannot say that there are true, but unprovable sentences; but the realist can by appealing to STT. As far as the issue concerns more general (that is, ontological and/or epistemological) forms of realism and anti-realism, some insights are provided by results about the full expressibility of semantics in syntax. The general philosophical problem considers the relation between the knowing subject and the object of knowledge. Following a modernized Ajdukiewicz’s proposal, the former is represented by syntax, that is, defines the subject inside language, but the latter can be identified with a model of this language. Since, due to TUT, models transcend languages or cannot be defined within them, the realists’ view on knowledge and reality, has some justification.

6. Final Remarks

STT employs logical tools throughout. Yet this theory is not a logical calculus in the sense in which propositional or predicate logic are. STT is metamathematical, and eventually axiomatic, if this approach is chosen. The status of T-equivalences provides a good illustration in this respect. They are neither logical tautologies nor material biconditionals. As consequences of SDT they have the status of mathematical theorems provable from axioms. This remark does not end the discussion about the character of T­-equivalences, but at least it outlines the direction which seems correct. Anyway, STT belongs to logic in a broad sense.

The philosophical content of STT plays an important role in philosophy of language, logic and mathematics, at least in clarifying some issues. On the other hand, the belief that STT can ultimately solve various problems of these parts of philosophy would be exaggerated. This statement even more concerns epistemology and ontology. On the other hand, as this article documents, although philosophical uses of the semantic theory of truth are problematic, Tarski’s semantic ideas are not philosophically sterile.

7. References and Further Reading

The readings below include only general books on Tarski and his basic writings. Further bibliographical references are available in the books mentioned.

  • Beeh, V., 2003, Die halbe Wahrheit. Tarskis Definition & Tarski’s Theorem, Paderborn, Mentis.
  • Butler, M. K. ,2017, Deflationism and Semantic Theories of Truth, Manchester, Pendlebury Press.
  • Casari, E.,2006, La matematica della verità. Strumenti matematici della semantica logica, Torino, Bollati.
  • Cieśliński, C., 2017, The Epistemic Lightness of Truth. Deflationism and its Logic, Cambridge, Cambridge University Press.
  • David, M.,1994, Correspondence and Disquotation. An Essays on the Nature of Truth. Oxford, Oxford University Press.
  • De Fioro, C., 2013, La forma della verità. Logica e filosofia nell’opera di Alfred Tarski, Milano, Mimesis.
  • Glanzberg, M., 2018, ed. The Oxford Handbook of Truth, Oxford, Oxford University Press.
  • Gruber, M., 2016, Alfred Tarski and the “Concept of Truth in Formalized Languages. A Running Commentary with Consideration of the Polish Original and the German Translation, Dordrecht, Springer.
  • Halbach,V., 2011, Axiomatic Truth Theories, Cambridge, Cambridge University Press.
  • Horsten, L., 2011, The Tarskian Turn. Deflationism and Axiomatic Truth, Cambridge, Mass., The MIT Press, Cambridge, Mass.
  • Kirkham, R. L., 1992, Theories of Truth. A Critical Introduction, Cambridge, Mass, The MIT Press.
  • Künne, W., 2005, Conceptions of Truth, Oxford, Oxford University Press.
  • Martin, R. L., 1984, ed., Recent Essays on Truth and the Liar Paradox, Oxford, Clarendon Press.
  • Moreno, L. F., 1992, Wahrheit und Korrespondenz bei Tarski. Eine Untersuchung der Wahrheitstheorie Tarskis als Korrepondenztheorie der Wahrheit, Würzburg, Köningshausen & Neumann.
  • Pantsar, M., 2009, Truth, Proof and Gödelian Arguments. A Defence of Tarskian Truth in Mathematics, Helsinki, University of Helsinki.
  • Patterson, D., 2012, Alfred Tarski Philosophy of Language and Logic, Hampshire, Palgrave Macmillan.
  • Patterson, D. 2008, ed., New Essays on Tarski and Philosophy, Oxford, Oxford University Press.
  • Puntel, L. B.,1990, Grundlagen einer Thorie der Wahrheit, Berlin, de Gruyter.
  • Rojszczak, A., 2005, From the Act of Judging to the Sentence. The Problem of Truth Bearers from Bolzano to Tarski, Dodrecht, Springer.
  • Simons, P., 1992, Philosophy and Logic in Central Europe from Bolzano to Tarski. Selected Essays, The Hague, M. Nijhoff.
  • Stegmüller, W., 1957, Das Wahrheitsbegriff und die Idee der Semantik, Springer, Wien.
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Author Information

Jan Woleński
Email: jan.wolenski@uj.edu.pl
University of Information Technology, Management and Technology
Poland

Paradigm Case Arguments

From time to time philosophers and scientists have made sensational, provocative claims that certain things do not exist or never happen that, in everyday life, we unquestioningly take for granted as existing or happening. These claims have included denying the existence of matter, space, time, the self, free will, and other sturdy and basic elements of our common-sense or naïve world-view. Around the middle of the twentieth century an argument was developed that can be used to challenge many such skeptical claims based on linguistic considerations, which came to be known as the Paradigm Case Argument (henceforth, the PCA).

Consider, for instance, the following argument from a skeptic who denies that there are cases of seeing people. First, it cannot be said that we see the people who walk our streets, since they are mostly covered with clothes. All that we see, strictly speaking, are their faces and hands. But to see any such people stripped naked would be little better, since we then would be seeing only their facing surfaces while only imagining or anticipating, not seeing, their rear sides. With well-placed mirrors we might be able to see all their sides at once, but we are still seeing only their exterior, which does not constitute the whole person. No, to see these people proper we would need to have them opened up, with all their interior parts displayed for us too. But then we would no longer have a person, but a corpse or a display of people-parts. Hence there are no cases of seeing people.

A philosopher using the PCA could then counter this by pointing out that it is in fact a perfectly natural and proper use of the word ‘see’ to say that you see a person in ordinary cases where you are looking at a fully intact person with his or her clothes on. She might then, if necessary, describe situations where we do or would say this. She might point out that we teach or train children and also adults who are learning English how to use the expression ‘see a person’ with reference to everyday cases when one sees them clothed. (Teacher: ‘What do you see on page seven?’ Learner: ‘A person.’ Teacher: ‘That’s correct.’)  These are paradigm cases of seeing people, exemplars that we use when teaching and explaining the meaning of that expression. That being so, there is no logical room for a philosophical argument showing that these are not cases of seeing people. Trying to argue that they are not would be like trying to argue that the paintings of Picasso that the term ‘cubism’ was coined to denote are not cubist (because they do not depict geometrically exact cubes, say).

This article shows the PCA being applied to the more controversial topic of free will skepticism, examines its logical structure, and looks at some common objections to it. The appraisal of the PCA leads to issues of some depth and importance.

Table of Contents

  1. History and Significance of the Argument
  2. Paradigm Cases
  3. The PCA as Part of a Wider Response to the Skeptic
  4. Malcolm’s Version of the PCA
  5. Flew’s Version of the PCA
  6. Critical Responses to Flew’s PCA
    1. Challenging the First Premise
    2. Challenging the Second Premise
    3. The Charge of Irrelevance
  7. “Ordinary Language is Correct Language”
  8. Ordinary Usage as Practices
  9. Conclusion
  10. References and Further Reading

1. History and Significance of the Argument

The PCA is closely associated with the linguistic philosophy movement that peaked in the mid-twentieth century, when many philosophers were urging that philosophical questions and problems should be approached by paying careful attention to the language that we use for expressing them. More specifically, it was associated with the ordinary language philosophy approach within that broader movement, where the emphasis was on examining the ordinary use of terms. Both advocates and critics of the PCA have claimed that it is foundational to those philosophical outlooks and key to understanding them (for example, Flew 1966, p. 261; Gellner 1959, pp. 30–32; Parker-Ryan 2010, p. 123).

The first explicit presentation of the PCA was in a classic paper of the ordinary language philosophy tradition by Norman Malcolm, originally published in 1942, called ‘Moore and Ordinary Language’ (also see Malcolm 1963). Malcolm studied under and was influenced by G. E. Moore and Ludwig Wittgenstein at Cambridge. He then returned to the USA and became a leading exponent of Wittgenstein’s philosophy there. He believed that the PCA was inchoate in Moore’s famous ‘proof’ (1939) of an external world, and he also stated (1963, p. 183) that grasping it was essential for understanding some of Wittgenstein’s most distinctive remarks on the nature of philosophy, such as, ‘Philosophy must not interfere in any way with the actual use of language, so it can in the end only describe it. For it cannot justify it either. It leaves everything as it is’ (Wittgenstein 2009/1953, §124). Anthony Flew was another prominent early exponent of the PCA, who applied and defended it in a series of articles beginning in the 1950s.

The argument was employed by Malcolm, Flew, and others to defend the existence of a variety of things from skeptical attack, such as cases of acting freely (Black 1958; Danto 1959; Flew 1954 & 1955a; Hanfling 1990; Hardie 1957), causation (Black 1958), solidity (Stebbing 1937; Urmson 1953), space and time (Malcolm 1992/1942), material things and perceptions of material things (Malcolm 1992/1942; 1963), and certain knowledge of empirical propositions (Malcolm 1992/1942). For convenience, in what follows people who argue against the existence of such things are called ‘skeptics’, and people who use the PCA to counter such arguments are called ‘defenders’.

2. Paradigm Cases

The PCA exploits the idea of a paradigm case. Minimally, a paradigm case of something is a case that is supposed to come within the denotation or extension of the relevant word. But what is more, it is supposed to centrally come within its denotation; it is supposed to be a model example or exemplar, something about which we are inclined to say, ‘That’s an X if anything is’ or ‘If that’s not an X, I don’t know what is’. It is the kind of case that psychologists who study concepts would call a ‘prototypical category member’ and which has been found to be associated with various psychological phenomena, such as tending to first spring to mind when people are told to think of examples of an X, or being more rapidly categorized as an X compared to other category members in categorization tasks. This exemplar status makes it especially fit for the purpose of explaining the meaning of the relevant word in ostensive definitions (and its being used for that purpose reinforces its exemplar status in turn).

A particularly striking example of a paradigm case in this sense (an exemplar of an exemplar, if you will) might be the International Prototype of the Kilogram, a lump of platinum kept in Paris that was used to define what a kilogram is, such that anything else was a kilogram in weight if and only if it was the same weight as this object. The cases that the defender refers to as paradigm Xs are thought of as playing a similar meaning-setting role in relation to the relevant term ‘X’ (though this comparison has its limits; for example, the cases might not have come to play that role through explicit stipulation or formal decision). The problem, then, that the defender has with the skeptic is that in denying that there are any Xs, the skeptic seems to be denying that what apparently are paradigm cases of Xs are Xs, which would be analogous to denying that the International Prototype of the Kilogram is a kilogram in weight.

3. The PCA as Part of a Wider Response to the Skeptic

Of course, when the skeptic denies that there are any Xs, he does so due to some reasons or arguments. The PCA, however, does not directly engage with the arguments that the skeptic gives or the significant complexities they can give rise to. This is because, from the defender’s perspective, the skeptic’s claims can ‘be seen to be false in advance of an examination of the arguments adduced in support of them’ (Malcolm 1963, p. 181; also see Malcolm 1992/1942, p. 114), since the PCA is supposed to show that the skeptical claim must be wrong. In other words, for the defender, the skeptical argument (assuming it is logically valid) should be regarded as a reductio ad absurdum of a premise in the argument, since it leads to an absurd or impossible conclusion.

It is this apparently brusque way of treating the skeptic’s arguments that provoked suspicion and even hostility towards the PCA on the part of some critics. Thus some have sarcastically referred to it as a ‘remarkably economical device for resolving complex philosophical disputes’ (Beattie 1981, p. 78), or as ‘a very simple way of disposing of immense quantities of metaphysical and other argument, without the smallest trouble or exertion’ (Heath 1952, p. 1). For others it seems to take the fascination and wonder out of philosophy by its summary rejection of intriguing claims and arguments (Watkins 1957a, p. 26). Why the defender feels entitled to treat the skeptic’s arguments in this way is explained in section eight.

Defenders do not give the skeptic’s arguments quite the short shrift that these remarks suggest, however, since they see the PCA as being only a part of an adequate philosophical response to the skeptic. Accordingly, both Malcolm and Flew stated that to truly free us from the skeptic’s position, reminding us of ordinary linguistic usage is not enough. We also need to reconstruct and examine the reasoning (Malcolm 1951, p. 340; 1992/1942, p. 123) or to identify the ‘intellectual sources’ (Flew 1966, p. 264) that drew us towards the skeptical conclusion. (The importance of this is especially evident in the free will debate, where even philosophers who sympathize with the PCA defense of free will can still feel troubled by the skeptical arguments.) This part of the response to skepticism involves examining the skeptical arguments, and it can also involve unearthing any unstated presuppositions, comparisons, or pictures that might be informing those arguments. Sometimes these sources get their intellectual power over us precisely from the fact that we are not explicitly conscious of them, and they can lose this power when we become conscious of them (Wittgensteinians sometimes call this the ‘therapeutic’ part of the investigation). For instance, regarding the argument that we never see people—a sort of argument that is not unprecedented (see Campbell 1944–45, pp. 14–18; Descartes 2008/1641, p. 23)—the implicit assumption might be that in order to truly see something you must see all its parts or aspects, or the implicit comparison might be with cases of seeing a movie or a play, which one has not properly done unless one has seen it from beginning to end (if we miss a bit, we qualify our statement: ‘I saw most of it’). In sum, defenders believe that ‘the application of a PCA is only a begin-all and not a be-all and end-all of the satisfactory treatment’ of the skeptic’s challenge (Flew 1982, p. 117; 1966 pp. 264-265).

It is also recognized by some defenders that identifying the paradigm cases of something is a far cry from giving an account or theory of it. If something is a paradigm case of an X it is so because of certain features that it has and does not have, and philosophers often want to know what these features are, though they cannot simply be ‘read off’ some paradigm cases. Identifying paradigm cases can then be only a ‘jumping-off point for establishing the relevant rules and conventions’ (Black 1973, p. 271) governing the term, and a preliminary to developing an alternative account of the phenomenon to the one implicit in the skeptic’s argument.

4. Malcolm’s Version of the PCA

A close reading of the literature on the PCA reveals that there is not one but two different kinds of arguments that go by the name ‘paradigm case argument’, the first of which is especially evident in Malcolm’s 1942 paper and which is of more limited application. Distinguishing between these versions is important as not doing so can lead to confusion in the critical appraisal of these sorts of arguments.

The key feature of what we may call ‘Malcolm’s version’ is that it exploits the idea that there are certain expressions ‘the meanings of which must be shown and cannot be explained’ (Malcolm, 1992/1942, p. 120). Color terms are often mentioned to illustrate this; to make someone fully understand what ‘yellow’ means you must go beyond verbal explanations and produce a sample. Consider, for instance, a philosopher who claims that space and time do not exist. Malcolm first uses Moore’s method of ‘translating into the concrete’ (Moore 1918, p. 112), where an abstract statement is considered in terms of its specific implications. Thus he understands this as amounting to the denial that anything is ever to the left of anything else, that anything is ever above anything else, that anything ever happens earlier or later than anything else, and so on. It is the denial that such states of affairs ever exist. Furthermore, for a philosopher to actually make such a denial (as opposed to just parroting words), she must understand the meanings of the expressions contained therein. She must understand what it means to say that one thing is under another, that one event occurred after another, and so forth.

But how, Malcolm asks, could one ever have come to understand the meaning of such expressions as ‘after’, ‘to the left of’, ‘above’, and ‘under’? Only, he maintains, by our being shown or being acquainted with actual instances (or ‘paradigms’) of things being to the left of other things, of things being above other things, and so on (1992/1942, p. 120). Therefore, for Malcolm, spatial and temporal relations must exist for us to understand the meanings of such expressions and thus, ironically, the existence of space and time is a precondition for the possibility of denying their existence. Or at least the skeptic owes us an explanation of how he can understand spatial and temporal vocabulary on the assumption that spatial and temporal relations do not exist (Soames 2003, p. 166).

The skeptic could respond, however, by simply denying that he understands spatial and temporal vocabulary. That is, the skeptic’s claim might be that such vocabulary has no intelligible meaning, a claim which he perhaps misleadingly expressed by saying ‘Space and time don’t exist’ (as misleading as it would be to say ‘Square circles don’t exist’, as if to imply that there is an intelligible description there that nothing happens to satisfy). And Malcolm does suggest something of this sort in saying that the skeptic’s real point is that these ideas are subtly self-contradictory. However, Malcolm claims that no expression that has a descriptive use is self-contradictory, and he maintains that these expressions do have descriptive uses.

Taking their cue from Malcolm, some commentators have interpreted the PCA as applying only to expressions whose meanings are so fundamental or irreducible that they can be conveyed only ostensively (for example, Alexander 1958, p. 119). Certain defenders were then reproached for attempting paradigm case arguments with expressions apparently not of this type (Passmore 1961, p. 115; Watkins 1957a, p. 29). For instance, the most intense discussion of the PCA was in relation to the expression ‘free will’, which should probably not be regarded as this kind of expression. It was noted that the meanings of certain expressions can be formed and learned by our associating them with an abstract specification or definition. In other cases, our understanding can be derived from examples, but examples that are fictional, like when we learn what miracles are by reading about miraculous events in myths and stories (Watkins 1957a, p. 27). In both cases it remains an open question whether the expression denotes anything real. Given that ‘free will’ could be an expression of those types, no inference can be made from the fact that ‘free will’ has a meaning or is understood by us to the conclusion that there is free will.

However, a different version of the PCA exists that does not rely on the idea that the meaning of the relevant expression ‘must be shown and cannot be explained’. To see this, we will look in some detail at how the PCA works in relation to the controversial topic of free will skepticism.

5. Flew’s Version of the PCA

Next we will examine a particular application of the PCA, Anthony Flew’s use of it to rebut skepticism about actions done of one’s own free will, which we may call ‘free actions’ for short. By focusing on a particular application, and the one that has generated the most discussion, we can examine the argument’s logical features in some depth. The following quotations, then, are Flew’s presentation of it from his earlier papers on the topic. Though these were the most frequently quoted and discussed presentations of the PCA, we will see that they were problematic and that he reached a more mature understanding of it in his later work. These problems largely stem from clinging to Malcolm’s model of the PCA with a concept for which it is not appropriate.

Crudely: if there is any word the meaning of which can be taught by reference to paradigm cases, then no argument whatever could ever prove that there are no cases whatsoever of whatever it is. Thus, since the meaning of ‘of his own freewill’ can be taught by reference to such paradigm cases as that in which a man, under no social pressure, marries the girl he wants to marry (how else could it be taught?): it cannot be right, on any grounds whatsoever, to say that no one ever acts of his own freewill. For cases such as the paradigm, which must occur if the word is ever to be thus explained (and which certainly do in fact occur), are not in that case specimens which might have been wrongly identified: to the extent that the meaning of the expression is given in terms of them they are, by definition, what ‘acting of one’s own freewill’ is. (Flew 1955a, p. 35)

Here is another more concise statement of the argument:

As the meaning of expressions such as ‘of his own free will’ is and must ultimately be given by indicating cases of the sort to which it is pre-eminently and by ostensive definition applicable, and not in terms of some description (which might conceivably be found as a matter of fact not to apply to anything which ever occurs); it is out of the question that anyone ever could now discover that there are not and never have been any cases to which these expressions may correctly be applied. (Flew 1954, p. 54)

There are at least two errors with this. Firstly, Flew claims in places that the meaning of ‘free will’ must be given by referring to paradigm cases. But this is not right. As suggested above, it seems possible that its meaning could be given with a definition (‘A free action is an action that . . .’). It would then be an open question whether there is anything satisfying the definition. Flew came to think that this ‘must’ claim was unnecessarily strong, and that for his argument to work it is enough that the meaning of ‘free action’ can be given by referring to paradigm cases (1957, p. 37).

But secondly, even if the meaning of ‘free action’ can be given by referring to paradigm cases, that would not entail that there must be cases of free action (that is, Flew is wrong in saying that the paradigm cases ‘must occur if the word is ever to be thus explained’). For cases can be real or hypothetical, and it is not necessary that the paradigm cases occur for it to be possible to explain the meaning of a term by describing them (Chisholm 1951, pp. 327–328; Hallett 2008, p. 86). Indeed, even Flew himself, in the first passage, seems to describe a hypothetical case of a man who under no social pressure marries the woman he wants to marry to explain the meaning of ‘free will’ (at least he does not tell us that he is referring to some actual case he is familiar with). We all know that such cases occur of course, but it is a contingent fact that they do (our world might have been one where all marriages were arranged and obligatory) and that fact has no bearing on the pedagogical usefulness of the case.

Thus it would not be the mere fact that the meaning of ‘free action’ is or can be explained in terms of paradigm cases that guarantees that there are free actions. It would, rather, be the fact that the meaning of ‘free action’ can be explained in terms of certain paradigm cases, plus the fact that such paradigm cases actually occur which would guarantee that there are free actions. This two-step structure of the PCA is noted by Marconi when he says, ‘it is not enough, to refute skepticism about miracles, that the turning of water into wine would be ordinarily described as a miracle, for it is far from uncontroversial that such an event ever took place’ (2009, pp. 118–119).

Flew elucidates the structure of the argument along these lines, and achieves a more mature understanding of the PCA, in a later paper. There he says that the ‘logical form of this argument type consists in two steps: The first is an insistence upon (what is taken to be) a plain matter of fact [that is, that certain cases exist or happen] . . . The second step consists in the assertion that examples such as those presented just are paradigm cases of whatever it is which it is being so paradoxically denied’ (1982, p. 116; also see Donnellan 1967, p. 108). Thus Flew’s paradigm case argument for free actions consists of two premises.

P1: As ‘a plain matter of fact’, cases exist where a man marries the woman he loves and wants to marry without threats, pressure, or compulsion.

P2: Such cases are paradigm cases of free actions.

            Conclusion: Free actions exist.

Here we can see that one of the premises is an existential statement, with the other saying that the thing quantified over is a paradigm case of whatever the skeptic is denying. In other words, one premise says that there exist cases matching a particular description, while the other says that anything matching such a description is a paradigm case of an X (where ‘X’ refers to what the skeptic claimed not to exist). Together they yield the conclusion that there are Xs.

But that is not all, since the PCA is known to draw on linguistic considerations somehow. This is not evident in the above argument schema, so where do they enter into it? They enter into it, it seems, in justifying the second premise. Thus the defender will say that those cases are paradigms of free actions because the meaning of ‘free action’ is taught or explained with reference to such cases, or because we ordinarily say of such cases that the agent ‘acted of his own free will’.

The justificatory significance of ordinary linguistic usage is discussed below. But now that we have identified the basic structure of Flew’s argument, let us first look at the various avenues of criticism available to the skeptic.

6. Critical Responses to Flew’s PCA

a. Challenging the First Premise

Critics of Flew’s PCA have tended to grant premise 1 as just being an uncontroversial empirical truth. Yet perhaps premise 1 could be resisted if we insist on understanding ‘compulsion’ or ‘being forced/constrained’ in a particular way, such that any kind of deterministic cause ‘compels’ its effect or ‘forces’ the effect to happen, so that nobody could act without compulsion in a deterministic universe (see Beebee 2013, p. 110; Hardie 1957, p. 21). Here the analytic effort would move to the ideas of compulsion or of being forced, which would need to be clarified. So although the premise here is supposed to be a statement of plain empirical fact, it could be challenged through the development of a conceptual point.

b. Challenging the Second Premise

But the main focus of attention has been on premise 2. Are such marriages indeed paradigm cases of acting freely? Or if we tend to judge that they are, is this only because of certain assumptions we are making about those cases that were unmentioned in Flew’s description, assumptions that might be open to challenge?

Some critics have argued that advocates of the PCA err by assuming a sharp distinction between teaching the meaning of a word by presenting cases and by giving criteria. For mixtures of these can also occur when we explain the meaning of a word with reference to cases, but cases that are interpreted as satisfying certain criteria (Ayer 1963, pp. 17–18; Gellner 1959, p. 34; Passmore 1961, pp. 115–116). Consider, for instance, a superstitious society where people believe in miracles. There, when explaining what a miracle is, people might refer to cases such as when the leader suddenly and inexplicably recovered from a grave illness, and others involving a sharp turnaround in fortune, but it is being assumed that these turnarounds satisfy the description of being caused by the intervention of a spiritual being. Notice that here the meaning of ‘miracle’ is being explained with reference to real cases, but this does not prove that there are miracles. For the cases are being interpreted in a certain way and the interpretation could be wrong. Could it be the same with the marriage cases? Do we think they are cases of acting freely only because of some contentious background features that we assume to apply to them?

This thinking is evident in David Papineau’s criticism of the PCA when he says, ‘Maybe ordinary people are happy to apply the term “free will” to such actions as drinking a cup of coffee or buying a new car. But this is only because they are implicitly assuming that these actions are not determined by past causes. But in fact they are wrong in this assumption. All human actions are determined by past causes’ (1998, p. 133). Similarly, John Passmore grants that it is natural for us to describe grooms as acting freely in the circumstances described by Flew, but he adds that ‘we have also learned criteria: we have been told that a person acts of his own free will only when his action proceeds from an act of will . . . [with] the metaphysical peculiarity of being uncaused’ (1961, p. 118; also see Ayer 1963, p. 18; Lucas 1970, p. 12). Passmore’s implication is that in saying that the groom acted freely, we are implicitly assuming that he satisfied this criterion.

Note that these philosophers are making claims about what ordinary speakers mean when they talk of free actions, and thus about the ordinary or ‘folk’ concept of free action, saying that it involves the idea of an uncaused or undetermined act. They are, in that respect, engaging in ‘ordinary language philosophy’ with Flew, and disputing his (more implied than stated) characterization of the ordinary concept. However, it is not enough for them to simply claim that this is a feature of the ordinary concept of a free action. There is an onus on them to support that claim with methods or evidence appropriate for this task.

But what support could they provide? An old-school ordinary language philosopher like Flew would appeal to ordinary linguistic usage to support the idea that free action is, roughly, doing what you want to do without pressure or duress, pointing out that this explains the fact that we say of a groom who marries the woman he loves and wants to marry that he marries of his own free will, but not of the groom in an arranged marriage or shotgun marriage. As an old-schooler, moreover, he would be confident that he knows well what the ordinary use of ‘free will’ is just by being fluent in English. Others who think that philosophy should be more ‘scientific’ in its methods would think it necessary to gather some empirical data on ordinary speakers’ judgments through surveys. (Interestingly, one such study yielded ideas similar to Flew’s; see Monroe and Malle 2010.) However, Papineau’s and Passmore’s criterion—that a free action is one not determined by past causes—does not seem to explain this usage at all. For we might not doubt that in both happy marriages and ones involving coercion the groom’s saying ‘I do’ can be causally explained—crudely, by love in the former and fear in the latter—and that neither sort of explanation is any less deterministic than the other. We would not speak of these cases differently if this was our criterion of free action, and it is not clear what practical usefulness the expression would have on that understanding.

Another kind of support for claims about what speakers mean or are implicitly assuming is the speakers’ own admissions or acknowledgments. When someone describes an event as a miracle, for instance, we can elicit his acknowledgment that in doing so he was thinking that a deity intervened. But will we be able to elicit from an ordinary speaker the acknowledgment that when he said that Debora married of her own free will, he meant that her marrying was not determined by past causes? Can we regard something as part of what a person meant in saying something if he does not acknowledge it as part of what he meant? Papineau and Passmore would need to allay the suspicion that their characterization of the ordinary meaning of ‘free action’ is an imposition from philosophical theory. It is not clear, for instance, where exactly we have ‘been told’ the criteria for free action that Passmore says we have been told, besides in the philosophy classroom.

Of course, these critics’ assumption that a free act is uncaused or undetermined must have come from somewhere, and Flew and Malcolm insisted that a thorough investigation of the ‘intellectual sources’ of the skeptic’s claim must be carried out, to identify the comparisons, pictures, analogies, and so forth that lure us towards it. Any PCA will seem shallow without this concomitant.

To sum up, these ways of challenging the paradigm case argument involve contesting the defender’s claim about what the relevant expression ordinarily means. But this requires that the skeptic play and beat the ordinary language philosophers (in the wide sense of those who work on elucidating the meanings of ordinary expressions, which could include certain experimental philosophers) at their own game. Skeptics who dispute a defender’s claim about what ordinary speakers identify as the paradigm cases of something, or about what exactly ordinary speakers are assuming in making such identifications, must supply evidence appropriate for determining the character of ordinary concepts, a burden which, of course, also applies to the defenders.

Another philosopher who questioned whether Flew’s description identifies a paradigm case of free action is MacIntyre (1957). Suppose we are told that the groom’s falling in love with the bride was due to a hypnotic suggestion (assuming such things are authentic). MacIntyre maintains that in that case, he would not have married of his own free will (though it could be autonomy that is lacking here, rather than free will; on this distinction, see Christman 2015, section 1.1; Piper 2010, section 2c). The defender would reply that though such an etiology was not explicitly ruled out by Flew’s description of the case, we were supposed to imagine that this was an ordinary case and thus that no such extraordinary things happened. But to this MacIntyre says that there ‘is no relevant difference in the logical status between explanations in terms of endocrine glands [or whatever the explanation is in ordinary cases] and those which refer us to hypnotic suggestion’ (1957, p. 31).

This kind of move—claiming that there is no important difference between putative paradigm cases of free action and of unfree action—is a familiar one from free will skeptics, and it is independent of the particulars of the paradigm case argument. It also leads to stalemate, since given that sameness and difference are symmetrical relations we can argue the other way around just as cogently: we can take our intuitions about the free action case for granted and say that because the unfree action case is no different in its essentials, it is, despite initial appearances, a case of free action (see Beebee 2013, p. 85).

c. The Charge of Irrelevance

Other critics have taken a different, more concessionary approach to dealing with the PCA over the free will issue. Rather than contesting Flew’s characterization of the ordinary meaning of ‘free will’, they agree with it, but maintain that this is just not the concept of free will that is relevant to the philosophical debates. For instance, Danto agrees with Flew that ‘when, in ordinary contexts, we say that Smith married of his own free-will, we mean only that there was no shotgun being pointed at him by an angry father (or something like this). We do not deny that marriages are predictable, or even that this marriage was’ (1959, p. 124). We just mean that he was not made to do it against his will, pressured or strong-armed into doing something he did not want to do (Ibid., p. 123). However, ‘ordinary language so construed is simply irrelevant to the celebrated problem of the freedom of the will’ (p. 121), which is a ‘metaphysical problem’ that can be solved only with a ‘metaphysical solution’ (p. 124). Similarly, some philosophers have been explicit in saying that the free will that philosophers are curious about is not the free will that we speak of in daily life (Hardie 1957, p. 30; van Inwagen 2008, p. 329, note 1). Relatedly, others try to distinguish freedom of action from freedom of will and shift the debate towards the latter idea (see McKenna and Pereboom 2016, p. 10). The former idea roughly corresponds to what Flew was talking about, while the latter is supposedly something quite different and concerns choice or decision rather than action, and is less in common currency.

Though the sharp disparity between the views of the defender and the skeptic would be well explained by this idea that they are ‘talking past each other’, operating with different notions, there is a problem with it. There is an unwritten rule (or a ‘conversational maxim’, to use a Gricean expression) that we must tell our readers that we are using some expression in an unusual sense if we are doing so. This is to prevent misunderstanding and confusion, since we naturally interpret a person’s words to have their ordinary signification unless told to do otherwise. However, most philosophers, not to mention psychologists and neuroscientists, do not say that they are using ‘free will’ or ‘free action’ in some special or unusual sense in their written works on this topic. Thus, if they are doing this, then many of them are being irresponsible by not being upfront about it. This omission would be excusable if it were common knowledge that ‘free will’ is being used in some non-standard sense in the literature, but this is hardly true, especially considering that some philosophers have said the exact opposite: that in the free will debate we are investigating whether free will exists as ordinarily conceived (see, for example, Jackson 1998, p. 31).

In light of these conflicting indications, it is simply not clear whether in the debates about the existence of free action it is free action in the ordinary sense that is being discussed. One way to find clarity on this, however, might be through reflection on the related phenomenon of moral responsibility. Most philosophers have not been interested in free will just for its own sake but because of its importance for moral responsibility, believing that whether we can be held morally accountable for our actions, and can be deserving of praise and blame, turns on whether we can act freely. Thus, to the question ‘What sense of free will are you talking about?’, some might reply, ‘The one that matters for moral responsibility’. However, this might not be of great help because even if there is some ‘metaphysical’ notion of free will that is critical for moral responsibility, the ordinary notion of free will is also important for it. For ordinarily if we are told that someone did something terrible, but are then told that he did not do it of his own free will, we will (if we believe this) infer that he is less responsible for having done it.

7. “Ordinary Language is Correct Language”

Let us look again at premise 2 of Flew’s PCA. This stated that cases matching a certain description are paradigm cases of free action. But how does a defender support such a claim? By referring to linguistic considerations. By saying that these are the kinds of cases that we ordinarily or standardly call ‘free actions’, or that these are the kinds of cases that we would refer to when teaching or explaining the meaning of ‘free action’. Furthermore, we can take the former to be the most fundamental consideration because the meaning of a term can be taught or explained correctly or incorrectly, depending on whether the instruction reflects the ordinary use, and besides, much of our native language is not learned from explicit instruction.

But can we safely infer from the fact that a certain sort of case or thing is ordinarily called ‘X’ that it is in fact an X? It seems easy to find reasons to dismiss this principle. After all, didn’t people in superstitious societies ordinarily refer to certain events as miracles, or to the Sun as a deity, while being incorrect in saying those things?

The idea that if something is ordinarily called ‘an X’ then it is an X was expressed by Malcolm in his statement that ‘ordinary language is correct language’ (Malcolm 1992/1942, p. 118, p. 120), which came to be regarded as a central slogan of ordinary language philosophy. As a slogan, however, this needs deciphering. Malcolm explained what he meant in saying this by distinguishing between two kinds of mistakes that can be made when making a statement, being mistaken about the facts, and using incorrect language (1992/1942, p. 117). The distinction can be illustrated with a case adapted from Malcolm. Suppose that Jones and Smith see an animal in some bushes at a distance, and Jones claims it is a wolf while Smith claims it is a fox. After it emerges from the bushes, Jones clearly sees that it has the characteristics of a fox and that he was mistaken. This was a factual mistake. But imagine another case where they both see the animal clearly and are in full agreement on what its characteristics are, though Jones claims it is a wolf while Smith claims it is a fox. Though the form of their disagreement is the same as before, we now have a linguistic rather than a factual disagreement: they disagree about what a thing of this sort is called. At least one of them is mistaken about the meaning of these words. (Though Malcolm contrasts ‘factual’ with ‘linguistic’ disagreement here, he would not deny that a linguistic mistake is based on a factual error (see Malcolm 1940). That a word has the particular meaning that it has is, of course, a kind of fact. This contrast might therefore be better described as one between linguistic and non-linguistic facts, and one might want to press Malcolm to clarify it further.)

But then Malcolm asks us to imagine the second disagreement again, though with Jones acknowledging that an animal of this sort is ordinarily called ‘a fox’ while maintaining that it is nevertheless incorrect to call it that and correct to call it ‘a wolf’. According to Malcolm, this would be absurd. It is absurd, he says, because ordinary language is correct language. To refute Jones’ claim here it suffices to say, ‘But that’s not what people call it.’

In his discussion of the paradigm case argument, Diego Marconi criticizes this view. He agrees that if some things are correctly called ‘Xs’ then they are Xs (2009, p. 116). But he disagrees that if some things are ordinarily called ‘Xs’ then they are correctly called ‘Xs’. For people might only be calling them ‘Xs’ because they appear to be Xs when in fact they are not Xs (p. 119). This seems right as far as it goes. However, if people are always calling some things ‘Xs’ because they appear to be Xs while not being Xs, then they are like Jones who called a fox ‘a wolf’ because it appeared to be a wolf to him: they are factually mistaken. Malcolm’s idea was that if some things are ordinarily called ‘Xs’ and if no factual mistakes are being made about them, then they are Xs. That is, Malcolm’s slogan represented an attempt to characterize a notion of linguistic correctness, saying that, assuming no factual mistakes are being made about it, the correct thing to call something is what everyone calls it (but for a hard case, see Watkins 1957a, p. 28). The factual/linguistic error distinction is indispensable for understanding the slogan.

8. Ordinary Usage as Practices

It is possible to gain a deeper understanding of why the defender puts so much weight on ordinary usage. But first let us return to an earlier point. We saw earlier that according to the defender, the PCA allows us to reject the skeptical position that there are no Xs without having to examine the skeptical argument. What is the source of this supposed imperviousness to skeptical argument? Can such an apparently dogmatic attitude be tolerated in philosophy? Consider again the skeptic who argued that there are no cases of seeing people. The defender responded by making the simple point that we ordinarily say that we see people in cases where we look at them clothed, cases that were deemed not to be cases of seeing people by the skeptical argument. But why exactly does the fact that we ordinarily say that make it correct to say that? And why should that ordinary usage be unassailable?

The reason is that the defender thinks she is describing what could be called a linguistic practice, custom, convention, or rule. She is trying to point out that it is our practice or custom, or a rule of our language, to call cases of this sort cases of seeing people. Now such things as practices, customs, or rules are open to criticism in various ways. For instance, a rule of a game can be criticized for making the game too long, too complicated, too inconvenient, too dangerous, or less exciting, and rules are sometimes changed to improve games along these lines. But it cannot be criticized for being incorrect, since practices, customs, or rules cannot be correct or incorrect.

Consider the rule in chess that the bishops can move only diagonally, for instance. What sense can there be in saying that this rule is correct? It is, indeed, one of the rules of chess. It is correct to say that this is a rule of chess. The statement that this is a rule of chess is correct. A move may be correct by being in conformity with it. But the rule itself is not correct; it is simply followed, and its being followed makes it one of the rules of chess (though something can also be a rule in virtue of being decreed by a relevant authority, even if people ignore it). Admittedly, we might sometimes speak loosely of a ‘correct rule’. But ‘correct’ here is redundant; ‘These are the correct rules of chess’ is just an emphatic way of saying, ‘These are the rules of chess’. For we have no understanding of what an incorrect rule of chess would be. Would moving the bishop vertically and horizontally be an example? No, since we can reprimand someone doing that by saying, ‘That’s not the rule for the bishop’. (It would confuse him to say ‘That is indeed a rule for the bishop, but an incorrect one’.)

So when a defender says, ‘We (ordinarily) call cases of this sort cases of seeing a person’, she is trying to say, ‘It is our practice/custom/rule to call cases of this sort cases of seeing a person’, and as such it is not the kind of thing that could be refuted by an argument. It is not something that could be proven by any argument either, just as a rule of chess can be neither proven nor refuted (though statements as to what are the rules of chess can be proven or refuted). Wittgenstein called this ‘bedrock’, where ‘I am inclined to say: “This is simply what I [or better, what we] do”’ (2009/1953, §217; also see §654). As practices or rules of our ‘language-game’ they are self-standing; they are things that philosophers ‘cannot justify’ in an evidential sense and must ‘leave as they are’.

But if a linguistic practice cannot be correct or incorrect, how does this help the defender? For didn’t the defender want to claim that it is correct to say that such-and-such a case is a case of seeing a person? Indeed, but note what she is claiming here: that it is correct to say that such-and-such a case is a case of seeing a person. The statement is what is correct here, not the practice, and it is correct by being in conformity with the practice. The point here is that though practices cannot be correct or incorrect, they are determiners of correctness. Thus a move in chess can be correct by being in conformity with the rules of chess, or a man’s manner of addressing the Queen can be correct by being in conformity with the accepted customs for addressing the Queen. Similarly, certain kinds of statements can be correct (not just grammatically correct, but true) by being in conformity with the rules of English. Thus the statement that some case, C, is a case of an X can be a correct and true statement by being in conformity with the practice of calling Cs ‘X’. (To take a simple example, ‘This color is orange’ can be true and correct by being in line with our practice of calling that color ‘orange’.) And this can be a practice just because it is followed, because the relevant people ordinarily do it.

Thus the paradigm case argument works in part by reminding us of what our linguistic practices are, practices that determine what it is to play the ‘game’ of speaking the relevant language, practices that the skeptic too, in unguarded moments or as a layperson, can be seen to participate in. This, however, is not to say that we should never break the linguistic rules that we currently follow. No prohibition is being urged here on creativity or novelty in the use of language; we are not being urged to never stray from the bounds of conventional and correct speech. The defender only wishes to maintain, against the skeptic, that calling certain things cases of seeing people, calling certain other ones cases of acting freely, and so forth, is not incorrect speech, insofar as it is in conformity with our linguistic customs to do so. Nor is it to deny that those linguistic practices can be criticized as problematic for reasons unrelated to correctness or truth, such as for pragmatic, moral, or political reasons.

9. Conclusion

So, does the paradigm case argument work? There does not seem to be anything intrinsically fallacious about it at least, but this general sort of question is not a good one to ask. First, we have seen that it is problematic to speak of the paradigm case argument, since two versions of it can be distinguished. But more importantly, it may be a bad question to ask because every topic to which it is applied may have its own peculiarities, such that a PCA may work in one application but not in another. For instance, we have seen that with free will skepticism there is a possibility that ‘free will’ is being used in a technical or unusual sense, which would make a PCA type of argument inapplicable to that topic, though nothing similar might be going on with some other topics. Applications of the PCA thus should be judged on a case-by-case basis.

Assessing the influence of the PCA on the analytic philosophical tradition is less easy than it would seem. By one measure, that of observing philosophers explicitly using or referring to the argument and accepting its conclusions, we would have to say that its influence has not been great. However, it is unclear just how much weight we should put on that measure since, as Gilbert Harman said, a ‘philosopher’s acceptance of the paradigm case argument need not be revealed in any explicit statement of the argument, since this acceptance may show itself in the philosopher’s attitude towards skepticism’ (1990, p. 7; also see Gellner 1959, p. 32).

For instance, this acceptance might be manifested in a philosopher’s tendency to treat things commonly or ‘intuitively’ identified as paradigms cases of an X as a datum for the purpose of developing a theory of X (by, for instance, trying to extract necessary or sufficient conditions from the cases), despite the existence of skeptical traditions that deny the existence of Xs. It is not uncommon to see philosophers proceeding in this way (sometimes called ‘the method of cases’) in positive theory development. If pushed to justify this procedure, the philosopher could (but might not) resort to something like the PCA. Skeptics might insist that this philosopher has no right to assume that those ‘paradigm cases’ are genuine paradigms without refuting their skeptical arguments. But defenders can attempt to turn the tables on the skeptics by requesting that they answer these questions. Any skeptical argument against the existence of any X must be based on some conception or analysis, implicit though it may be, of what X is. But how can we know that we have the right conception or analysis of X? Is there a better alternative to using the method of cases? And if not, might depending on the method of cases commit us to non-skepticism about X?

10. References and Further Reading

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  • Ayer, A. J. (1963). Philosophy and language. In The Concept of a Person and Other Essays. London; Basingstoke: Macmillan, pp. 1–35.
  • Beattie, C. (1981). The paradigm case argument: its use and abuse in education. Journal of Philosophy of Education, 15(1), pp. 77–86.
  • Beebee, H. (2013). Free Will: An Introduction. Basingstoke: Palgrave Macmillan.
  • Black, M. (1973). Paradigm cases and evaluative words. Dialectica, 27(1), pp. 261–272.
  • Black, M. (1958). Making something happen. In Determinism and Freedom in the Age of Modern Science (S. Hook, ed.). New York: New York University Press, pp. 31–45.
  • Blanchard, B. (1962). Reason and Analysis. London: George Allen and Unwin Ltd. See chap. 7.
  • Butchvarov, P. (1964). Knowledge of meanings and knowledge of the world. Philosophy, 39(148), pp. 145–160.
  • Campbell, C. A. (1944–45). Common-sense propositions and philosophical paradoxes. Proceedings of the Aristotelian Society, 45, pp. 1–25.
  • Chappell, V. C. (1961). Malcolm on Moore. Mind, 70(279), pp. 417–425.
  • Chisholm, R. (1951). Philosophers and ordinary language. The Philosophical Review, 60(3), pp. 317–328.
  • Christman, J. (2015). Autonomy in moral and political philosophy. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/autonomy-moral/.
  • Danto, A (1959). The paradigm case argument and the free-will problem. Ethics, 69(2), pp. 120–124.
  • Descartes, R. (2008/1641). Meditations on First Philosophy. Trans. M. Moriarty. Oxford: Oxford University Press.
  • Donnellan, K. (1967). Paradigm-case argument. In The Encyclopedia of Philosophy (P. Edwards, ed.). New York: Macmillan, pp. 106–113.
  • Eveling, H. S. & Leith, G. O. M. (1958). When to use the paradigm-case argument. Analysis, 18(6), pp. 150–152.
  • Flew, A. G. N. (1982). The paradigm case argument: abusing and not using the PCA. Journal of Philosophy of Education, 16(1), pp. 115–121.
  • Flew, A. G. N. (1966). Again the paradigm. In Mind, Matter, and Method: Essays in Philosophy and Science in Honor of Herbert Feigl (P. K. Feyerabend & G. Maxwell, eds.). Minneapolis: University of Minnesota Press, pp. 261–272.
  • Flew, A. G. N. (1957). ‘Farewell to the paradigm-case argument’: a comment. Analysis, 18(2), pp. 34–40.
  • Flew, A. G. N. (1955a). Philosophy and language. The Philosophical Quarterly, 5(18), pp. 21–36.
  • Flew, A. G. N. (1955b). Divine Omnipotence and Human Freedom. In New Essays in Philosophical Theology. Ed. A. Flew and A. MacIntyre. London: SCM, pp. 144–169.
  • Flew, A. G. N. (1954). Crime or disease. The British Journal of Sociology, 5(1), pp. 49–62.
  • Gellner, E. (1959). Words and Things: A Critical Account of Linguistic Philosophy and a Study in Ideology. Great Britain: Victor Gollancz.
  • Hallett, G. L. (2008). Linguistic Philosophy: The Central Story. Albany, N. Y.: State University of New York Press. See chapter 10.
  • Hanfling, O. (1990). What is wrong with the paradigm case argument? Proceedings of the Aristotelian Society, 91, pp. 21–38.
  • Hardie, W. F. R. (1957). My own free will. Philosophy, 32(120), pp. 21–38.
  • Harman, G. (1990). Skepticism and the Definition of Knowledge. London; New York: Routledge. See chapter 1.
  • Harre, R. (1958). Tautologies and the paradigm-case argument. Analysis, 18(4), pp. 94–96.
  • Heath, P. L. (1952). The appeal to ordinary language. The Philosophical Quarterly, 2(6), pp. 1–12.
  • Houlgate, L. D. (1962). The paradigm-case argument and ‘possible doubt’. Inquiry, 5(1–4), pp. 318–324.
  • Jackson, F. (1998). From Metaphysics to Ethics: A Defence of Conceptual Analysis. Oxford: Clarendon Press.
  • King-Farlow, J. & Rothstein, J. M. (1964). Paradigm cases and the injustice to Thrasymachus. The Philosophical Quarterly, 14(54), pp. 15–22.
  • Lucas, J. R. (1970). The Freedom of the Will. Oxford: Oxford University Press.
  • MacIntyre, A. C. (1957). Determinism. Mind, 66(261), pp. 28–41.
  • McKenna, M. and Pereboom, D. 2016. Free Will: A Contemporary Introduction. New York; London: Routledge.
  • Malcolm, N. (1963). George Edward Moore. In Knowledge and Certainty: Essays and Lectures by Norman Malcolm. Englewood Cliffs, N. J.: Prentice-Hall, Inc, pp. 163–183.
  • Malcolm, N. (1951). Philosophy for philosophers. The Philosophical Review 60(3), pp. 329–340.
  • Malcolm, N. (1992/1942). Moore and ordinary language. In The Linguistic Turn (R. Rorty, ed.). Chicago and London: The University of Chicago Press (pp. 111–124). Originally published in (1942) The Philosophy of G. E. Moore (Paul A. Schilpp, ed.). Evanston and Chicago: Northwestern University Press (pp. 345–368).
  • Malcolm, N. (1940). Are necessary propositions really verbal? Mind, 194, pp. 189–203.
  • Marconi, D. (2009). Being and being called: paradigm case arguments and natural kind words. The Journal of Philosophy, 106(3), pp. 113–136.
  • Monroe, A. E. & Malle, B. F. (2010). From uncaused will to conscious choice: the need to study, not speculate about people’s folk concept of free will. Review of Philosophy and Psychology, 1(2), pp. 211–224.
  • Moore, G. E. (1939). Proof of an external world. Proceedings of the British Academy, 25, pp. 273–300.
  • Moore, G. E. (1918). The conception of reality. Proceedings of the Aristotelian Society, 18(1), pp. 101–120.
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  • Passmore, J. (1961). Philosophical Reasoning. London: Duckworth. See chapter 6.
  • Parker-Ryan, S. (2010). Reconsidering ordinary language philosophy: Malcolm’s (Moore’s) ordinary language argument. Essays in Philosophy, 11(2), pp. 123–149.
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  • Richman, R. J. (1962). Still more on the argument of the paradigm case. Australasian Journal of Philosophy, 40(2), pp. 204–207.
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Author Information

Kevin Lynch
Email: kevinlynch405@eircom.net
Huaqiao University
China

Duality in Logic and Language

Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely unrelated. Consequently, if the term ‘duality’ is used in two different senses in one and the same work, the authors often explicitly warn about the potential confusion.

This article focuses exclusively on duality phenomena involving the interaction between an ‘external’ and an ‘internal’ negation of some kind, which arise primarily in logic and linguistics. A well-known example from logic is the duality between conjunction and disjunction in classical propositional logic: φψ is logically equivalent to ¬(¬φ¬ψ), and hence ¬(φψ) is logically equivalent to ¬φ¬ψ. A well-known example from linguistics concerns the duality between the aspectual particles already and still in natural language: already outside means the same as not still inside, and hence, not already outside means the same as still inside (where inside is taken to be synonymous with not outside). Examples such as these show that dualities based on external/internal negation show up for a wide variety of logical and linguistic operators.

Duality phenomena of this kind are highly important. First of all, since they occur in formal as well as natural languages, they provide an interesting perspective on the interface between logic and linguistics. Furthermore, because of their ubiquity across natural languages, it has been suggested that duality is a semantic universal, which can be of great heuristic value. Finally, duality principles play a central role in Freudenthal’s famous proposal for a language for cosmic communication.

Many authors employ the notion of duality as a means to describe the specific details of a particular formal or natural language, without going into any systematic theorizing about this notion itself. Next to such auxiliary uses, however, there also exist more abstract, theoretical accounts that focus on the notion of duality itself. For example, these theoretical perspectives address the group-theoretical aspects of duality, or its interplay with the so-called Aristotelian relations. This article examines a wide variety of dualities in formal and natural languages, and it discusses some of the more theoretical perspectives on duality.

The article is organized as follows. Sections 1 and 2 provide an extensive overview of the most important concrete examples of duality in logic and natural language. Section 3 describes a detailed framework (based on the notion of a Boolean algebra) that allows systematical analysis of these dualities. Section 4 presents a group-theoretical approach to duality phenomena, and Section 5 draws an extensive comparison between duality relations and another type of logical relation, namely those that characterize the Aristotelian square of opposition.

As to the technical prerequisites for this article, Sections 1 and 2 should be accessible to everyone with a basic understanding of philosophical logic. In Sections 3, 4 and 5, the use of some other mathematical tools and techniques is unavoidable; these sections require a basic understanding of discrete mathematics (in particular, Boolean algebra and elementary group theory).

Table of Contents

  1. Duality in Logic
  2. Duality in Natural Language
  3. Theoretical Framework
  4. A Group-Theoretical Approach to Duality
  5. Duality Relations and Aristotelian Relations
  6. References and Further Reading

1. Duality in Logic

Conjunction and disjunction. The most widely known example of duality in logic is undoubtedly that between conjunction and disjunction in classical propositional logic (CPL). Because of their semantics, i.e. the way they are standardly interpreted in CPL, these connectives can be defined in terms of each other, and consequently, only one of them needs to be taken as primitive. For example, if conjunction () and negation (¬) are taken as primitives, then disjunction () can be defined as follows:

φψ:≡¬(¬φ¬ψ). Alternatively, if disjunction is taken as primitive, then conjunction can be defined as follows:
φψ:≡¬(¬φ¬ψ).

Furthermore, each of these equivalences can be derived from the other one; for example, if (???) is taken as primitive, then we obtain (???) as follows:

¬(¬φ¬ψ)¬¬(¬¬φ¬¬ψ)φψ.

Finally, in both cases we obtain the well-known laws of De Morgan. For example, if conjunction is taken as primitive, then (???) follows immediately from (???), while (???) follows from (???) via (???):

\begin{equation}  \label{eq4}\neg(\varphi\vee\psi) & \equiv & \neg\varphi\wedge\neg\psi  \end{equation}
\begin{equation}  \label{eq5}\neg(\varphi\wedge\psi) & \equiv & \neg\varphi\vee\neg\psi.  \end{equation}

Equivalences such as (???-???) exhibit the duality between conjunction and disjunction. They clearly show the interaction between an internal negation (which attaches to each of the individual formulas φ and ψ, and thus occurs inside the scope of the conjunction/disjunction connective) and an external negation (which occurs outside the scope of the connectives). Equivalences (???-???) show that applying both internal and external negation to a disjunction yields the corresponding conjunction, and vice versa. Similarly, (???-???) show that the internal negation of a disjunction is logically equivalent to the external negation of the corresponding conjunction, and vice versa. All these equivalences are manifestations of the underlying semantics of the conjunction and disjunction connectives in CPL.

Universal and existential quantifiers. Another well-known case of duality concerns the universal and existential quantifiers in classical first-order logic (FOL). The situation here is largely analogous to that of conjunction and disjunction. Because of their semantics, i.e. the way they are standardly interpreted in FOL, these quantifiers can be defined in terms of each other, and consequently, only one of them needs to be taken as primitive. For example, if the universal quantifier () is taken as primitive, the existential quanifier () can be defined as follows:

xφ:≡¬x¬φ.

Conversely, if the existential quantifier is taken as primitive, then the universal quantifier can be defined as follows:

xφ:≡¬x¬φ.

Again, each of these equivalences can be derived from the other one; for example, if (???) is taken as primitive, then we obtain (???) as follows:

¬x¬φ¬¬x¬¬φxφ.

Finally, in both cases we obtain the well-known quantifier laws. For example, if the universal quantifier is taken as primitive, then (???) follows immediately from (???), while (???) follows from (???) via (???):

\begin{equation}\label{eq9}\neg\exists x \varphi & \equiv & \forall x\neg\varphi,\end{equation}
\begin{equation}\label{eq10}\neg\forall x\varphi & \equiv & \exists x\neg\varphi\end{equation}

Equivalences such as (???-???) exhibit the duality between the universal and the existential quantifier. Again, they show the interaction between an internal negation (which occurs inside the scope of the quantifier) and an external negation (which occurs outside the scope of the quantifier). Equivalences (???-???) show that applying both internal and external negation to an existential quantifier yields the corresponding universal quantifier, and vice versa. Similarly, (???-???) show that the internal negation of an existential quantifier is logically equivalent to the external negation of the corresponding universal quantifier, and vice versa. All these equivalences are manifestations of the underlying semantics of the universal and existential quantifiers in FOL.

Modal operators. Another rich source of dualities is the broad family of modal logics. For example, in alethic modal logic, necessity (◻) and possibility () are dual to each other (???-???), while in deontic logic, obligation (O) and permission (P) are usually taken as duals (???-???):

\begin{equation}\label{eq11}\Box\varphi \equiv \neg\Diamond\neg\varphi, \hspace{0.3cm} & \hspace{0.3cm} \neg\Box\varphi \equiv \Diamond\neg\varphi\end{equation}
\begin{equation}\label{eq12}\Diamond\varphi \equiv \neg\Box\neg\varphi, \hspace{0.3cm} & \hspace{0.3cm} \neg\Diamond\varphi \equiv \Box\neg\varphi,\end{equation}
\begin{equation}\label{eq13}O\varphi \equiv \neg P \neg\varphi, \hspace{0.3cm} & \hspace{0.3cm} \neg  O  \varphi \equiv P \neg\varphi,\end{equation}
\begin{equation}\label{eq14}P \varphi \equiv \neg O \neg\varphi, \hspace{0.3cm} & \hspace{0.3cm} \neg P \varphi \equiv O \neg\varphi.\end{equation}

Blackburn et al. (2001) provide many other modal examples from concrete application domains, such as temporal logic, propositional dynamic logic and hybrid logic, and more mathematically motivated examples, such as the dualities involving the difference modality and the universal modality. In general, an n-ary modal operator is called a  triangle (Δ), and its dual a nabla ():

\begin{equation}\label{eqnew01}\Delta(\varphi_1,\dots,\varphi_n) &\equiv & \neg\nabla(\neg\varphi_1,\dots,\neg\varphi_n),\end{equation}
\begin{equation}\label{eqnew02}\nabla(\varphi_1,\dots,\varphi_n) &\equiv & \neg\Delta(\neg\varphi_1,\dots,\neg\varphi_n).\end{equation}

The equivalences (???-???) again clearly illustrate the interaction between internal and external negation. Note, furthermore, that the internal negation is applied to all formulas (φ1,,φn). This was also the case with conjunction/disjuction (???-???) and with the universal/existential quantifiers (???-???) (although the latter case is trivial, since in equivalences (???-???) there is only a single formula (φ) to which the internal negation can be applied).

Interconnections. Many of the examples given above are systematically related to each other, and might thus be viewed as manifestations of the same underlying duality. First of all, it is well-known that the propositional connectives of conjunction and disjunction are related to the universal and existential quantifiers, respectively. For example, the formulas xPx and xPx can informally be viewed as expressing the conjunction PaPbPc and the disjunction PaPbPc, respectively.  This reveals a structural similarity between equivalences (???-???) and (???-???). Secondly, in Kripke semantics the modal operators are interpreted as quantifying over possible worlds. For example, the formulas ◻p and p can be interpreted as stating that p is true in all possible worlds and that p is true in at least one possible world, respectively. This reveals a structural similarity between equivalences (???-???) and (???-???).

2. Duality in Natural Language

Quantifiers and modalities in natural language. The most obvious class of natural language expressions that give rise to duality behavior, are the immediate counterparts of the logical operators discussed in Section 1. For example, the determiners all and some combine with a noun to yield noun phrases such as all books and some books, and seem to correspond directly to the quantifiers and . This correspondence is not entirely unproblematic, since it ignores linguistically relevant distinctions, such as the difference between every and all vis-à-vis collective and distributive predicates (Dowty 1987; Brisson 2003), and the distinction between quantificational and non-quantificational uses of some (Löbner 1987). Setting such considerations aside, however, one can say that the natural language determiners all and some are each other’s duals, just like the first-order quantifiers and are each other’s duals. Similarly, the duality relation between ◻ and in modal logic also shows up for a whole range of natural language expressions for necessity and possibility. In logic, ◻ and are almost invariably operators taking propositions as their arguments. In natural language, however, the modal notions are expressed in a variety of linguistic categories, such as modal adjectives (necessary vs. possible), modal adverbs (necessarily vs. possibly) or modal auxiliary verbs (must/should vs. can/may).

Conjunction and disjunction in natural language. The most prototypical duality in logic, namely that between the propositional connectives of conjunction and disjunction, only plays a minor role, if any, in the linguistic realm. The main reason is the ambiguity of natural language and and or, which is often explained pragmatically in terms of conversational implicatures (Horn 2004). For example, natural language conjunction very often conveys additional aspects of causality (φ and ψ φ and therefore ψ) or sequentiality (φ and ψ φ and afterwards ψ), whereas disjunction is notoriously ambiguous between an inclusive interpretation (φ or ψ φ or ψ, and perhaps both) and an exclusive interpretation (φ or ψ φ or ψ, but not both). These asymmetrical ambiguities of natural language conjunction and disjunction render the notion of duality less suitable for their linguistic and philosophical analysis, as observed by Humberstone (2011, p. 772):

for many logical purposes [] conjunction and disjunction are attractively treated in a symmetrical fashion. Inherent asymmetries in the informal conceptual apparatus we bring to bear on logic often make duality an inappropriate consideration to bring in for philosophical purposes, however.

Testing for duality. In logic, duality is a matter of definition or convention; in modal logic, for example, the duality between ◻ and follows from the way in which the semantics of these operators is defined. By contrast, in linguistics, duality is a much more empirical matter. In other words, duality relations between natural language expressions have to be argued for or demonstrated and may thus be refuted on empirical grounds. For that purpose, duality tests have been devised (Löbner 2011, p. 492ff.), which crucially rely on the relation of lexical inversion holding between predicates such as be on/off, be inside/outside or be here/gone. Testing for internal negation evaluates the equivalence between (i) a proposition O(P) with operator O and predicate P and (ii) a proposition O(P), with operator O=INEG(O) being the internal negation of O, and predicate P=LEXINV(P) being the lexical inverse of P; see (???). The examples in (???-???) illustrate the internal negations of the quantifiers:

\begin{equation}\label{eq19}O(P) & \equiv & \Tiny{INEG}\small(O)(\Tiny{LEXINV}\small{(P)})\end{equation}
\begin{equation}\label{eq20} \textbf{Some}~ lights~ are~ \textbf{on}. &\equiv & \textbf{Not all}~ lights~ are~ \textbf{off.}\end{equation}
\begin{equation}\label{eq21}\textbf{No}~ children~ are~ \textbf{inside.} &\equiv & \textbf{All}~ children~ are~ \textbf{outside.}\end{equation}

Testing for duality evaluates the equivalence between (i) a proposition which gives a negative answer to a polarity question of the form O(P) and (ii) a proposition O(P), with operator O=DUAL(O) being the dual of O, and predicate P=LEXINV(P) again being the lexical inverse of P; see (???). The examples in (???-???) illustrate the dialogue patterns establishing the duality of the universal and existential quantifiers:

\begin{equation}\label{eq22} \neg O(P) & \equiv & \Tiny{DUAL}\small{(O)}(\Tiny{LEXINV}\small{(P)})\end{equation}
\begin{equation}\label{eq23} Are~ \textbf{some}~ lights~ \textbf{on}? – No, & \equiv & \textbf{all}~ lights~ are~ \textbf{off}.\end{equation}
\begin{equation}\label{eq24} Are~ \textbf{all}~ children~ \textbf{inside}? – No, & \equiv & \textbf{some}~ children~ are~ outside.\end{equation}

The main reason for applying lexical inversion to the predicates in these tests, rather than straightforward grammatical negation by means of the negative particle not, is that the latter may yield scope ambiguities, depending on whether it is taken to express internal or external negation (Löbner 2011, p. 492ff.). For example, the negative particle not in the lefthand side of (???-???) may get the internal negation reading (???) as well as the external negation reading (???). Similarly, the modal auxiliary may in the lefthand side of (???-???) interacts differently with the negative particle not depending on the type of modality involved: in its epistemic use, it gets the internal negation reading (???), whereas in its deontic use, it gets the external negation reading (???).

\begin{equation}\label{eq25} \textbf{All}~ children~ are~ \textbf{not}~ inside. & \stackrel{1}{\equiv} & \textbf{All}~ children~ are~ \textbf{outside}.\end{equation}
\begin{equation}\label{eq26} &\stackrel{2}{\equiv}& \textbf{Not all}~ children~ are~ \textbf{inside}.\end{equation}
\begin{equation}\label{eq27}She~ \textbf{may not}~ stay. & \stackrel{1}{\equiv} & She~ \textbf{may}~ leave.\end{equation}
\begin{equation}\label{eq28} & \stackrel{2}{\equiv} & She~ \textbf{must}~ leave.\end{equation}

The negative particle not and the quantifier all in the lefthand side of (???-???) can take scope over each other: in (???), not occurs inside the scope of all (thereby transforming the predicate inside into its lexical inverse outside), while in (???), all occurs inside the scope of not. Such scope ambiguities also arise for other operators besides negation. For example, the quantifier all and the modal adverb necessarily in (???-???) can take scope over each other, thus giving rise to the de dicto reading (???) and the de re reading (???). However, scope distinctions cannot be fully reduced to the de dicto/de re distinction. After all, the latter is a binary distinction, whereas operators that take scope over each other can give rise to more than two distinct interpretations (Kripke 1977).

\begin{equation}\label{neweq1} \textbf{Everything}~ is~ \textbf{necessarily}~ self\textrm{-}identical. & \stackrel{1}{\equiv} & \Box\forall x(x = x),\end{equation}
\begin{equation}\label{neweq2} & \stackrel{2}{\equiv}& \forall x\Box(x=x).\end{equation}

Another complication arising from negation concerns the cognitive difficulty that people have with processing sentences that contain multiple negations. Because of these cognitive difficulties, some of the tests described above are less easily applicable to determine whether a certain relation holds between two expressions. For example, we not only have a duality between the positive quantifiers all and some, but also one between the negative quantifiers no and some not. The former duality is empirically confirmed by the dialogue patterns in (???-???). In contrast, the corresponding dialogue patterns for the latter duality in (???-???) contain three grammatical negations (no, no and not) and one lexical inversion (off), and therefore sound much less natural (even though they are logically impeccable).

\begin{equation}\label{eq29} Are~ \textbf{no}~ lights~ \textbf{on}?- No, &\equiv& \textbf{not all}~ lights~ are~ \textbf{off}.\end{equation}
\begin{equation}\label{eq30} Are~ \textbf{not all}~ lights~ \textbf{on}?- No, &\equiv& \textbf{no}~ lights~ are~ \textbf{off}.\end{equation}

Pronouns and adverbs of quantification. The universal and existential quantifiers are not only related to the determiners all and some, but also to a number of other linguistic categories. For example, when quantifying over people or objects, the determiners are morphologically integrated with the nouns body and thing into indefinite pronouns. Similarly, when quantifying over places, the determiners are morphologically integrated with the adverb where into compound adverbs. By contrast, adverbs that quantify over time and manner exhibit more idiosyncratic lexicalization patterns. Irrespective of such morphological details, all of the categories in the table below inherit the same basic duality pattern from the determiners, and thus, ultimately, from the logical quantifiers and .

¬ ¬ ¬¬
¬¬ ¬ ¬
every not every no some
everybody not everybody nobody somebody
everything not everything nothing something
everywhere not everywhere nowhere somewhere
always not always never sometimes
anyhow not anyhow no way somehow

Generalized quantifiers. Contemporary generalized quantifier theory (GQT) is able to deal with a considerably larger range of natural language quantifiers than the usual universal and existential ones (Barwise and Cooper 1981; Peters and Westerståhl 2006). These include quantifiers that cannot be expressed in first-order languages, such as most. Additionally, GQT allows for a more compositional treatment of quantification. Consider, for example, the sentences John runs and everybody runs, which have by and large the same syntactic structure (namely: noun phrase + verb phrase). While the first-order representations of the semantics of these sentences are vastly different–run(j) vs. x:run(x)–, their GQT representations are much more similar: John(run) vs. everybody(run).

GQT offers two (mathematically equivalent) perspectives on quantification: a functional and a relational perspective. Focusing on the former, a quantifier expression Q is taken to denote a set of subsets of the universe U of people, and for any unary predicate expression B, the formula Q(B) is true iff [[B]][[Q]]. For example, since [[everybody]]={XUU=X} and [[somebody]]={XUX} it is easy to see that everybody(run) is true iff U=[[run]] and that somebody(run) is true iff [[run]]. As expected, the external negation, internal negation and dual of the formula Q(B) are defined as ¬Q(B), Q(¬B) and ¬Q(¬B), respectively (with the convention that [[¬B]]=U[[B]]={xUx[[B]]}). For example, the dual of everybody(run) is ¬everybody(¬run), which is true iff UU[[run]], i.e. iff [[run]]. This shows that in GQT, too, the dual of everybody(run) is somebody(run). Finally, if the proper name John names the individual jU, then GQT defines the generalized quantifier [[John]]={XUjX} and thus we find that John(run) is true iff [[run]][[John]], iff j[[run]]. Note that the dual of John(run) is ¬John(¬run), which is true iff jU[[run]], iff j[[run]]. This shows that John(run) is dual to itself, which illustrates the fact that in GQT, proper names are self-dual (Gamut 1991, p. 238)).

We now turn to the alternative, relational perspective in GQT. This perspective focuses on sentences of the form Q(A,B), where Q is a quantifier expression and A and B are unary predicate expressions. The formula Q(A,B) is true iff ([[A]],[[B]])[[Q]]. Here are some well-known examples (with (U) denoting the powerset of U, i.e. (U)={XXU}):

rcl[[all]]={(X,Y)(U)×(U)XY}[[some]]={(X,Y)(U)×(U)XY}[[most]]={(X,Y)(U)×(U)|XY|>|XY|}[[some but not all]]={(X,Y)(U)×(U)XY and XY}[[exactly half of the]]={(X,Y)(U)×(U)|XY|=12|X|}[[thesing]]={(X,Y)(U)×(U)|X|=1 and XY}

The external negation, internal negation and dual of the formula Q(A,B) are defined as ¬Q(A,B), Q(A,¬B) and ¬Q(A,¬B), respectively. Note that, in contrast to the examples from logic discussed in Section 1, internal negation is not applied to all predicate expressions, but only to the second one. Here, too, generalized quantifiers can be their own dual or internal negation. For example, the internal negation of some but not all (man, run) is some but not all (man, ¬run), which is true iff [[man]](U[[run]]) and [[man]](U[[run]]) iff [[man]][[run]] and [[man]][[run]] iff some but not all (man,run) is true. This shows that some but not all is its own internal negation. Similarly, the proportional quantifier exactly half of the can be shown to be its own internal negation; for example, exactly half of the men are awake is equivalent to exactly half of the men are not awake.

The duality patterns of quantifiers such as most and many have been a matter of contention. Peterson (1979) proposed an analysis from which it follows that most and many are dual to each other. However, as pointed out by Horn (2006, p. 36), it seems unlikely that most(A,B) is in general equivalent to ¬many(A,¬B). Consider, for example:

Most Italians like pizza.
Not many Italians do not like pizza.
Many Italians do not like pizza.

If most and many were indeed dual, then (???) and (???) should be equivalent, while (???) and (???) should be contradictory. However, (???) is true, but, since there are indeed many Italians that do not like pizza, (???) is false and (???) is true. This shows that (???) and (???) are not equivalent, and that (???) and (???) are not contradictory either.

Other linguistic expressions. Duality patterns also arise among natural language expressions that do not directly correspond to logical operators or quantifiers. For example, König (1991) has suggested that the causative conjunction because and the concessive conjunction although are duals, based on dialogue tests for duality such as (???).

\begin{equation}\label{eq34} p~ \textbf{because}~ q? – No, & \equiv & p~ \textbf{although}~ \neg q.\end{equation}

However, based on other linguistic evidence and more general, methodological considerations, this proposal has been criticized by Iten (1998, 2005). Working in the framework of relevance theory, Iten argues that causative conjunctions make a significant contribution to the truth conditions of sentences in which they occur: p because q is true iff q is true, p is true, and q‘s being true is the cause of p‘s being true. By contrast, concessive conjunctions do not contribute to the truth conditions of sentences in which they occur: p although q is true iff q is true and p is true. Because of this discrepancy, Iten claims that sentences such as ¬(p because q) and p although ¬q do not have the same truth conditions, and consequently, because and although are not dual to each other.

The most widely studied example of linguistic duality, however, is that between the aspectual adverbs already and still (Löbner 1989, 1990, 1999; van der Auwera 1993; Mittwoch 1993; Michaelis 1996; Smessaert and ter Meulen 2004). The dialogue tests for duality in (???-???) suggest that already and still are indeed each other’s duals.

\begin{equation}\label{eq35} Is~ Bob~ \textbf{already}~ \textbf{outside}? – No, & \equiv & he~ is~ \textbf{still}~ \textbf{inside}.\end{equation}
\begin{equation}\label{eq36} Is~ Bob~ \textbf{still}~ \textbf{outside}? – No, & \equiv & he~ is~ \textbf{already}~ \textbf{inside}.\end{equation}

Similarly, using the equivalence tests for internal negation in (???-???), we find that the internal negation of already is no longer and that of still is not yet. Finally, the equivalences in (???-???) show that the external negation of already is not yet and that of still is no longer.

\begin{equation}\label{eq37} Bob~ is~ \textbf{already}~ \textbf{outside}. & \equiv & Bob~ is~ \textbf{no longer}~ \textbf{inside}.\end{equation}
\begin{equation}\label{eq38} Bob~ is~ \textbf{still}~ \textbf{outside}. & \equiv &  Bob~ is~ \textbf{not yet}~ \textbf{inside}.\end{equation}
\begin{equation}\label{eq39} It’s~ not~ the~ case~ that~ Bob~ is~ \textbf{already}~ \textbf{outside}. & \equiv & Bob~ is~ \textbf{not yet}~ \textbf{outside}.\end{equation}
\begin{equation}\label{eq40} It’s~ not~ the~ case~ that~ Bob~ is~ \textbf{still}~ \textbf{outside}. & \equiv & Bob~ is~ \textbf{no longer}~ \textbf{outside}\end{equation}

The two negative adverbs no longer and not yet are also dual to each other, as illustrated by the dialogues in (???-???). However, because of the multiple negative elements, these dialogues sound less natural than the ones in (???-???), even though all of them are equally logically correct (compare with the dialogues in (???-???) and (???-???) for the dualities between the standard quantifiers).

\begin{equation}\label{eq41} Is~ Bob~ \textbf{not yet}~ \textbf{outside}? – No, & \equiv & he~ is~ \textbf{no longer}~ \textbf{inside}.\end{equation}
\begin{equation}\label{eq42} Is~ Bob~ \textbf{no longer}~ \textbf{outside}? – No, & \equiv & he~ is ~\textbf{not yet}~ \textbf{inside}.\end{equation}

Phase quantification. In order to account for the duality patterns of the aspectual adverbs described in (???-???), Löbner (1989; 1990; 2011) has developed the theory of phase quantification. He considers a (linear) temporal scale, a reference time t on that scale, and a proposition p (which is either true or false at any timepoint of the scale). The semantics of aspectual adverbs crucially concerns single polarity transitions on this temporal scale. There are two types of such transitions: the truth value of p can change from false into true, or alternatively, from true into false. Furthermore, the reference time t can either be situated in the positive (p) phase or in the negative (¬p) phase of such a transition. In total, there are thus four cases to be distinguished:

    • t is in the positive phase of a polarity transition from falsity to truth

As illustrated in Figure 1(a), this corresponds to sentences such as Bob was already reading the paper at noon. The reference time (at noon) is situated in the positive phase (in which Bob was reading the paper), and thus occurs after the (actual) transition of starting to read (i.e. the transition from not reading to reading) has taken place.

Figure 1: Löbner’s Four Phase Diagrams

    • t is in the positive phase of a polarity transition from truth to falsity

As illustrated in Figure 1(b), this corresponds to sentences such as Bob was still reading the paper at noon. The reference time (at noon) is situated in the positive phase (in which Bob was reading the paper), and thus occurs before the (potential) transition of stopping to read (i.e. the transition from reading to not reading) has taken place.

    • t is in the negative phase of a polarity transition from falsity to truth

As illustrated in Figure 1(c), this corresponds to sentences such as Bob was not yet reading the paper at noon. The reference time (at noon) is situated in the negative phase (in which Bob was not reading the paper), and thus occurs before the (potential) transition of starting to read (i.e. the transition from not reading to reading) has taken place.

    • t is in the negative phase of a polarity transition from truth to falsity

As illustrated in Figure 1(d), this corresponds to sentences such as Bob was no longer reading the paper at noon. The reference time (at noon) is situated in the negative phase (in which Bob was not reading the paper), and thus occurs after the (actual) transition of stopping to read (i.e. the transition from reading to not reading) has taken place.

In the case of duality (already/still and not yet/no longer), the actual polarity of p thus remains unchanged, but the direction of the polarity transition gets reversed. By contrast, in the case of external negation (not yet/already and still/no longer) the actual polarity of p is switched, but the polarity transition remains unchanged. Finally, in the case of internal negation (not yet/still and already/no longer), both the actual polarity of p and the direction of the polarity transition are reversed. This shows that in the phase quantification analysis, internal negation is viewed as the combination of duality and external negation. Löbner has also used this analysis to account for asymmetries in lexicalization patterns: already and still are less marked than not yet, which in turn is less marked than no longer (also see Section 5). Finally, it should also be emphasized that this analysis has been generalized to other lexical domains besides the aspectual adverbs, such as scalar predicates and (the procedural interpretation of) the first-order quantifiers.

Language universals and universal languages. The overview presented in this section shows that duality phenomena are not only ubiquitous in formal logical languages, but also in natural languages. It has therefore been suggested that duality is a semantic universal, which can be of great heuristic value in comparative linguistic research (van Benthem 1991). Furthermore, duality also plays a central role in artificial languages, which can be viewed as occupying an intermediate position between formal and natural languages. For example, Lincos, which was developed by Freudenthal (1960) for the purpose of cosmic communication, contains duality principles for conjunction/disjunction (1.36.8), universal/existential quantification (1.36.9), necessity/possibility (3.25.1) and obligation/permission (3.32.3).

3. Theoretical Framework

General definition. We will now present a general theoretical framework in which duality phenomena can be described and analyzed. Consider Boolean algebras A=A,A,A,¬A,A,A and B=B,B,B,¬B,B,B (Givant and Halmos 2009), and consider n-ary operators O1,O2:AnB. The duality relations are defined as follows: O1 and O2 are

  • identical – abbreviated as ID(O1,O2) – iff
  • a1,,anA:O1(a1,,an)=O2(a1,,an),

  • each other’s external negation – abbreviated as ENEG(O1,O2) – iff
  • a1,,anA:O1(a1,,an)=¬BO2(a1,,an),

  • each other’s internal negation – abbreviated as INEG(O1,O2) – iff
  • a1,,anA:O1(a1,,an)=O2(¬Aa1,,¬Aan),

  • each other’s dual – abbreviated as DUAL(O1,O2) – iff
  • a1,,anA:O1(a1,,an)=¬BO2(¬Aa1,,¬Aan).

Special cases. The definition provided above is fully abstract and general, but by plugging in concrete Boolean algebras for A and B, we can recover the usual dualities as special cases. For example, in the language LCPL of classical propositional logic (CPL), we can define equivalence classes [φ]:={ψLCPLφψ} and consider the Lindenbaum-Tarski algebra BCPL:={[φ]φLCPL} It is well-known that BCPL is a Boolean algebra, and can thus be plugged in for A and/or B in the aforementioned definition. For example, if we consider conjunction and disjunction as binary operators ,:BCPL×BCPLBCPL (defined by [φ][ψ]:=[φψ] and [φ][ψ]:=[φψ]), this definition states that DUAL(,) iff

for all  [φ],[ψ]BCPL:[φ][ψ]=¬(¬[φ]¬[ψ]),

which is equivalent to the formulation (???) that was given above

for all φ,ψLCPL:φψ¬(¬φ¬ψ).

(Note that identity between elements in the Lindenbaum-Tarski algebra boils down to  logical equivalence between the formulas themselves.) Similarly, the first-order quantifiers can be seen as unary operators ,:BFOLBFOL where BFOL is the Lindenbaum-Tarski algebra of first-order logic (FOL), which is a cylindric algebra (Henkin et al. 1971), and thus a fortiori a Boolean algebra. Finally, by taking A and/or B to be other, more exotic Boolean algebras, the aforementioned definition also allows us to study duality relations in other, less well-known applications  (Demey and Smessaert 2016).

Relations vs. functions. All the duality relations have a number of special properties. For any relation R{ID,INEG,ENEG,DUAL}, one can show that

  • R is deterministic:
  • for all O1,O2,O3:AnB: if R(O1,O2) and R(O1,O3), O2=O3,
  • R is serial:
  • for all O1:AnB, there exists an O2:AnB such that R(O1,O2),
  • R is symmetric:
  • for all O1,O2:AnB:R(O1,O2) iff R(O2,O1).

The first two properties jointly state that for each O1, there is exactly one O2 such that R(O1,O2). This means that the relation R is essentially a function, and switching from relational to functional notation, we can thus write O2=R(O1).

For example, since DUAL(,), we can write =DUAL(), and say that is the (unique) dual of . However, since and are seen as binary operators on the Lindenbaum-Tarski algebra BCPL, it should be kept in mind that this uniqueness claim ultimately boils down to a logical equivalence claim (see above). For example, consider the operator O:BCPL×BCPLBCPL defined by O([φ],[ψ]):=¬(¬[φ]¬[ψ]) It then holds that DUAL(,) and DUAL(,O), which together entail that =O. The latter is an identity of functions, and thus means that for all [φ],[ψ]BCPL, we have [φ][ψ]=O([φ],[ψ])=¬(¬[φ]¬[ψ]) in other words: for all φ,ψLCPL it holds that φψ¬(¬φ¬ψ)

Since each R{ID,INEG,ENEG,DUAL} can be viewed as a function, the symmetry of the relation R can equivalently be expressed as follows: O2=R(O1) iff O1=R(O2), which is itself equivalent to the property that R(R(O))=O for all operators O:AnB. This means that the function R is an involution.

Obviously, the definitions of the duality relations/functions can harmlessly be transposed from operators O:AnB to the outputs of those operators. For example, if the operator O2:AnB is the dual of the operator O1:AnB, then for all a1,,anA, the element O2(a1,,an)B can be said to be the dual of the element O1(a1,,an)B. For example, in this way, we can say not only that is the dual of , but also that [φ][ψ] is the dual of [φ][ψ], for all [φ],[ψ]BCPL – or more informally, that φψ is ‘the’ dual (up to logical equivalence) of \(φψ, for all \(φ,ψLCPL.

Duality squares. For every operator O:AnB, one can define the set of four operators δ(O):={ID(O),ENEG(O),INEG(O),DUAL(O)} It is natural to view the set δ(O) as ‘generated’ by the operator O; however, it should be emphasized that δ(O) can be seen as generated by any of its elements. For example, if we consider DUAL(O), we find that δ(DUAL(O))= {ID(DUAL(O)),ENEG(DUAL(O)), INEG(DUAL(O)),DUAL(DUAL(O))}= {DUAL(O),INEG(O),ENEG(O),ID(O)}= δ(O). In general, for any Oδ(O), it holds that δ(O)=δ(O) (Peters and Westerståhl 2006, p. 134; Westerståhl 2012, p. 205).

The argument above is based on the fact that δ(O) is ‘closed under duality’, in the sense that applying any of the ID-, ENEG-, INEG- or DUAL-functions to its elements only yields operators that already belong to δ(O). This observation is the starting point for the group-theoretical perspective on duality that will be developed in Section 4. The operators in δ(o) thus constitute natural families (van Benthem 1991, p. 31; Peters and Westerståhl 2006, p. 26), which are often visualized by means of square diagrams. The diagram’s vertices represent the four operators (or formulas), and its edges and diagonals represent the various relations between those operators. Figure 2(a) shows the graphical convention that will be used in this article to visualize these relations.

Visually speaking, duality squares can be presented in a number of different ways, depending on which aspects the author wishes to emphasize. The most widely used presentation can be found in Figure 2(b), in which the ENEG-, TinyINEG- and DUAL-relations occupy the square’s diagonals, horizontal and vertical edges, respectively. This presentation thus emphasizes the analogy between the duality square and the well-known Aristotelian square, in which the contradiction, (sub)contrariety and subalternation relations also occupy the diagonals, horizontal and vertical edges, respectively (van Benthem 1991, p. 31; Jaspers 2005, p. 148; Peters and Westerståhl 2006, p. 25, Westerståhl 2012, p. 202); also see Section 5. Figure 2(c) shows an alternative layout, in which the DUAL-relations occupy the diagonals, thereby graphically reflecting the fact that DUAL is the combination of ENEG (which constitutes the vertical edges) and INEG (which constitutes the horizontal edges) (Löbner 1990, p. 69ff.; Konig 1991, p. 201); also see Section 4. Thirdly, Löbner (1999, p. 57; 2011, p. 488) has argued, on the basis of his phase quantification approach to duality (see Section 2), that INEG should be seen as the combination of ENEG and DUAL, and thus uses squares as in Figure 2(d), in which the former occupies the diagonals. Finally, it should be emphasized that the ID-relations are not visualized explicitly in any of these three ways of presenting duality squares, since they would simply constitute loops on all vertices of the squares.

Figures 3 and 4 show duality squares for some concrete dualities from logic and language (all these squares follow the presentation of Figure 2(b), and thus have ENEG-diagonals). The first three squares in Figure 3 correspond to the first three examples of duality in logic that were discussed in Section 1: (a) the propositional connectives of conjunction and disjunction, (b) the universal and existential quantifiers, and (c) the modal operators of necessity and possibility. Furthermore, it should be emphasized that the general perspective on duality in terms of external and internal negation also allows us to draw less standardized duality squares; for example, Figure 3(d) shows the less widely known duality square that is generated by the propositional connective of material implication (). Finally, the squares in Figure 4 correspond to two examples of duality in natural language that were discussed in Section 2, namely (a) the quantification adverbs everywhere/somewhere, and (b) the aspectual adverbs already/still.

 

Figure 2: (a) Graphical representations of the duality relations; presentationsof duality squares with (b)ENEG-diagonals, (c)DUAL-diagonals and (d)INEG-diagonals.

Figure 3: Duality squares from logic: (a) conjunction-disjunction, (b) universal-existential, (c) necessity-possibility, (d) implication.

Figure 4: Duality squares from linguistics: (a) everywhere-somewhere, (b) already-still.

Degenerate duality patterns. For some operators O:AnB, it might happen that DUAL(O)=O=ID(O), i.e. O is self-dual. In this case, one can also show that INEG(O)=ENEG(O), i.e. O’s internal and external negation coincide with each other. For example, as was already shown in Section 2, proper names are self-dual in generalized quantifier theory. For another example, consider the identity operator IA:AA (for any Boolean algebra A), which is defined by IA(a):=a. For any element aA, it holds that DUAL(IA)(a)=¬AIA(¬Aa)=¬A¬Aa=a=IA(a) and thus DUAL(IA)=IA, i.e. IA is self-dual. Similarly, for any element aA it holds that INEG(IA)(a)=IA(¬Aa)=¬Aa=¬AIA(a)=ENEG(IA)(a) and thus INEG(IA)=ENEG(IA).

Completely analogously, for some operators O:AnB, it can happen that INEG(O)=O=ID(O), i.e. O is its own internal negation. In this case, one can also show that DUAL(O)=ENEG(O), i.e. O’s external negation and dual coincide with each other. Consider, for example, the contingency operator C:BS5BS5, which is defined by C([φ]):=[φ]¬[φ]=[φ¬φ] (recall that BS5 is the Lindenbaum-Tarski algebra of the modal logic S5, which is a modal algebra (Blackburn et al. 2001), and thus a fortiori a Boolean algebra). For any [φ]BS5, it holds that INEG(C)([φ])=C(¬[φ])=¬[φ]¬¬[φ]=[φ]¬[φ]=C([φ]) and thus INEG(C)=C. Similarly, it holds that DUAL(C)([φ])=¬C(¬[φ])=¬(¬[φ]¬¬[φ])=¬([φ]¬φ)= ENEG(C)([φ]) and thus DUAL(C)=ENEG(C).

We have now discussed the possibility of an operator coinciding with its dual, or with its internal negation. This naturally leads to the question whether there are also operators that coincide with their external negation. It is easy to see, however, that there exist no non-trivial operators with this property. After all, if O:AnB is its own external negation, then for all n-tuples ¯aAn, it holds that O(¯a)=¬BO(¯a) and hence, B=O(¯a)B¬BO(¯a)=O(¯a)BO(¯a)=O(¯a) and also B=O(¯a)B¬BO(¯a)=O(¯a)BO(¯a)=O(¯a) which means that B is the trivial Boolean algebra in which B=B (in logical terms: B is the Lindenbaum-Tarski algebra of a logical system that is inconsistent).

Whenever an operator O is its own dual or internal negation, the set δ(O) does not contain four, but only two distinct operators (Peters and Westerståhl 2006, p. 134;Westerståhl 2012, p. 205), and thus cannot be visualized using an ordinary duality square. Recall the standard presentation of the duality square (with horizontal INEG- and vertical DUAL-edges) in Figure 2(b), which is repeated here as Figure 5(a). If O=DUAL(O), then δ(O)={ID(O),INEG(O)}, and thus, the duality square in Figure 5(a) degenerates into the binary horizontal duality diagram in Figure 5(b). Analogously, if O=INEG(O), then δ(O)={ID(O),DUAL(O)}, and thus, the duality square in Figure 5(a) degenerates into the binary vertical duality diagram in Figure 5(c).

Figure 5: (a) Ordinary duality square, (b) degenerate duality pattern for an operator that is its own dual, (c) degenerate duality pattern for an operator that is its own internal negation.

Beyond external and internal negation. In the introduction, it was emphasized that this article mainly focuses on duality phenomena that arise in logical and natural languages. As was illustrated in Sections 1 and 2, these dualities can informally be characterized in terms of internal and external negation. In this section, this informal characterization was made mathematically precise, by appealing to operators O:AnB and viewing the internal and external negation as the negations ¬A and ¬B of the source and target Boolean algebras A and B, respectively. However, it should be emphasized that in the broader mathematical perspective on duality (Gowers 2008; Kabakov et al. ~ 2014), internal/external negation plays a less central role. For example, in category-theoretic terms, conjunction and disjunction are characterized as follows (Mac Lane 1998; Davey and Priestley 2002):

φψ is the unique
formula π such that:
π entails φ
π entails ψ
– for all α: if α entails φ and ψ,
then α entails π
φψ is the unique
formula π such that:
φ entails π
ψ entails π
– for all α: if φ and ψ entail α,
then π entails α

From this perspective, the duality of conjunction and disjunction is thus not characterized in terms of internal and external negation, but rather in terms of systematically ‘reversing’ the direction of entailment (a similar connection between duality and ‘reversing’ the direction of polarity transitions shows up in Löbner’s phase quantification theory, as discussed in Section 2). This difference should not be exaggerated, however, as can already be seen from the law of contraposition, in which the ideas of negation and reversal are brought together: φψ¬ψ¬φ.

4. A Group-Theoretical Approach to Duality

The Klein four group. When ID, ENEG, INEG and DUAL are viewed as functions, they map each operator O:AnB onto the operators ID(O),ENEG(O), INEG(O),DUAL(O):AnB Since the input and output of the functions ID, ENEG, INEG and DUAL are of the same type (namely: operators AnB), they can be applied repeatedly. For example, starting with an operator O:AnB, we can apply INEG to it to obtain the operator INEG(O):AnB; by applying ENEG to the latter we obtain the operator ENEG(INEG(O)):AnB. It follows immediately from the definitions of the duality relations/functions that ENEG(INEG(O))=DUAL(O). Since this holds independently of the concrete operator O, we can write ENEGINEG=DUAL, which means that applying INEG and then ENEG (to some operator) yields the same result as applying DUAL (to that same operator). In a similar vein, since for all operators O:AnB it holds that INEG(INEG(O))=O=ID(O), we can write INEG INEG = ID. In this way, we obtain a large number of functional identities that descibe the behavior of the duality and internal/external negation functions:

IDID= ID= DUALDUALENEGENEG= ID= INEGINEGINEGENEG= DUAL= ENEGINEGINEGDUAL= ENEG= DUALINEGDUALENEG= INEG= ENEGDUAL

These identities can be summarized by stating that the functions ID, ENEG, INEG and DUAL jointly form a group that is isomorphic to the Klein four group V4 (German: Kleinsche Vierergruppe). Its Cayley table looks as follows:

IDENEGINEGDUALIDIDENEGINEGDUALENEGENEGIDDUALINEGINEGINEGDUALIDENEGDUALDUALINEGENEGID

 
The fact that duality behavior can be described by means of V4 was already noted by authors such as Piaget (1949), Gottschalk (1953), Löbner (1990), van Benthem (1991) and Peters and Westerståhl (2006). However, many of them used slightly differing labels for the group elements; here is an overview table:

Piaget Gottschalk Löbner Peters & Westerståhl
ID identité (I) identity (E) indentity
ENEG inversion (N) negational (N) negation outer negation
INEG réciprocation (R) contradual (C) subnegation inner negation
DUAL corrélation (C) dual (E) dual dual

This group-theoretical perspective also allows us to describe the degenerate cases of operators that are their own duals or their own internal negations. Note that these cases are characterized by the identities DUAL = ID and INEG = ID, respectively. Note that if DUAL = ID, then also ENEG = INEG, and thus V4 collapses into a group that is isomorphic to Z2; see the left and middle Cayley tables below and also recall Figure 5(b). Similarly, if INEG = ID, then also ENEG = DUAL, and thus V4 again collapses into a group that is isomorphic to Z2; see the right and middle Cayley tables below and also recall Figure 5(c).

IDINEGIDIDINEGINEGINEGID 01001110 IDDUALIDIDDUALDUALDUALID

Finally, it should be noted that the Klein four group V4 is isomorphic to the direct product of Z2 with itself, i.e. V4 Z2 × Z2 = Z22. Although this fact is well-known in group theory, its logico-linguistic significance has only recently begun to be explored. The Cayley table for Z2 × Z2 looks as follows:

(0,0)(1,0)(0,1)(1,1)(0,0)(0,0)(1,0)(0,1)(1,1)(1,0)(1,0)(0,0)(1,1)(0,1)(0,1)(0,1)(1,1)(0,0)(1,0)(1,1)(1,1)(0,1)(1,0)(0,0)

 
Comparing the Cayley tables for Z2 × Z2 and the Klein four group V4, we see that the concrete isomorphism looks as follows:
ID(0,0),ENEG(1,0),INEG(0,1),DUAL(1,1).
This group-theoretical isomorphism turns out to be very informative: 0 and 1 represent the number of times negation is being applied in a given Boolean algebra, and the left and right coordinates stand for the target and source Boolean algebra (i.e. external and internal negation), respectively. For example, ENEG corresponds to (1,0), which represents 1 external negation and 0 internal negations. Similarly, INEG corresponds to (0,1), which represents 0 external negations and 1 internal negation (keeping in mind that internal negation applies to all arguments). Using the conventions that ¬ 0Aa:=a and ¬ 1Aa:=¬ Aa for all aA, we thus find for any operator O:AnB and i, k{0,1}:
(i, k)(O)(a1,,an)=¬ iBO(¬ kAa1,,¬kAan).
Representing V4 as Z2×Z2 thus gives us a firm syntactic handle on duality: it shows how duality behavior arises out of the interplay of the independent behaviors (0 or 1) of an external and an internal negation (resp. left and right coordinate).

Composed operators. The group-theoretical account of duality can be extended in a number of different ways. For example, Demey (2012a) has used it to study the duality behavior of composed operators. Given operators O1:AnB and O2:BC, we will write O2O1:AnC for the composed operator that first applies O1 to the arguments, and then O2. For simplicity, we will assume that O2 is unary, but this assumption is not essential. In this article, we will focus on the basic example ◻ from modal syllogistics (Buridan 2001; Read 2012). A more linguistically motivated example, viz. possessives with multiple quantifiers, such as three athletes of each country, is discussed in Westerståhl (2012).

Each of O1 and O2 has its own internal and external negation, but it is easy to see that in the composed operator O2 O1, the external negation of O1 coincides with the internal negation of O2. As a consequence, the composed operator O2 O1 has three negations, namely external, intermediate, and internal (formally: ¬C, ¬B, and ¬A, respectively). Since each of these 3 negations may or may not be applied, O2 O1 gives rise to 23=8 operators. As an example, consider the case of ◻ in (???):
¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)¬O2¬O1¬¬x¬◻¬P(x)
In comparison to single operators, we see that composed operators have one additional negation, and hence, it should not be surprising that their duality behavior is not governed by Z2×Z2, but rather by Z2×Z2×Z2. Next to INEG and ENEG, there is also the intermediate negation function MNEG, and the isomorphism given in (???) is generalized to the one defined by (???):
ID(0,0,0),ENEG(1,0,0),MNEG(0,1,0),INEG(0,0,1).
In analogy to (???), it is now again possible to succinctly describe the effects of these operations:
(i,j,k)(O2O1)(a1,,an)=¬ iCO2¬jBO1(¬ kAa1,,¬kAan).
We also see that composed operators give rise to a much richer duality behavior than single operators. Recall that in the case of single operators, duality can be seen as the combination of the external and internal negations (DUAL = ENEGINEG). In the case of composed operators, however, we have three negations, and thus three pairwise combinations: ENEGINEG, ENEGMNEG, and MNEGINEG. Although the first of these seems to be closest to what is classically called ‘duality’, the other two can plausibly be seen as (non-standard) duality operations too. Finally, there is also the operation ENEGMNEGINEG, which operates on all negations simultaneously.

Visualizing these duality patterns cannot be done by means of a square, but rather requires a duality cube. For example, Figure 6 shows a duality cube for the composed operator ◻ ; analogously, Westerståhl (2012) draws a duality cube for possessives with multiple quantifiers. Demey (2012a) makes use of the group-theoretical perspective to study the internal structure of this cube. It is a well known group-theoretical fact that the group Z2×Z2×Z2 has exactly 7 subgroups that are isomorphic to V4. These can naturally be partitioned into three families, based on their number of ‘basic’ operations (i.e. operations governing a single negation: ENEG, MNEG and INEG): (a) the first family consists of three groups that contain two basic operations, (b) the second family consists of three groups that contain one basic operation, and (c) the third family consists of a single group that does not contain any basic operations. Examples of groups from each of these families are given in (???a–c), respectively.
(a){ID,ENEG,INEG,ENEGINEG}(b){ID,ENEG,MNEGINEG,ENEGMNEGINEG}(c){ID,ENEGINEG,MNEGINEG,ENEGMNEG}
Each of these groups defines two complementary ‘duality squares’, and we thus find a total number of 7×2=14 ‘duality squares’ inside the duality cube. (We are using the term ‘duality square’ inside scare quotes here, because some of these squares visualize non-standard duality operations that involve MNEG; see above.) Note that, in contrast to the groups of families (a) and (b), the non-ID elements of the group in family (c) pairwise share a basic operation. Demey (2012a) argues that this difference in group-theoretical structure correlates with a difference in geometric embedding of the squares inside the cube.

Generalized Post duality. The group-theoretical account described above conforms to the basic requirement that internal negation be applied to all arguments of a given operator; see the k-superscripts in (???) and (???). Although the most canonical examples of duality indeed obey this requirement (recall the example of conjunction/disjunction from Section 1), there are also operators whose duality behavior seems to violate this requirement. For example, it was shown in Section 2 that in the relational perspective on generalized quantifiers, internal negation is applied only to the second argument—so that the internal negation of Q(A,B) is Q(A,¬B), rather than Q(¬A,¬B). Similarly, in syllogistics one can independently study the effects of predicate negation—as in Q(A,¬B)—and of subject negation—as in Q(¬A,B) (Keynes 1884; Johnson 1921; Reichenbach 1952; Hacker 1975). Finally, in public announcement logic, the dual of [ !φ ] ψ is defined as [ !¬φ ] ¬ψ, so the internal negation of the binary [ !  ]  operator is applied only to its second argument (ψ) (Demey 2012b).

Figure 6: Duality cube for the composed operator ◻

If we drop the requirement that internal negation be applied to all arguments, the behavior that arises is called generalized Post duality (Humberstone 2011, p. 410ff.; Urquhart 2008). Consider an n-ary operator O:AnB. This operator has 1 external and n independent internal negations. Since each of these n+1 negations may or may not be applied, O gives rise to 2n+1 operators. As an example, consider the binary operator of conjunction:
¬O(¬,¬)¬(¬p¬q) ¬O(¬,¬)¬(¬p¬q)¬O(¬,¬)¬(¬p¬q) ¬O(¬,¬)¬(¬p¬q)¬O(¬,¬)¬(¬p¬q) ¬O(¬,¬)¬(¬p¬q)¬O(¬,¬)¬(¬p¬q) ¬O(¬,¬)¬(¬p¬q)
In comparison to the ordinary duality behavior of a binary operator, we thus have n+1 rather than 2 independent negations, and generalized Post duality behavior is governed by the group Zn+12 rather than Z22 (Libert 2012). Next to ENEG, the operation of INEG is split into INEG1,...,INEGn, with INEGi operating on the operator’s ith argument, for 1  i  n. Furthermore, the isomorphism given in (???) can be generalized to the one defined by (???):

ID(0,0,0,...,0,0)ENEG(1,0,0,...,0,0)INEG1(0,0,0,...,0,0)INEGn(0,0,0,...,0,1).

In analogy to (???), the effects of these operations can be described succinctly by means of (???). Note that (???) can be seen as a special case of (???), by requiring that k1=k2==kn.

(i,k1,,kn)(O)(a1,,an)=¬ iBO(¬ k1Aa1,,¬knAan).

As was the case with the duality behavior of a composed operator, we see that the generalized duality behavior of an n-ary operator is much richer than its ‘ordinary’ duality behavior. Consider again the binary operator of conjunction. If both arguments can be negated independently, there are several combinations of external and internal negation (ENEGINEG1, ENEGINEG2 and ENEGINEG1INEG2), all of which can plausibly be called duality operations. (The last one of these involves negating all arguments, and thus coincides with ‘ordinary’ duality.) As a consequence, visualizing the generalized duality behavior of conjunction requires a duality cube, as in Figure 7. Note that the diagonal plane that spans the front left and back right vertical edges of this cube corresponds to the ‘ordinary’ duality square for conjunction (see Figures 2(c) and 3(a)).

Finally, it should be noted that the duality cubes in Figures 6 and 7 are highly similar, which is due, of course, to the fact that they are two distinct manifestations of the group Z32 (and can thus serve as two distinct concrete interpretations of the abstract cube in Moretti (2012, p. 88)). This illustrates the strong connection between the ‘ordinary’ duality behavior of composed operators on the one hand and the generalized duality behavior of single (binary) operators on the other. Both cases involve creating an additional negation: the former achieves this by ‘splitting’ the operator, while the latter achieves it by ‘splitting’ the argument positions.

Figure 7: ‘Generalized Post duality’ cube for the binary operator .

5. Duality Relations and Aristotelian Relations

The Aristotelian relations. Next to the duality relations, there is another widely known set of logical relations, namely the Aristotelian relations, which were originally defined in the logical works of Aristotle (Ackrill 1961). These are defined relative to some background logical system S, which is assumed to have connectives expressing Boolean negation (¬), conjunction () and implication (), and a model-theoretic semantics (). Formally, the Aristotelian relations are defined as follows: the formulas φ and ψ are said to be
S-contradictoryiffS¬(φψ)andS¬(¬φ¬ψ),S-contraryiffS¬(φψ)andS¬(¬φ¬ψ),S-subcontraryiffS¬(φψ)andS¬(¬φ¬ψ,S-subalternationiffSφψandSψφ,
When the system S is clear from the context, it is often left implicit (Smessaert and Demey 2014). Informally, two formulas are contradictory iff they cannot be true together and cannot be false together; they are contrary iff they cannot be true together but may be false together; they are subcontrary iff they cannot be false together but may be true together; they are in subalternation iff the first one entails the second one but not vice versa. Finally, it should be noted that this definition of the Aristotelian relations can be generalized to arbitrary Boolean algebras, just like the definition of the duality relations provided in Section 3 (Demey and Smessaert 2016). However, since this generalization is less relevant for our current concerns, it will not be discussed here.

The Aristotelian relations holding between a given set of formulas are often visualized by means of Aristotelian diagrams (based on graphical conventions such as the one shown in Figure 8(d)). The most widely known of these diagrams is the so-called ‘square of oppositions’, which comprises 4 formulas and the 6 Aristotelian relations holding between them. For example, Figure 8 shows Aristotelian squares involving (a) the propositional connectives of conjunction and disjunction, (b) the universal and existential quantifiers, and (c) the modal operators of necessity and possibility.

Figure 8: ‘Aristotelian squares: (a) conjunction-disjunction, (b) universal existential, (c) necessity possibility; (d) graphical representations of the Aristotelian relations.

Similarities. The Aristotelian squares in Figure 8(a–c) closely resemble the duality squares in Figure 3(a–c), respectively. In particular: (i) on the diagonals, the duality relation ENEG corresponds to the Aristotelian relation of contradiction, (ii) on the vertical edges, the duality relation DUAL corresponds to the Aristotelian relation of subalternation, and (iii) on the horizontal edges, the duality relation INEG corresponds to the Aristotelian relations of contrariety and subcontariety. These strong similarities might explain why authors such as D’Alfonso (2012), Meles (2012) and Schumann (2013) have come close to straightforwardly identifying the two types of squares—for example, by using Aristotelian terminology to describe the duality square (or vice versa), or by viewing one as a generalization of the other.

Furthermore, both Aristotelian and duality diagrams have been used by linguists to explain certain lexicalization patterns in natural languages. For example, Horn (1989) and Jaspers (2005) make use of the Aristotelian relations to explain the so-called non-lexicalization of the O-corner, i.e. the observation that natural languages have primitive lexical items for the quantifiers all, some and none, but not for not all (the latter’s lexicalization as a single word—for example: *nall— does not occur in natural language). The same asymmetry can be found in the lexicalization pattern of the propositional connectives: natural languages have primitive lexical items for and, or and nor, but not for not and (the latter’s lexicalization as a single word—for example: *nand—does not occur in natural language). These linguistic phenomena are also explained by Löbner (1990, 2011), but his phase quantification account is based on the duality relations, rather than the Aristotelian relations. Finally, it should be noted that the Aristotelian account of these lexical asymmetries has recently been generalized beyond the square by Seuren and Jaspers (2014).

Dissimilarities. As noted by Löbner (2011), Chow (2012) and Westerståhl (2012), there are also several differences between the duality square and the Aristotelian square. For example, although duality seems to correspond to subalternation, the former relation is symmetric, while the latter is asymmetric. Furthermore, although both sets of relations contain four members, there is no clean one-to-one mapping in either direction: on the one hand, the Aristotelian relations of contrariety and subcontrariety correspond to a single duality relation (INEG), and on the other hand, the duality relation ID does not correspond to any Aristotelian relation whatsoever. (However, Smessaert and Demey (2014) introduce a quasi-Aristotelian relation that holds precisely between a formula and itself, and thus does correspond to the duality relation ID.)

Another difference concerns sensitivity to the specific axioms of the background logic (Demey 2015). Consider, for example, the modal operators ◻, : BSBS, where BS is the Lindenbaum-Tarski algebra of some normal modal logic S. The Aristotelian relation holding between these operators depends on the logical system S: in normal modal systems that are at least as strong as KD, there is a subalternation from ◻p to p, but in weaker normal modal systems, there is no Aristotelian relation at all between these two formulas (Hughes and Cresswell 1996). Nevertheless, in all of these modal systems, it is the case that ◻φ is logically equivalent to ¬¬φ for all formulas φLS, and hence [φ]=¬¬[φ] for all [φ]BS. This means exactly that DUAL (◻, ), and hence the duality relation holding between ◻ and holds independently of the specific axioms of the logical system S.

At this point, it might be objected that the duality relations are logic-sensitive after all; for example, conjunction and disjunction are dual to one another in classical propositional logic (CPL), but not in intuitionistic propositional logic (IPL). However, the Lindenbaum-Tarski algebra of IPL is itself not a Boolean algebra (but rather a Heyting algebra), and thus falls outside the scope of the definition of the duality relations that was provided in Section 3.

Another difference between the duality and the Aristotelian relations is that the former, but not the latter, are functional. As was already discussed in Section 3, every formula has exactly one internal negation, exactly one external negation, and exactly one dual (up to logical equivalence). By contrast, the Aristotelian relations are not functional: for example, a given formula might be contrary to several (non-equivalent) formulas. As illustrated by Smessaert (2012), this difference becomes much more apparent if we move from squares to larger diagrams. For example, Figures 9(a–b) show an Aristotelian and a duality diagram for the same set of six modal formulas. Consider the formula p. Within the Aristotelian hexagon, this formula has two (non-equivalent) contraries, namely ◻¬p and p¬p. From a duality perspective, the first of these two formulas is the internal negation of ◻p, but the second one stands in no duality relation at all to ◻p. The duality ‘hexagon’ in Figure 9(b) thus ultimately turns out to consist of two independent components: the ordinary duality square in Figure 9(c) and the degenerate duality pattern (containing two formulas that are their own internal negations) in Figure 9(d).

Figure 9: (a) Aristotelian hexagon (for a modal system that is at least as strong as KD, (b) duality ‘hexagon’, and (c–d) its two components.

Finally, it should also be noted that it is perfectly possible for two operators/formulas to stand in a duality relation without standing in any Aristotelian relation, or vice versa. Moving to the level of diagrams, this means that it is possible for four operators/formulas to constitute a duality square without constituting an Aristotelian square, or vice versa (Löbner 1986). For example, the aspectual adverbs already, still, not yet and no longer constitute a duality square—see Figure 4(b)—, but not an Aristotelian square: for example, already and still are each other’s duals, but there is no subalternation between them in either direction. Analogously, the modal formulas ◻p, ◻◻¬p, ¬p and p¬p constitute an Aristotelian square (embedded inside the Aristotelian hexagon in Figure 9(a) with a counterclockwise rotation of 120◦), but not a duality square: for example, ◻p and p¬p are contraries, but there is no duality relation between them. In fact, looking at these four modal formulas in the duality ‘hexagon’ in Figure 9(b), we see that ◻p◻¬p and p¬p by themselves constitute a degenerate duality pattern (Figure 9(d)), while ◻p and ¬p belong to another, ‘real’ duality square (Figure 9(c)).

6. References and Further Reading

  • Ackrill, J. (1961). Aristotle’s Categories and De Interpretatione. Clarendon Press, Oxford.
  • Barwise, J. and Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4:159–219.
  • Blackburn, P., de Rijke, M., and Venema, Y. (2001). Modal Logic. Cambridge University Press, Cambridge.
  • Brisson, C. (2003). Plurals, All, and the nonuniformity of collective predication predication. Linguistics and Philosophy, 26:129–184.
  • Buridan, J. (2001). Summulae de Dialectica. Translated by Gyula Klima. Yale University Press, New Haven, CT.
  • Chow, K. (2012). General patterns of opposition squares and 2n-gons. In Beziau, J.-Y. and Jacquette, D., editors, Around and Beyond the Square of Opposition, pages 263–275. Springer, Basel.
  • D’Alfonso, D. (2012). The square of opposition and generalized quantifiers. In Beziau, J.-Y. and Payette, G., editors, Around and Beyond the Square of Opposition, pages 219–227. Springer, Basel.
  • Davey, B. A. and Priestley, H. A. (2002). Introduction to Lattices and Order (Second Edition). Cambridge University Press, Cambridge.
  • Demey, L. (2012a). Algebraic aspects of duality diagrams. In Philip T. Cox, B. P. and Rodgers, P., editors, Diagrammatic Representation and Inference, Lecture Notes in Computer Science (LNCS) 7352, pages 300–302. Springer, Berlin.
  • Demey, L. (2012b). Structures of oppositions for public announcement logic. In Beziau, J.-Y. and Jacquette, D., editors, Around and Beyond the Square of Opposition, pages 313–339. Springer, Basel.
  • Demey, L. (2015). Interactively illustrating the context-sensitivity of Aristotelian diagrams. In Christiansen, H., Stojanovic, I., and Papadopoulos, G., editors, Modeling and Using Context, LNCS 9405, pages 331–345. Springer.
  • Demey, L. and Smessaert, H. (2016). Metalogical decorations of logical diagrams. Logica Universalis, 10:233–292.
  • Dowty, D. (1987). Collective predicates, distributive predicates, and All. In Marshall, F., editor, Proceedings of the 3rd Eastern States Conference on Linguistics (ESCOL), pages 97–115. Ohio State University, Columbus, OH.
  • Freudenthal, H. (1960). Lincos. Design of a Language for Cosmic Intercourse. North-Holland, Amsterdam.
  • Gamut, L. (1991). Logic, Language, and Meaning.
    Givant, S. and Halmos, P. (2009). Introduction to Boolean Algebras. Springer, New York, NY.
  • Gottschalk, W. H. (1953). The theory of quaternality. Journal of Symbolic Logic, 18:193–196.
  • Gowers, T., editor (2008). The Princeton Companion to Mathematics. Princeton University Press, Princeton, NJ.
    Hacker, E. A. (1975). The octagon of opposition. Notre Dame Journal of Formal Logic, 16:352–353.
  • Henkin, L., Monk, J. D., and Tarski, A. (1971). Cylindric Algebras, Part I. NorthHolland, Amsterdam.
  • Horn, L. (2006). The border wars: A neo-Gricean perspective. In von Heusinger, K. and Turner, K., editors, Where Semantics Meets Pragmatics, pages 21–48. Elsevier, Amsterdam.
  • Horn, L. R. (1989). A Natural History of Negation. University of Chicago Press, Chicago, IL.
  • Horn, L. R. (2004). Implicature. In Horn, L. R. and Ward, G., editors, Handbook of Pragmatics, pages 3–28. Blackwell, Oxford.
  • Hughes, G. E. and Cresswell, M. J. (1996). A New Introduction to Modal Logic. Routledge, London.
  • Humberstone, L. (2011). The Connectives. MIT Press, Cambridge, MA.
  • Iten, C. (1998). Because and although: a case of duality? In Rouchota, V. and Jucker, A. H., editors, Current Issues in Relevance Theory, pages 59–80. John Benjamins, Amsterdam.
  • Iten, C. (2005). Linguistic Meaning, Truth Conditions and Relevance: The Case of Concessives. Palgrave Macmillan, Basingstoke/New York (NY).
  • Jaspers, D. (2005). Operators in the Lexicon. On the Negative Logic of Natural Language. LOT Publications, Utrecht.
  • Johnson, W. (1921). Logic. Part I. Cambridge University Press, Cambridge.
  • Kabakov, F. A., Parkhomenko, A. S., Voitsekhovskii,
    M. I., and Fofanova, T. S. (2014). Duality principle. In Encyclopedia of Mathematics. Springer, available at
    http://www.encyclopediaofmath.org/index.php?title=Duality principle&oldid=35095.
  • Keynes, J. N. (1884). Studies and Exercises in Formal Logic. MacMillan, London.
  • Konig, E. (1991). Concessive relations as the dual of causal relations. In Zaefferer, D., editor, Semantic Universals and Universal Semantics, volume 12 of Groningen-Amsterdam Studies in Semantics, pages 190–209. Foris, Berlin.
  • Kripke, S. (1977). Speaker’s reference and semantic reference. In French, P., Uehling, Jr., T., and Wettstein, H., editors, Contemporary perspectives in the philosophy of language, pages 6–27. University of Minnesota Press, Minneapolis, MN.
  • Libert, T. (2012). Hypercubes of duality. In Beziau, J.-Y. and Jacquette, D., editors, Around and Beyond the Square of Opposition, pages 293–301. Springer, Basel.
  • Löbner, S. (1986). Quantification as a major module. In Groenendijk, J., de Jongh, D., and Stokhof, M., editors, Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers, pages 53–85. Foris, Dordrecht.
  • Löbner, S. (1987). Natural language and generalized quantifier theory. In Gardenfors, P., editor, Generalized Quantifiers, pages 181–201. Reidel, Dordrecht.
  • Löbner, S. (1989). German. schon – erst – noch: an integrated analysis. Linguistics and Philosophy, 12:167–212.
  • Löbner, S. (1990). Wahr neben Falsch. Duale Operatoren als die Quantoren naturlicher Sprache. Max Niemeyer Verlag, Tubingen.
  • Löbner, S. (1999). Why German schon and noch are still duals: a reply to van der Auwera. Linguistics and Philosophy, 22:45–107.
  • Löbner, S. (2011). Dual oppositions in lexical meaning. In Maienborn, C., von Heusinger, K., and Portner, P., editors, Semantics: An International Handbook of Natural Language Meaning, volume I, pages 479–506. de Gruyter Mouton, Berlin.
  • Mac Lane, S. (1998). Categories for the Working Mathematician. Springer, Berlin.
  • Meles, B. (2012). No group of opposition for constructive logics: The intuitionistic and linear cases. In Beziau, J.-Y. and Payette, G., editors, Around and Beyond the Square of Opposition, pages 201–217. Springer, Basel.
  • Michaelis, L. (1996). On the use and meaning of already. Linguistics and Philosophy, 19:477–502.
  • Mittwoch, A. (1993). The relationship between schon/already and noch/still: A reply to Löbner. Natural Language Semantics, 2:71–82.
  • Moretti, A. (2012). Why the logical hexagon? Logica Universalis, 6:69–107.
  • Peters, S. and Westerståhl, D. (2006). ˚ Quantifiers in Language and Logic. Oxford University Press, Oxford.
  • Peterson, P. (1979). On the logic of “few”, “many”, and “most”. Notre Dame Journal of Formal Logic, 20:155–179.
  • Piaget, J. (1949). Traite de logique. Essai de logistique operatoire. Colin/Dunod, Paris.
  • Read, S. (2012). John Buridan’s theory of consequence and his octagons of opposition. In Beziau, J.-Y. and Jacquette, D., editors, ´ Around and Beyond the Square of Opposition, pages 93–110. Springer, Basel.
  • Reichenbach, H. (1952). The syllogism revised. Philosophy of Science, 19:1–16.
  • Schumann, A. (2013). On two squares of opposition: the Lesniewski’s style formalization of synthetic propositions. Acta Analytica, 28:71–93.
  • Seuren, P. and Jaspers, D. (2014). Logico-cognitive structure in the lexicon. Language, 90:607–643.
  • Smessaert, H. (2012). The classical Aristotelian hexagon versus the modern duality hexagon. Logica Universalis, 6:171–199.
  • Smessaert, H. and Demey, L. (2014). Logical geometries and information in the square of oppositions. Journal of Logic, Language and Information, 23:527–565.
  • Smessaert, H. and ter Meulen, A. (2004). Temporal reasoning with aspectual adverbs. Linguistics and Philosophy, 27:209–261.
  • Urquhart, A. (2008). Emil Post. In Gabbay, D. M. and Woods, J., editors, Handbook of the History of Logic. Volume 5. Logic from Russell to Church. Elsevier, Amsterdam.
  • van Benthem, J. (1991). Linguistic universals in logical semantics. In Zaefferer, D., editor, Semantic Universals and Universal Semantics, volume 12 of Groningen-Amsterdam Studies in Semantics, pages 17–36. Foris, Berlin.
  • van der Auwera, J. (1993). ‘Already’ and ‘still’: beyond duality. Linguistics and Philosophy, 16:613–653.
  • Westerståhl, D. (2012). Classical vs. modern squares of opposition, and beyond. In Beziau, J.-Y. and Payette, G., editors, The Square of Opposition. A General Framework for Cognition, pages 195–229. Peter Lang, Bern.

Author Information

Lorenz Demey
Email: lorenz.demey@kuleuven.be
Catholic University of Leuven
Belgium

and

Hans Smessaert
Email: hans.smessaert@kuleuven.be
Catholic University of Leuven
Belgium

The Meaning of Life: Contemporary Analytic Perspectives

Depending on whom one asks, the question, “What is the meaning of life?” is either the most profound question of human existence or else nothing more than a nonsensical request built on conceptual confusion, much like, “What does the color red taste like?” or “What is heavier than the heaviest object?” Ask a non-philosopher, “What do philosophers discuss?” and a likely answer will be, “The meaning of life.” Ask the same question of a philosopher within the analytic tradition, and you will rarely get this answer. The sources of suspicion about the question within analytic philosophy, especially in earlier periods, are varied. First, the question of life’s meaning is conceptually challenging because of terms like “the” “meaning” and “life,” and especially given the grammatical form in which they are arranged. Second, it is often asked with transcendent, spiritual, or religious assumptions at the fore about what the world “should” be like in order for there to be a meaning of life. In so far as the question is entangled with such ideas, the worry is that even if the concept of a meaning of life is coherent, there likely is not one.

Despite such suspicions and relative disinterest in the question of life’s meaning among analytic philosophers for a large part of the twentieth century, there is a growing body of work on the topic over roughly the last two decades. Much of this work focuses on developing and defending theories of meaning in life (see Section 2.d. for more on the distinction between meaning in life and the meaning of life) via conceptual analyses of the necessary and sufficient conditions for meaningful life. A smaller, though no less important, subset of work in this growing field focuses on why we even use “meaning” in the first place to voice our questions and concerns about central facets of the human condition.

This article surveys important trajectories in discussions of life’s meaning within contemporary analytic philosophy. It begins by introducing key aspects of the human context in which the question is asked. The article then investigates three ideas that illumine what meaning means in this context: sense-making, purpose, and significance. The article continues by surveying important topics that provide a greater understanding of what is involved in our requests for meaning. After briefly surveying theories of meaning in life, it concludes with discussions of death and futility, followed by important areas of research that remain under-investigated.

Table of Contents

  1. The Human Context
  2. The Contemporary Analytic Context: Prolegomena
    1. The Meanings of “Meaning”
      1. Sense-Making
      2. Purpose
      3. Significance
    2. The Word “Life”
    3. The Definite Article
    4. Meaning of Life vs. Meaning in Life
    5. What is the Meaning of x?
    6. Interpretive Strategies
      1. The Amalgam Approach
      2. The Single Question Approach
  3. Theories of Meaning in Life
    1. Supernaturalism
    2. Subjective Naturalism
    3. Objective Naturalism
    4. Hybrid Naturalism
    5. Pessimistic Naturalism: Nihilism
    6. Structural Contours of Meaning in Life
  4. Death, Futility, and a Meaningful Life
  5. Underinvestigated Areas
  6. References and Further Reading

1. The Human Context

The human desire for meaning finds vivid expression in the stories we tell, diaries we keep, and in our deepest hopes and fears. According to twentieth century Freudian psychoanalyst Bruno Bettelheim, “our greatest need and most difficult achievement is to find meaning in our lives” (Bettelheim 1978: 3). Holocaust survivor and psychiatrist Viktor Frankl said that the human will to meaning comes prior to either our will to pleasure or will to power (Frankl 2006: 99).

Questions about meaning arise and take shape within varied contexts: when struggling to make an important decision about what to do with our lives, when trapped in a job we hate, when wondering if there is more to life than the daily hum-drum, when diagnosed with a terminal illness, when experiencing the loss of a loved one, when feeling small while looking up at the night sky, when wondering if this universe is all there is and why it is even here in the first place, when questioning whether life and love will have a lasting place in the universe or whether the whole show will end in utter and everlasting desolation and silence.

Lurking behind many of our questions about meaning is our capacity to get outside of ourselves, to view our lives from a wider standpoint, a standpoint from which to understand the setting for our lives and question the “why?” of what we do. Humans possess self-awareness, and can take an observational, self-reflective viewpoint on our lives. In this, we are able to shift from mere automatic engagement to observation and evaluation. We do more than simply respond to streams of stimuli. We step back and question who we are and what we do. Shifting our focus to the widest standpoint—sub specie aeternitatis (literally, from the perspective of eternity; a universal perspective)—we wonder how such infinitesimally small and fleeting creatures like ourselves fit in the grand scheme of things, within vast space and time. We worry about whether a reality of such staggering magnitude, at the deepest level, cares about us (for related discussions, see Fischer 1993; Kahane 2013; Landau 2011; Nagel 1971, 1989; and Seachris 2013).

That our concerns about meaning are often cosmically-focused is instructive. Despite the current theoretical emphasis in analytic philosophy on the more terrestrially-focused idea of meaning in life, questions about meaning are very often cosmic in scope. In the words of sociologist Peter Berger, in seeking life’s meaning, many are attempting to locate it “within a sacred and cosmic frame of reference” of trying to plumb the connection “between microcosm and macrocosm” (Berger 1967: 27). This is an important reason why God, transcendence, and other ideas embodied and expressed in religion are so often thought to be relevant to life’s meaning.

2. The Contemporary Analytic Context: Prolegomena

Relatively speaking, not too long ago many analytic philosophers were suspicious that the question of life’s meaning was incoherent. Such views found expression in popular culture too, for example, in Douglas Adams’ widely read book The Hitchhiker’s Guide to the Galaxy. The story’s central characters visit the legendary planet Magrathea and learn about a race of hyper-intelligent beings who built a computer named Deep Thought. Deep Thought’s purpose was to answer the ultimate question of life, the universe, and everything, that answer being a bewildering 42. Deep Thought explained that this answer was incomprehensible because the beings who designed it, though super-intelligent, did not really know what they were asking in the first place. Asking for life’s meaning might be like this, in which case 42 is as good of an answer as any other.

Some analytic philosophers in the twentieth century, in the wake of logical positivism, shared Deep Thought’s suspicion. They were particularly weary of the traditional formulation—What is the meaning of life? Meaning, it was thought, belongs in the linguistic realm. Words, sentences, and other linguistic constructions are the proper bearers of meaning, not objects, events, or states of affairs, and certainly not life itself. Some philosophers thought that in asking for life’s meaning, we use an ill-chosen expression to voice something real, perhaps an emotional response of awe or wonder at the staggering fact that anything exists at all. Yet, experiencing such feelings and asking a meaningful question are two different things altogether.

Asking what something means, though, need not be a strictly semantic activity. We ask for the meanings of all kinds of things and employ “meaning” in a wide variety of contexts in everyday life, only some of which are narrowly linguistic. Paying careful attention to the meanings of “meaning” provides important clues about what life’s meaning is all about. Three connotations in particular are instructive here: sense-making, purpose, and significance.

a. The Meanings of “Meaning”

Meaning-talk is common in everyday discourse. Most ordinary uses of “meaning” tend to cluster around three basic ideas: (1) sense-making (which can include the ideas of intelligibility, clarification, or coherence), (2) purpose, and (3) significance (which can include the idea of value). The following list of statements and questions captures the richly varied ways in which we employ the concept of meaning on a regular basis.

Meaning as Sense-Making

  1. What you said didn’t mean a thing.
  2. What did you mean by that statement?
  3. Do you know what I mean?
  4. What did you mean by that face? (overlaps with purpose)
  5. What is the meaning of that book? (what is it about?)
  6. What is the meaning of this? (for example, when asked upon returning home to find one’s house ransacked)

Meaning as Purpose

  1. What did you mean by that face? (overlaps with intelligibility)
  2. The tantrum is meant to catch his dad’s attention.
  3. What is the meaning of that book? (why was it written?)
  4. I really mean it!
  5. I didn’t mean to do it. I promise!

Meaning as Significance

  1. That was such a meaningful
  2. This watch really means something to me.
  3. That is a highly meaningful event in the life of that city.
  4. What do his first six months in office mean for the country (likely overlaps with intelligibility)
  5. That is a meaningful
  6. That is a meaningless
  7. You mean nothing to me.

i. Sense-Making

This category is an important ordinary sense of meaning and connotes ideas like intelligibility, clarification, and coherence. Something has meaning if it makes sense; it lacks meaning if it does not. One way of understanding sense-making is through the idea of proper fit. Words, concepts, propositions, but also events and states of affairs, make sense and are meaningful if and when they fit together properly; if they lack such fit, they make no sense and are meaningless. This applies narrowly. For example, it makes no sense to ask, “What is brighter than the brightest light source?” It does not fit with the concept brightest to ask what is brighter, but it has a broader application too. We say things like:

  1. It does not make sense for the president to send in troops given the geopolitical situation in the region.
  2. Asking philosophy students to perform long-division on their midterm makes no sense.

In each of these situations, we perceive a lack of fit—a lack of fit between a decision and circumstances surrounding that decision or between reasonable expectations about what one will find on a philosophy exam and what one actually finds. There is a kind of absurdity here. Perceiving this weaker lack of fit will be a product of beliefs, norms, and other epistemic, evaluative, and social commitments. Therefore, determining whether or not something, in fact, involves a lack of fit in this broader sense often will be a messier task than in cases of narrow sense-making.

Ascertaining meaning, then, is often about fitting something into a larger context or whole: words into sentences, paragraphs, novels, or monographs; musical notes into measures, movements, and symphonies (i.e., the movement from mere sound to music), parts of a photograph within the entire photograph. Meaning is about intelligibility within a wider frame, about “inserting small parts into a larger, integrated context” (Svendsen 2005: 29). Similarly, we can plausibly view our requests for the meaning of life as attempts to secure the overarching context through which to make sense of our lives in the universe (see Thomson 2003: 132-138). Our focus here is on existentially weighty matters that define and depict the human condition: questions and concerns surrounding origins, purpose, significance, value, suffering, and death and destiny. We want answers to our questions about these matters, and want these answers to fit together in an existentially satisfying way. We want life to make sense, and when it does not, we are haunted by the specter of meaninglessness.

ii. Purpose

Requests for meaning are very often requests for purpose. We want to know whether we have a purpose(s) and if so, what it is. Many assume that there is a cosmic purpose around which to order our lives. A cosmic purpose likely would require transcendence or God. Someone must intend it all in order for there to be a purpose of it all. One might reject the idea of cosmic purpose, though, and still frame the question about life’s meaning as one largely about purpose. In this case, meaningful life (or meaning in life) is about ordering one’s life around self-determined purposes.

We also distinguish actions done on purpose from those done by accident. We use meaning (or meant) to contrast willful from non-willful action. We say things like, “I really mean it” to indicate the ‘full’ operation of our will. Alternatively, our child might say, “I didn’t mean it, I promise!” to indicate that she did not intend to spill her glass of milk. This sense of “meant” is also relevant for life’s meaning. We want sufficient autonomy, and when it is absent or severely mitigated, we worry about the meaningfulness of our lives (see Mawson 2016; Sartre 1973). Most of us do not want to walk through life haphazardly, nor in a way that is largely determined apart from our own consent. Likely one aspect of meaningful life, then, is life lived with our wills sufficiently engaged, one lived on purpose. These two shades of purpose are probably related. We want to really mean it as we select and align our lives with aims that will provide the salient structural rhythms to our day-to-day existence. In other words, we do not want to be alienated from the purposes that guide our lives.

Purpose and sense-making often are connected. Purpose itself, via future-targeted goals that shape pre-goal activity, provide important aspects of the structure that serves as the framework through which life fits together and makes sense. Lives that fit together and make sense—meaningful lives—are those that are sufficiently teleological. Working to attain goals at various levels of life-centrality is likely a facet of life properly fitting together and therefore being meaningful. Teleological threads connecting discreet life episodes are then necessary for a robust kind of sense-making in life. Lives lacking this are threatened with a sort of unintelligibility that results from being insufficiently structured by a telos. In the words of philosopher Alasdair MacIntyre:

When someone complains…that his or her life is meaningless, he or she is often and perhaps characteristically complaining that the narrative of their life has become unintelligible to them, that it lacks any point, any movement toward a climax or a telos (MacIntyre 2007: 217).

iii. Significance

Meaning often conveys the idea of significance, and significance tracks a related cluster of notions like mattering, importance, impact, salience, being the object of care and concern, and value, depending on context. We contrast trivial discussions about the mundane with deep discussions about important matters, referring to the latter as meaningful or significant. Physical objects deeply enmeshed in our life stories are meaningful. We view actions and events that have salient implications as significant, and in cases where that significance has positive value, as meaningful (whether a person can lead a meaningful life in virtue of making large negative impacts is a growing topic of discussion as the field seeks to understand the connection between meaning and morality; see Campbell and Nyholm 2015). Finding the cure for that disease was meaningful because it had such a large positive impact within a certain frame of cares and concerns. This shade of meaning is also in view in cases where some piece or set of data crosses a threshold of salience against background information. That such a large percentage of the population living under certain conditions is getting a particular disease is statistically significant or statistically meaningful. In this way, sense-making and significance senses of meaning connect.

Alternatively, when something does not matter to us, we might say, “That means nothing to me.” It was just a meaningless conversation; it was inconsequential. That game did not matter because the playoffs were already set. The wrapping paper does not matter, what is on the inside of the package counts. That piece of information is not meaningful relevant to the aims and questions guiding one’s inquiry. Spending your life sitting on the couch and watching sitcom re-runs on Netflix is meaningless; you do nothing that matters, you do nothing of importance or value, and so on.

Something’s significance is often and largely gauged in relation to a perspective, horizon, or point of reference, all of which can be dynamic. Something that is significant from one vantage point may, and often does, lose its significance when viewed from a broader horizon. Scraping your knee at age four is significant, at least from a four-year old’s perspective. When looking back decades later, its significance wanes. Most events important enough to make it into local lore will not matter enough to be included in a national history, let alone world and, especially, cosmic history. One quickly sees resources available from which to generate pessimistic meaning of life concerns vis-à-vis human significance as one broadens horizons, eventually terminating in the widest cosmic perspective.

Significance is often distinctly normative and person-al. When we say that something is meaningful in the sense of being significant, important, or mattering, we make a kind of evaluative claim about what is good or valuable. Additionally, significance is often connected with being the object of a person’s evaluations, cares, and concerns. Things are, most naturally, significant to someone.

Insofar as meaning is thought to have an affective dimension, that dimension likely intersects with significance. If my grandmother’s necklace is meaningful to me, it has value, it matters, and affective states fitting a certain psychological profile, like being deeply stirred or moved, often accompany such assessments of value and mattering. Though this may not make such affective states a further type of meaning or constitutive of meaning, these states reliably track instances of significance or perceived significance.

Like sense-making and purpose, significance is relevant to life’s meaning. In broad terms, one way of construing meaningful life is as a life that matters and has positive value. This, of course, admits of various understandings of mattering that, at one level, might track the objective naturalist, subjective naturalist, hybrid naturalist, and supernaturalist debate (see Section 3 below): matters to whom and according to what standard? Additionally, some find it difficult to separate personal and cosmic concerns over significance. Cosmic concerns, for many, are also intensely personal. If the universe as a whole lacks significance, some worry that their individual lives lack significance, or at least the kind that they think a deeply meaningful life requires.

b. The Word “Life”

Understanding what life’s meaning is all about is complicated, not just because of the expansive semantic range of “meaning,” but also because it is not immediately clear how we should understand the word “life” in the question. In asking for life’s meaning, we are not, at least most of us, asking for the meaning of the word “life.” Neither are we asking about how being alive is different from being non-living or how being organic is different from being inorganic. What then are we asking, and what is the scope of that request? Our question(s) about life’s meaning likely range over the following options:

Life1 = individual human life (meaning of my life)

Life2 = humanity as a whole (meaning of human existence)

Life3 = all biological life (meaning of all living organisms collectively)

Life4 = all of space-time existence (meaning of it all)

Life5 = rough marker for those aspects of human life that have a kind of existential gravitas and are of immense concern and the subject of intense questioning by human beings (see Section 2.e. below)

Each of these options for understanding “life” in the traditional formulation tracks possible interpretations of the question. The targets of our questions and concerns about meaning are varied in scope. We ask questions about our own, personal existence as well as questions about the entire show, and one might think that questions about personal meaning are connected to questions about cosmic meaning. Life5 provides a way of bringing important aspects of each together (see Section 2.e.)

c. The Definite Article

Another thorny issue for the traditional formulation is its incorporation of the definite article—the. It implies that there is only one meaning of life, which violates common inclinations that meaning is the sort of thing that varies from person to person. What makes one life meaningful is different from what makes another meaningful. One person might derive large doses of meaning from her career, another through gardening. For this reason, many are suspicious of the definite article.

There is good reason, though, to question this suspicion. First, it might reveal confusion about what meaning even is in the first place. Indeed, one of the aims of those working in the field is to clarify just what meaning is. Here, it is worth noting that many plausible theories of meaning have an objective component, indicating that not just anything goes for meaning. However, even if meaning were solely a matter of, say, being fulfilled, notice that the following two claims are still consistent: (1) the meaning of life is about being fulfilled and (2) sources of fulfillment are exceedingly diverse. Life’s meaning in this case is about being fulfilled (consistent across persons), but sources of fulfillment vary from person to person.

Second, one might also reasonably think that there is a single meaning of life at the cosmic level that itself is consistent with a rich variety of ways to lead a meaningful life (meaning in life at the terrestrial, personal level). Thinking through possibilities like this will connect with claims about what is true about the world, for example, whether there is a God with a plan for the cosmos and whether there is an overarching meaning to it all. In a case like this, there might be a single meaning of life, but the sense of meaning in which there is a single meaning could be different from the sense of meaning in which there are varied meanings. Regardless of the complexities here, the point is that one should not too quickly dismiss the definite article as contributing to intractable theoretical and practical problems for thinking about life’s meaning.

d. Meaning of Life vs. Meaning in Life

In what has become a standard distinction in the field, philosophers distinguish two ideas: the meaning of life (MofL) and meaning in life (MinL). Claims like the following are prevalent, “one can find meaning in her life, even if there is no grand, cosmic meaning of life.” MofL is more global or cosmic in scope, and often is intertwined with ideas like God, transcendence, religion, or a spiritual, sacred realm. In asking for life’s meaning, one is often asking for some sort of cosmic meaning, though she may also be asking for the meaning of her individual life from the perspective of the cosmos since many think the meaning of their individual lives is tied to whether or not there is a meaning of it all.

MinL is focused on personal meaning; the meaning of our individual lives as located in the web of human endeavors and relationships sub specie humanitatis—within the frame of human cares and concerns. Many think that we can legitimately talk about life having meaning in this sense regardless of what is true about the meaning of the universe as a whole.

One can see how the various sense of meaning discussed earlier in this entry intersect at both levels—MofL and MinL. For example, if sense-making is in view at the cosmic level, we might ask questions like the following: “What’s it all about?” or “How does it all fit together?” At the terrestrial, personal level, our sense-making questions might, rather, take the following shape: “What is my life about?” “How does my life fit together?” or “Is my life coherent?” If significance is in view at the cosmic level, we might ask, “Do our lives really matter in the grand scheme of things?” whereas terrestrially, personally, we might ask, “Does my life matter to me, my family, friends, or my community?”

e. What is the Meaning of x?

The locution, “What is the meaning of x?” need not be understood narrowly as the request for something semantic, say, for a definition or description. There are additional non-linguistic contexts in which this request makes perfect sense (see Nozick 1981). Some of them even share striking similarities to the question of life’s meaning. One in particular is especially relevant.

Sometimes we are confronted with circumstances that we do not yet sufficiently understand, in which case we might naturally respond by asking, “What’s this all about?” or “What’s going on here?” or “What happened?” or “What’s happening?” or “What does this mean?” or “What is the meaning of this?” In asking such questions, we are in search of sense-making and intelligibility. We walk in on our children fighting and demand: “What is the meaning of this?” Mary Magdalene and Mary the mother of James come to find a stone rolled away from a Roman guarded tomb. The burial linens are there, but Jesus’ body is nowhere to be found. One can imagine them thinking, “What is the meaning of this?”

We naturally invoke the formula “What is the meaning of x?” in situations where x is some fact, event, phenomena, or cluster of such things, and about which we want to know, in the words of New Testament scholar and theologian, N. T. Wright, its “implication in the wider world within which this notion makes the sense it makes” (Wright 2003: 719). Such requests track our desire to make sense of a situation, to render it intelligible with the further aim of acting appropriately in response—a kind of epistemic map to aid in practical, normative navigation.

Taking our cue from these ordinary examples, to inquire about life’s meaning is plausibly understood as asking something similar to our requests for the meaning of our children’s scuffle or of Jesus’ empty tomb. Over the course of our existence, we encounter aspects of the world that have a kind of existential gravitas in virtue of their role in defining and depicting the human condition. They capture our attention in a unique way. The word “life,” then, is a rough marker for these existentially-weighty aspects (Life5 in Section 2.b. above), aspects of life that give rise to profound questions for which we seek an explanatory framework (perhaps even a narrative framework) in order to make sense of them. These aspects of the world are akin to the portion of the scuffle and empty tomb above to which we already have limited informational access: yelling and throwing in the case of the scuffle, and the various pieces and clues observed at the empty tomb. Like the parent or Mary Magdalene in those situations, we lack important parts of life’s context, and we desire to fill in these existentially relevant gaps in our knowledge, and then live accordingly. We are in search of life’s meaning, where that meaning is, at center, a kind of overarching sense-making framework for answering and fitting together answers to our questions about origins, purpose, significance, value, suffering, and destiny.

f. Interpretive Strategies

i. The Amalgam Approach

The currently favored strategy for interpreting the traditional formulation of the question—What is the meaning of life?—is the amalgam approach. On this pluralist view, the question is not thought to be a single question at all, but rather an amalgam of numerous other questions, most of which share family resemblances. The question is, on this view, simply a place-holder (some think ill-conceived) for these other questions and is, itself, not capable of being answered in this form. Though it has no answer in this form, other questions about purpose, significance, value, worth, origins, and destiny might. We at least know what we ask when we ask them, so the thought goes. Suspicion of the traditional formulation often accompanies the amalgam view since that formulation makes use of the definite article (“the”), the word “meaning,” and the word “life,” which together in the grammatical form in which they are found contribute to a thorny interpretive challenge. Perhaps the best strategy according to many proponents of the amalgam interpretation, is simply to jettison the traditional formulation and focus on trying to answer some among this other cluster of questions that collectively embody what we are concerned about when we inquire into life’s meaning.

ii. The Single Question Approach

Though the amalgam interpretation is the most popular view among those writing on life’s meaning within analytic philosophy, a few others have favored an approach that views the traditional formulation as a single question capable of being answered in that form (see Seachris 2009, 2019; Thomson 2003). A promising strategy here is to prioritize the sense-making connotation of meaning. On this version of the interpretive approach, asking about the meaning of life is first about seeking a sense-making explanation (perhaps even narrative explanation) for our questions and concerns about origins, purpose, significance, value, suffering, and destiny. Contrary to the amalgam interpretation, on this view, the question of life’s meaning is asking for a single thing—a sense-making explanation. It is, of course, an explanation squarely focused on all this other meaning of life “stuff.”  This explanation can be thought of as a worldview or metanarrative. This approach is an organic interpretive strategy that seeks a single answer (e.g., narrative explanation) that unifies or integrates answers to all the sub-questions that define and depict the human condition. It provides the conceptual resources to account for both MofL and MinL. The cosmic and the personal, the epistemic and the normative, and the theoretical and the practical are inseparable in our search for meaning. The sense-making framework that we seek links all of this as we pursue meaningful lives in light of our place within the grand scheme of it all.

This version of the single-question approach, with its emphasis on sense-making, is closely related to the concept of worldview. Worldviews provide answers to the existentially weighty set of questions that brings into relief the human condition. As philosopher Milton Munitz notes:

. . . [people] may say that what they are looking for [when asking the question of life’s meaning] is an account of the “big picture” with whose aid they would be able to see not only their own individual personal lives, but the lives of everybody else, indeed of everything of a finite or limited sort, human or not. . . . The expression of such a concern involves, at bottom, the appeal to a “worldview” or “world picture.” This undertakes to give a description of the most inclusive setting within which human life is situated . . . (Munitz 1993: 30).

To offer a worldview, then, is to offer a putative meaning of life—a sense-making framework focused squarely on the set of questions and concerns surrounding origins, purpose, significance, value, suffering, and destiny.

Looking back further into the origin of the worldview concept strengthens the connection between worldview and life’s meaning, and offers important clues that a worldview provides a kind of sense-making meaning. Nineteenth century German historian and philosopher, Wilhelm Dilthey, spoke of a worldview as a concept that “. . . constitutes an overall perspective on life that sums up what we know about the world, how we evaluate it emotionally, and how we respond to it volitionally.” Worldviews possess three distinct yet interrelated dimensions: cognitive, affective, and practical. They address both MofL and MinL. A worldview is motivated out of a desire to answer what he calls the “riddle of existence:”

The riddle of existence faces all ages of mankind with the same mysterious countenance; we catch sight of its features, but we must guess at the soul behind it. This riddle is always bound up organically with that of the world itself and with the question what I am supposed to do in this world, why I am in it, and how my life in it will end. Where did I come from? Why do I exist? What will become of me? This is the most general question of all questions and the one that most concerns me (Dilthey 1980: 81-82).

Dilthey’s cluster of questions that motivate worldview construction are those same questions to which we want answers in seeking life’s meaning. In this way, life’s meaning might just be a sense-making framework. It is not a stretch to say that life’s meaning is that which worldview’s aim to provide.

3. Theories of Meaning in Life

Beyond important preliminary discussions over the nature of the question itself and its constituent parts, one will find competing theories of meaning in life. Here, the debate is over the question of what makes a person’s life meaningful, not over the question of whether there is a cosmic meaning of it all (though, again, some think the two cannot be so easily disentangled). The four most influential views of meaning in life are: (1) Supernaturalism, (2) Objective Naturalism, (3) Subjective Naturalism, and (4) Hybrid Naturalism. (5) Nihilism is not a theory of meaning, rather, it is the denial of meaning, whether cosmic or personal. Objective, subjective, and hybrid naturalism are all optimistic forms of naturalism. They allow for the possibility of a meaningful existence in a world devoid of finite and infinite spiritual realities. Pessimistic naturalism, or what is commonly called “nihilism,” is generally, though not always, thought to be an implication of an entirely naturalistic ontology, though vigorous debate exits about whether naturalism entails nihilism.

a. Supernaturalism

Roughly, supernaturalism maintains that God’s existence, along with “appropriately relating” to God, is necessary and sufficient for securing a meaningful life, although accounts diverge on the specifics. Among countless others, historic representatives of supernaturalism in the Near-Eastern ancient world and in subsequent history include Qoheleth (the one called “Teacher” in the Old Testament book of Ecclesiastes), Jesus, the Apostle Paul, Augustine, Aquinas, Jonathan Edwards, Blaise Pascal, Leo Tolstoy, C. S. Lewis, and many contemporary analytic philosophers.

Meaningful life, on supernaturalism, consists of claims along metaphysical, epistemological, and relational-axiological axes. Metaphysically, meaningful life requires God’s existence because, for example, conditions that ground properties necessary for meaning like objective value are thought to be most plausibly anchored in a being like God (See Cottingham 2005; Craig 2008). It also requires, at some level orthodoxy (right belief) and orthopraxy (right life and practice), though again, much debate exists on the details. In addition to God’s existence, meaning in life requires that a person be appropriately related to God, perhaps as expressed in one’s beliefs and especially in one’s devotion, worship, and the quality of her life lived with and among others as, for example, embodied in Jesus’ statement of the greatest commandments (cf. Matt. 22:34-40).

Pascal captures the spirit of supernaturalism in this passage from the Pensées:

What else does this craving, and this helplessness, proclaim but that there was once in man a true happiness, of which all that now remains is the empty print and trace? This he tries in vain to fill with everything around him, seeking in things that are not there the help he cannot find in those that are, though none can help, since this infinite abyss can be filled only with an infinite and immutable object; in other words by God himself (Pascal 1995: 45).

As does St. Augustine at the beginning of his Confessions:

. . . you have made us for yourself, and our heart is restless until it rests in you (St. Augustine 1963: 17).

It is worth noting that there are versions of supernaturalism that do not view God as necessary for meaningful life, but nonetheless claim that God and relating to God in appropriate ways would significantly enhance meaning in life. This more moderate form of supernaturalism allows for the possibility of meaningful life, in some measure, on naturalism (see Metz 2019 for a helpful taxonomy of the conceptual space here).

Supernaturalist views, whether stronger or more moderate, connect with questions and concerns about the problem of evil, post-mortem survival, and ultimate justice. It is often thought that a being like God is needed to “author and direct” the narrative of the universe, and, in some sense, the narratives of our individual lives to a good and blessed ending (involving both closure and teleological senses of ending, though not an absolute termination sense; see Seachris 2011). Many worry that, on naturalism, life does not make sense or is absurd (a kind of sense-making meaning; see Section 2.a.i. above) if there is no ultimate justice and redemption for the ills of this world, and if the last word is death and dissolution, followed by silence, forever.

b. Subjective Naturalism

Subjective naturalism is an optimistic naturalistic view in claiming that life can be robustly meaningful even if there is no God, after-life, or transcendent realm. In this, it is like objective and hybrid forms of naturalism. According to subjective naturalism, what constitutes a meaningful life varies from person to person, and is a function of one getting what one strongly wants or by achieving self-established goals or through accomplishing what one believes to be really important. Caring about or loving something deeply has been thought by some to confer meaning in life (see Frankfurt 1988). Some subjectivist views focus on affective states of a certain psychological profile, like fulfillment or satisfaction for example, as constituting the essence of meaningful life (see Taylor 1967). Subjectivism is appealing to some in light of perceived failures to ground objective value, either naturally, non-naturally, or supernaturally, and in accounting for the widespread view that meaning and fulfillment are closely connected.

A worry for subjective naturalism, analogous to ethical worries about moral relativism, is that this view is too permissive, allowing for bizarre or even immoral activities to ground meaning in life. Many protest that surely deep care and love, by themselves, are not sufficient to confer meaningfulness in life. What if someone claims to find meaning by measuring and re-measuring blades of grass or memorizing the entire catalogue of Netflix shows or, worse, torturing people for fun? Can a life centering on such pursuits be meaningful? A strong, widespread intuition here inclines many towards requiring a condition of objective value or worth on meaning. Subjectivism still has thoughtful defenders, though, with some proposals moving towards grounding value inter-subjectively—in community and its shared values—as opposed to in the individual exclusively. It is also worth noting that one could be a subjectivist about meaning while being an objectivist about morality. In this way, a fulfilled torturer might lead a meaningful, though immoral life. Meaning and morality, on this view, are distinct values that can, in principle, come into conflict.

c. Objective Naturalism

 Objective naturalism, like subjective naturalism, posits that a meaningful life is possible in a purely physical world devoid of finite and infinite spiritual realities. It differs, though, in what is required for meaning in life. Objective naturalists claim that a meaningful life is a function of appropriately connecting with mind-independent realities of objective worth (contra subjectivism), and that are entirely natural (contra supernaturalism). Theories differ on the nature of this connection. Some require mere orientation around objective value, while others require a stronger causal connection with good outcomes (see Smuts 2013). Again, objective naturalism is distinguished from subjective naturalism by its emphasis on mind-independent, objective value. One way of putting the point is to say that wanting or choosing is insufficient for a meaningful life. For example, choosing to spend one’s waking hours memorizing the inventory of one’s local Target store, even if this activity results in fulfillment, is likely insufficient for meaning on objective naturalism. Rather, meaning is a function of linking one’s life to objectively valuable, mind-independent conditions that are not themselves the sole products of what one wants and chooses. On objective naturalism it is possible to be wrong about what confers meaning on life—something is meaningful, at least partly, in virtue of its intrinsic nature, irrespective of what is believed about it. This is why spending salient portions of one’s life memorizing department store inventories is not meaningful on objective naturalism, even if the person strongly desires to do this.

One worry for objective naturalism is that it may have a harder time accounting for cases of neural atypicality, for example, a person with ASD who is deeply fulfilled by activities that seem to lack intrinsic value or worth. Does a person who is not a plumber and for whom pipes and interactions with pipes provide salient goals, a kind of coherence to his life, and enjoyable experiences fail to acquire meaning because it all largely revolves around a fascination with pipes? Might subjectivist views better account for the lives of those among us whose interests and interactions with the world are strikingly different, and for whom such interests are the result of neural atypicality?

Critics of objective naturalism might also press the point that proponents of this view conflate meaning and morality or at least conflate important aspects of these two putatively different kinds of value. One value might be objectively shaped, whereas the other might not.

d. Hybrid Naturalism

Many researchers think that there is something right about both objectivist and subjectivist views, but that each on its own is incomplete. Susan Wolf has developed what has come to be one of the more influential theories of meaning in life over the last decade or so, the fitting-fulfillment view. Her view includes both objective and subjective conditions, and is captured by the slogan, “Meaning arises when subjective attraction meets objective attractiveness” (Wolf 1997: 211). Meaning is not present in a life spent believing in, being fulfilled by, or caring about worthless projects, but neither is it present in a life spent engaging in worthwhile, objectively valuable projects without also believing in, being fulfilled by, or caring about them. Many think hybridist views capture what is best about objectivism and subjectivism while avoiding the pitfalls of each.

In their naturalistic forms, such theories of meaning are inconsistent with supernaturalism. However, one can imagine supernaturalist forms of each of these views. One might be a supernaturalist who thinks that meaning wholly or largely consists in subjective fulfillment in the Divine—a kind of subjectivism, or that meaning consists in orientation around objective value, again grounded in the Divine—a kind of objectivism. One could also formulate distinctly supernaturalist hybrid views.

e. Pessimistic Naturalism: Nihilism

In opposition to all optimistic views about the possibility of meaningful life, is pessimistic naturalism, more commonly called nihilism. Roughly, nihilism is the view that denies that a meaningful life is possible because, literally, nothing has any value. Nihilism may be understood as a combination of theses and assumptions drawn from both supernaturalism and naturalism: (i) God or some supernatural realm is likely necessary for value and a meaningful life, but (ii) no such entity or realm exists, and therefore (3) nothing is ultimately of  value and there is, therefore, no meaning. Other forms of nihilism focus on states like boredom or dissatisfaction, arguing that boredom sufficiently characterizes life so as to make it meaningless, or that human lives lack the requisite amount of satisfaction to confer meaning upon them.

f. Structural Contours of Meaning in Life

If meaning is a distinct kind of value that a life can have, and if the three senses of meaning above (see Section 2.a. above) capture the range of ideas encompassed by meaning, then these ideas can help illumine the conceptual shape of meaning in life. Each of the ordinary senses of “meaning” provides strategies for conceptualizing the broad structural contours of meaningful life.

Sense-making: An intelligible life; one that makes sense (broad sense-making), that fits together properly, and exhibits a kind of coherence (for example, relationally, vocationally, morally, spiritually, and so on), perhaps even narrative coherence.

Purpose: A life saliently oriented around purposes, goals, and aims, and lived on purpose in which the person’s autonomy is sufficiently engaged.

Significance: A life that matters (and has positive value)—intrinsically in virtue of the kind of life that it is and extrinsically in virtue of its implications and impacts, especially within the narrow (e.g., familial) and broad (e.g., cultural) relational webs of which the person is a part.

Though one can view these as largely different ways of thinking about what a meaningful life is, one might think that there is a more organic relationship between them. Here is one strategy through which all three senses of meaning might coalesce and bring into relief the full structural contours of meaningful life in a unified way:

Meaningful Life = A life that makes sense, that fits together properly (sense-making) in virtue of appropriate orientation around goals (purpose), other (atelic) activities (see Setiya 2017), and relationships that matter and have positive value (significance).

Philosophers may want to follow social scientists here in thinking more about this tripartite conception of meaning. Psychologists, for example, are increasingly using similar accounts in experimental design and testing. One prominent psychologist working in the area of meaning proposes a definition of meaning in life that incorporates a similar triad that prioritizes sense-making:

Meaning is the web of connections, understandings, and interpretations that help us comprehend our experience and formulate plans directing our energies to the achievement of our desired future. Meaning provides us with the sense that our lives matter, that they make sense, and that they are more than the sum of our seconds, days, and years (Steger 2012: 165).

4. Death, Futility, and a Meaningful Life

Life’s meaning is closely linked with a cluster of related issues including death, futility, and endings in general. These are important themes in the literature on meaning, and are found in a wide array of sources ranging from the Old Testament book of Ecclesiastes to Tolstoy to Camus to contemporary analytic writing on the topic. Worries that death, as conceived on naturalism, threatens meaning lead into discussions about futility. It is a commonly held view that life is futile if all we are and do eventually comes to nothing. If naturalism is true and death is the end . . . period . . . then life is futile, so the argument goes. Left undeveloped, it is not entirely clear what people mean by this, though the sentiment behind the idea is intense and prevalent.

In order to explore the worry further, it is important to get clearer on what is meant by futility. In ordinary cases, something is futile when the accomplishment or fulfillment of what is aimed at or desired is impossible. Examples of futility include:

It is futile for a human being to try to both exist and not exist at the same time and in the same sense.

It is futile to try and jump to Mars.

It is futile to try and write an entire, 300-page novel, from start to finish, in one hour.

On the preceding account of futility, the existential angst that accompanies some instance of futility is proportional to how one feels about what it is that is futile. The extent to which one is invested—for example, emotionally and relationally—in attempting to reach some desired end will affect how she responds to real or perceived futility (“perceived” because one could be wrong about whether or not something is, in fact, futile). Imagine that a person has a curiosity to experience flying as a falcon flies. It would be futile to attempt to fly as a falcon flies. Though this person might be minimally distressed as a result of not being able to experience this, it is doubtful he would experience soul-crushing angst. Contrast this with a situation where one has trained for years to run an ironman triathlon, but one week prior to the event, she is paralyzed from the neck down in a tragic automobile accident. To now try and compete in the triathlon without mechanical assistance would be futile. Given the importance of this goal in the person’s life, she would appropriately feel significant existential angst at not being able to compete. Years of training would be unrewarded. Deep hopes would be dashed. A central life goal is now forever unfulfilled. The level of existential angst accompanying futility, then, is proportional to the level of one’s investment in some desired end and the relative desirability of that end.

The preceding analysis is relevant to futility and life’s meaning. What might people have in mind when they say that life itself is futile if naturalism is true and death is the last word of our lives and the universe? The discrepancy here from which a sense of futility emerges is between central longings of the human heart and a world devoid of God and an afterlife, which is a world incapable of fulfilling such longings. There is a stark incongruity between what we really want (even what we might say we need) and a completely and utterly silent universe that does not care. There is also a discrepancy between the final state of affairs where quite literally nothing matters, and the current state of affairs where many things seem to matter (e.g., relationships, personal and cultural achievements, and scientific advancements, among others). It seems hard to fathom that things with such existential gravitas are but a vapor in the grand scheme of things. We might also call this absurd, since absurdity and futility are connected, both of which are partly encapsulated in the idea of a profound incongruity or lack of fit.

Futility, in this way, connects to hope and expectations about fulfillment and longevity. In some circumstances, we are inclined to think that something is characterized by futility if it does not last as long as we think it should last given the kind of thing that it is. If you spend half a day building a snow fort and your children destroy it in five minutes, you will be inclined to think that your efforts were futile even though you accomplished your goal of building the fort. You will not, however, think your efforts were futile if the fort lasts a few days and provides you and your children with several fun adventures and a classic snowball fight. It needs to last long enough to serve its purpose.

Some say that an average human lifetime with average human experiences is sufficient to satiate core human longings and for us to accomplish central purposes (see Trisel 2004). Others, however, think that only eternity is long enough to do justice to those aspects of the human condition of superlative value, primarily and especially, happiness and love, the latter understood roughly as commitment to the true good or well-being of another. Some things are of such sublime character that for them to be extinguished, even after eons upon eons, is truly tragic, so the thinking goes. Anything less than forever is less than enough time, and leads to a sense of futility. We want the most important things in life—especially happiness, love and relationships—to last indefinitely. But if naturalism is true, all will be dissolved in the death of ourselves and the universe; it will be as if none of this ever happened. If the important stuff of life that we are so invested in lasts only a short while, many worry that life itself is deeply and ultimately futile.

Futility, then, is sometimes linked with how something ends. With life’s meaning in view, many worry that its meaning is jeopardized if, in the end, all comes indelibly to naught. Such worries have been articulated in what some call Final Outcome Arguments (see Wielenberg 2006). A final outcome argument is one whose conclusion is that life is somewhat or wholly meaningless or absurd or futile because of a “bad” ending. Such arguments can have weaker and stronger conclusions, ranging from a “bad” ending only slightly mitigating meaning all the way to completely destroying meaning. What they all have in common, however, is that they give the ending an important say in evaluating life’s meaning.

Why think that endings have such power? Many have argued that giving them this power arbitrarily privileges the future over the past. Thomas Nagel once said that “. . . it does not matter now that in a million years nothing we do now will matter” (Nagel 1971: 716). Why should we think the future is more important than, or relevant at all to the past and the present? But perhaps Nagel is mistaken. There may, in fact, be good reasons to think that how life ends is relevant for evaluating its meaning (see Seachris 2011). Whichever conclusion one adopts, principled reasons must be offered to settle the question of which viewpoint—the distant future or the immediate present—takes priority in appraisals of life’s meaning.

5. Underinvestigated Areas

Within value theory, an under-investigated area is how meaning fits within the overall normative landscape. How is it connected, if at all, with ethical, aesthetic, and eudaimonistic value, for example? What sorts of relationships, conceptual, causal or otherwise, exist between the various values? Do some reduce to others? Can profoundly unethical lives still count as meaningful? What about profoundly unhappy lives? These and other questions are on the table as a growing number of researchers investigate them.

Another area in need of increased attention is the relationship between meaning and suffering. Suffering intersects with our attempts to make sense of our lives in this universe, motivates our questions about why we are here, and gives rise to our concerns about whether or not we ultimately matter. We wonder if there is an intelligible, existentially satisfying narrative in which to locate—make sense of—our visceral experience of suffering, and to give us solace and hope. Evil in a meaningful universe does not cease from being evil, but it can be more bearable within these hospitable conditions. Perhaps the problem of meaning is more fundamental than the problem of evil. Also relevant is what can be called the eschatological dimension of the problem of evil—is there any hope in the face of pain, suffering, and death, and if so, in what does this hope consist? Addressing future-oriented considerations of suffering will naturally link to perennial meaning of life topics like death and futility. Additionally, it will motivate further discussion over whether the inherent human desire for a felicitous ending to life’s narrative, including, for example, post-mortem survival and enjoyment of the beatific vision or some other blessed state is mere wishful thinking or a cousin to our desire for water, and thus, a truly natural desire that points to an object capable of fulfilling it.

Equally under-investigated is how the concept of narrative (and meta-narrative) might shed light on the meaning of life, and especially what talk of life’s meaning is often all about. Historically, most of the satisfying narratives that in some way narrated the meaning of life were also religious or quasi-religious. Additionally, many of these narratives count as narratives in the paradigmatic sense as opposed to non-narrative modes of discourse. However, with the rise of naturalism in the West, these narratives and the religious or quasi-religious worldviews embedded within them, began to lose traction in certain sectors. Out of this milieu emerged more angst-laden questioning of life’s meaning accompanied by the fear that a naturalistic meta-narrative of the universe fails to be existentially satisfying. More work is needed by cognitive scientists, theologians, and philosophers on our narrative proclivities as human beings, and how these proclivities shape and illumine our pursuit of meaning.

Finally, a number of pressing practical and ethical questions, especially focusing on marginalized populations, deserve more careful attention. For example, how might the actual lives and experiences of persons with disabilities inform and constrain theories of meaning in life? Do their lives call into question certain theories of meaning? What does the practice of solitary confinement reveal about the human need of meaning? Does the profound lack of meaning in such circumstances provide a reason to impose stricter limitations on its use? How might the human need for meaning (see Bettelhiem 1978; Frankl 2006) be leveraged to understand and then address systemic societal issues like homelessness and opioid addiction? How can understanding seemingly pathological expressions of our yearning for meaning help make sense of and respond to nationalism and terrorism?

Analytic philosophy, once deeply skeptical of and indifferent to the meaning of life, is now the source of important and interesting new theorization on the topic. There is even something of a subfield emerging, consisting of researchers devoting significant time and energy to understanding conceptual and practical aspects of life’s meaning. The topic is being approached with an analytic rigor that is leading to progress and opening exciting avenues for promising new breakthroughs. The philosophical waters, though still murky, are clearing.

6. References and Further Reading

  • Adams, E. M. “The Meaning of Life.” International Journal for Philosophy of Religion 51 (April 2002): 71-81.
  • Antony, Louise M., ed. Philosophers Without Gods: Meditations on Atheism and the Secular Life. Oxford: Oxford University Press, 2007.
  • Audi, Robert. “Intrinsic Value and Meaningful Life.” Philosophical Papers 34 (2005): 331-55.
  • Augustine. The Confessions of St. Augustine. Trans. by Rex Warner. New York: Mentor, 1963.
  • Baggini, Julian. What’s It All About? Philosophy & the Meaning Of Life. Oxford: Oxford University Press, 2004.
  • Baumeister, Roy F. Meanings of Life. New York: The Guilford Press, 1991.
  • Baumeister, Roy F., Kathleen D. Vohs, Jennifer Aaker, and Emily N. Garbinsky. “Some Key Difference between a Happy Life and a Meaningful Life.” Journal of Positive Psychology 8:6 (2013): 505-516.
  • Benatar, David. Better Never to Have Been: The Harm of Coming into Existence. Oxford: Oxford University Press, 2009.
  • Benatar, David. The Human Predicament: A Candid Guide to Life’s Biggest Questions. New York: Oxford University Press, 2017.
  • Benatar, David, ed. Life, Death & Meaning: Key Philosophical Readings on the Big Questions. Lanham, MD: Rowman & Littlefield Publishers, 2004.
  • Berger, Peter. The Sacred Canopy. New York: Doubleday, 1967.
  • Bernstein, J. M. “Grand Narratives.” in Paul Ricouer: Narrative and Interpretation, ed. David Wood, 102-23. London: Routledge, 1991.
  • Bettelheim, Bruno. The Uses of Enchantment. New York: Knopf, 1978.
  • Bielskis, Andrius. Existence, Meaning, Excellence: Aristotelian Reflections on the Meaning of Life. London: Routledge, 2017.
  • Blessing, Kimberly A. “Atheism and the Meaningfulness of Life.” in The Oxford Handbook of Atheism. New York: Oxford University Press, 2013: 104-118.
  • Bortolotti, Lisa, ed. Philosophy and Happiness. Hampshire, UK: Palgrave Macmillan, 2009.
  • Bradley, Ben. “Existential Terror.” Journal of Ethics 19 (2015): 409-18.
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Author Information

Joshua Seachris
Email: jseachris@nd.edu
University of Notre Dame
U. S. A.

Cognitive Penetrability of Perception
and Epistemic Justification

Perceptual experience is one of our fundamental sources of epistemic justification—roughly, justification for believing that a proposition is true. The ability of perceptual experience to justify beliefs can nevertheless be questioned. This article focuses on an important challenge that arises from countenancing that perceptual experience is cognitively penetrable.

The thesis of cognitive penetrability of perception states that the content of perceptual experience can be influenced by prior or concurrent psychological factors, such as beliefs, fears and desires. Advocates of this thesis could, for instance, claim that your desire to have a tall daughter might influence your perception, so that she appears to you to be taller than she is. Although cognitive penetrability of perception is a controversial empirical hypothesis, it does not appear implausible. The possibility of its veracity has been cited in order to challenge positions that maintain that perceptual experience has inherent justifying power.

This article presents some of the most influential positions in contemporary literature about whether cognitive penetration would undermine perceptual justification and why it would or would not do so.

Some sections of this article focus on phenomenal conservatism, a popular conception of epistemic justification that more than any other has been targeted with objections that appeal to the cognitive penetrability of experience

Table of Contents

  1. Cognitive Penetrability of Perception and its Consequences
    1. What is Cognitive Penetrability?
    2. The Epistemic Problem of Cognitive Penetrability
  2. Responses to the Epistemic Problem of Cognitive Penetrability
    1. Internalist Resolute Solutions
      1. The Defeasibility Approach
      2. The Intuitive Plausibility Approach
      3. The Different Epistemic Status Approach
    2. Externalist Concessive Solutions
    3. Internalist Concessive Solutions
      1. Process Inferentialism
      2. The Receptivity Approach
      3. The Knowledge-How Account
      4. Presentational Conservatism
    4. Other Options
      1. Sensible Dogmatism
      2. The Imagining Account
      3. The Analogy with Emotions
      4. The Sensorimotor Theory of Perception
  3. Conclusion
  4. References and Further Reading

1. Cognitive Penetrability of Perception and its Consequences

a. What is Cognitive Penetrability?

Our perceptual experiences present to us (accurately or not) facts in the world. For instance, you can have an experience as if a bird is singing or as if this ball is red. In these cases, that a bird is singing and that this ball is red can be said to be the representational contents of your experiences.

The cognitive penetrability of perception is a controversial empirical thesis that holds that the content of perceptual experience can partly be shaped by prior or concurrent psychological factors, such as beliefs, desires, traits, moods, entertained hypotheses, conjectures, emotions, expectations, hopes, wishes, doubts, suspicions, attitudes or knowledge that can be acquired through the right training. Whether cognitive penetrability of perception is a real phenomenon is investigated by cognitive science (Raftopoulos and Zeimbekis 2015). Relevant scientific experiments are described for instance in Payne (2001), Hansen et al. (2006), and Stokes and Payne (2011).

To familiarize ourselves with the notion of cognitive penetrability of perception, let us consider two imaginary cases of cognitive penetration: Siegel’s (2013a, 2017) Angry Jack and Markie’s (2005, 2006, 2013) Expert and Novice case (adjusted for the purposes of this article).

Angry Jack

Jill believes without good reason that Jack is angry. When she meets Jack, under the influence of her unjustified belief that Jack is angry, she sees Jack as being angry. Based on her perceptual experience as if Jack is angry, she retains the same belief and, perhaps, her confidence that Jack is angry is even enhanced. Had she not had the prior belief that Jack is angry with her, she would not have seen him as being angry.

Expert and Novice

Two friends are gold prospectors. One of them is an expert at identifying gold. He has learned to do so through long experience. He began with a list of identification rules and consciously applied them. He then reached the point where he could “just see” that a nugget is gold. The other friend is a novice. He has a general sense of what gold looks like, but he is not very good at its visual identification. He nevertheless craves for making a discovery. When the two friends happen to look at a nugget in a pan, the expert’s developed gold-identification abilities come into play, and he has the perceptual experience as if the nugget is gold. The expert believes accordingly. The novice’s strong desire that it be gold comes into play too, and he also has the perceptual experience as if the nugget is gold. The novice believes accordingly. Had the novice not had a strong desire to find gold, he would not have had the perceptual experience as if the rock is gold. Had the expert not had very developed gold-identification abilities, he would not have had the experience as if the rock is gold.

These two cases are supposed to be situations in which the contents of the relevant perceptual experiences are somewhat influenced by the subject’s prior mental states. Jill’s experience is influenced by her prior belief that Jack is angry. The novice’s experience is influenced by his strong desire to find gold, and the expert’s experience is influenced by his knowledge and experience. They are possible cases of cognitive penetration of perception.

As we see in the next section, the problem that cognitive penetrability poses to theories of perceptual justification rests on the intuition that in at least some cases in which perceptual experience is cognitively penetrated, justification is affected negatively. For instance, despite her experience as if Jack is angry, there seems to be something wrong in claiming that Jill has justification for believing that Jack is angry. The same applies to the novice’s case.

Arguably, there are also cases of good cognitive penetration of perception: namely, situations in which the subject’s experience is actually a good basis for some of her beliefs just because it is cognitively penetrated.

An example might be the expert’s cognitively penetrated experience as if the pebble is gold in Expert and Novice. Siegel (2012) provides another possible example in which a cognitively penetrated experience of an expert radiologist inspecting the X-ray of a patient is contrasted with a non-penetrated experience of a non-expert who attends to the same X-ray. Lyons (2011) suggests further examples involving perceptual learning as cases of good cognitive penetration. Perceptual learning is a process based on training and experience that ends up producing changes in the subject’s perceptual abilities (Connolly 2017). Perceptual learning is a form of diachronic cognitive penetration. Lyons also imagines a case of synchronic good cognitive penetration—the Snake Case—involving the sharpening of one’s snake-detection skills in virtue of one’s unjustified belief or fear that there are snakes in one’s trail.

Before going deeper into the relations between cognitive penetration and epistemic justification, we need to have a more accurate picture of what cognitive penetration of perceptual experience consists of.

Not just any kind of influence on perception by psychological states produces cognitive penetration. Some mental states might influence perceptual experience indirectly simply because they change the location from where the subject receives the perceptual stimuli. For example, if I desire to watch TV, I will turn my head towards the TV. So my experience will change from representing the monitor of my laptop to representing the TV. The change in perception imputable to cognitive penetration must not be explainable in terms of a reception of different perceptual stimuli due to body movements, defects of our sensory organs or—more controversially—a difference in the spatio-temporal locations attended to by the subject’s covert attention (Stokes 2012 and Vance 2014).

Siegel (2012) for instance excludes voluntary shift of attention from the definition of cognitive penetration. Nevertheless, she mentions as interesting cases of cognitive penetration that involve relative indifference to stimuli or an attentional selection bias in favor of only particular loci of the stimuli.

For the time being, let us follow Siegel (2012) in accepting that in most cases of cognitive penetration this counterfactual would be satisfied: if S had a cognitive mental state different from the one she actually has, but attended to the same perceptual stimuli as those she actually attends to, S would not have the same perceptual experience. For instance, if the belief that Jack is angry were not part of Jill’s mental state, but Jill still attended to the very same features of Jack’s face, she would not have the perceptual experience as if Jack is angry.

Many philosophers of mind and epistemologists agree that perceptual experience has at least two interplaying components: sensory impressions (for example, colors, smells and tastes), and concepts (for example, the concept of bird and the concept of ball). These philosophers would claim that in order to have the experience as if, say, this ball is red, you need to combine a round and a red sense impression together with the concepts of ball and red into one suitable representational state.

As we later see, the thesis that the perceptual experience of a subject S can be cognitively penetrated is often interpreted in a disjunctive fashion as stating that the sensory impression component or the conceptual component of S’s experience can be cognitively penetrated. In the first case, S’s prior or concurrent mental states would directly change the low-level, non-conceptual part/stage of S’s experience. For instance, suppose that under the influence of her belief that Jack is angry, Jill comes to have visual sensations that typically lead to the formation of higher-level conceptual angry-face-representation. On the grounds of these sensations, it does appear to her that Jack is angry. In the second case, S’s prior or concurrent states would directly affect the part/stage of S’s experience that is conceptual. One could interpret the novice prospector case as an example of this: the novice’s strong desire to find gold produces an experience that, thanks to the concepts embedded in it, represents the pebble before him as gold.

It is important to distinguish S’s perceptual experiences and S’s doxastic states that can accompany these experiences. A perceptual experience as if P may be accompanied by a belief or judgment that P, but this belief or judgment would not be a part of the perceptual experience. Suppose for instance that S does have a perceptual experience as if this ball is red. Concurrently, S may or may not believe or judge that this ball is red. In the same way, one’s perceptual experience as if P may be accompanied by one’s reflective belief that one has a perceptual experience as if P, but this reflective belief would be something distinct from the perceptual experience. Suppose again that S has a perceptual experience as if this ball is red. Concurrently, S may or may not entertain a reflective belief that she has an experience as if this ball is red.

It does not seem implausible that S’s previous or concurrent mental states could directly influence S’s perceptual or reflective beliefs without affecting S’s perceptual experiences. Imagine, for instance, that though Jill does have a perceptual experience as if Jack is not angry, she forms an inaccurate perceptual belief that Jack is angry because she fears that Jack is angry. Alternatively, imagine that although Jill has a perceptual experience as if Jack is not angry, she forms a mistaken reflective belief that she has a perceptual experience as if Jack is angry, due to her belief that Jack is angry

Most of the philosophers involved in the debate on cognitive penetrability would not consider cases like those just described to be genuine examples of cognitive penetration of perceptual experience. The basic problem is that they do not concern effects of S’s mental states on S’s perceptual experience.

Nevertheless, for a comprehensive conception of cognitive penetrability of perception that includes cases like the ones just described, see Lyons (2011). Siegel (2015, 2017) discusses another comprehensive view according to which previous or concurrent mental states of the subject can affect the subject’s perceptions, conceived of in a broadened sense to include also, for instance, experiential judgments and patterns of attention. However, Siegel is careful in using the expression “perceptual farce” just to refer to this general view and in distinguishing it from the more specific view that perceptual experience is cognitively penetrable.

The remainder of this article takes cognitive penetrability to be a phenomenon pertaining to the conceptual component or the sensory impression component of experience.

b. The Epistemic Problem of Cognitive Penetrability

Perceptual experience is, so to speak, the tribunal by which most beliefs can be checked with respect to their epistemic status. The epistemological problem of cognitive penetrability essentially stems from a clash of two conflicting intuitions about the credentials of this tribunal. The first intuition says that perceptual experiences in general possess the kind of intrinsic features that would make the beliefs based on them justified. The second, contrasting intuition says that badly cognitively penetrated experiences—such as the experiences of Jill in Angry Jack and the novice in Expert and Novice—cannot actually justify the beliefs based on them (see Lyons 2016). As it will shortly become clear, the philosophical question underlying this clash of intuitions is whether the causal history—or etiology—of an experience can affect its justificatory power.

It is important to appreciate that although cognitive penetrability is a controversial empirical hypothesis, scientific investigation is not crucially relevant to this epistemological debate. Those who share the intuition that perceptual experiences have intrinsic features that make the beliefs based on them justified typically take this claim to be true a priori of any possible contentful experience as such. In consequence, if cognitive penetration were incompatible with the justificatory power of perceptual experience, even if our hardwiring ruled out cognitive penetrability, the mere possibility of a rational being suffering from cognitive penetration of perception would constitute a threat to that intuition (Markie 2013 and Tucker 2019).

To probe these complex issues, we need now to introduce some basic epistemological notions and individuate one theory of perceptual justification to use as a good example.

Internalists about epistemic justification claim that all the factors that make a subject S possess justification for believing a proposition are (i) reflectively accessible to S or (ii) mental states of S. In case (i), the view is called accessibilism; in case (ii), it is called mentalism. Factors that provide S with justification could for instance be other beliefs of S or her experiences. Externalists about justification deny both (i) and (ii) (see Pappas 2014 and Poston 2018). For example, according to a prominent form of externalism called reliabilism, what renders a belief of S justified is its being produced by a (statistically) reliable process, regardless of whether the process is reflectively accessible to S or not, and of its being wholly mental or not (see Goldman 1979).

Phenomenal conservatism (Huemer 2001 and 2007) is the theory of epistemic justification that many if not most early twenty-first century internalists invoke to account for the justificatory power of experiences. (See Audi 1993 and Pryor 2000 for similar views.) In accordance with it, it is a priori true that:

(PC) If S has a seeming that P, S thereby has prima facie justification for believing P.

Seemings (or appearances) are typically conceived of as experiences provided with a propositional content. (Some phenomenal conservatives think of a perceptual seeming as, specifically, the conceptual component of an experience. For others, a perceptual seeming is made of the conceptual component together with the sensory impression component of an experience.) Although seemings may include more than perceptual experiences—some philosophers think there are, for example, rational, moral and mnemonic seemings—we focus here on perceptual seemings.

(PC) is to be interpreted as stating that if S has a seeming that P and no defeating evidence, S possesses both prima facie and all things considered justification for believing P; whereas if S does have defeating evidence, S possesses only prima facie justification for believing P. Defeating evidence can be any reason for S to believe that P is false or that the seeming that P is deceptive. The ‘thereby’ in (PC) indicates that S’s justification for P comes solely from her seeming that P. Since it does not result from any belief of S, this justification is immediate.

Phenomenal conservatism is customarily taken to be an internalist—both accessibilist and mentalist—theory of justification because it fits with (though it does not entail) the assumption that S’s justification depends only on mental factors reflectively accessible to S—namely, S’s appearances and the absence of defeating evidence.

Let us now investigate the problem of cognitive penetrability in relation to phenomenal conservatism. This is indeed the theory of justification that has been mostly discussed in this context. (See Siegel 2012 and Tucker 2014 about the significance of cognitive penetrability for other theories of epistemic justification.)

Phenomenal conservatism accounts for the internalist intuition that perceptual experiences in general have intrinsic features capable of justifying the beliefs based on them. Suppose S has an experience with content P. If (PC) is correct, S thereby has at least prima facie justification for believing P. Phenomenal conservatism has attracted objections by many epistemologists—both internalist and externalist—who share the contrasting intuition that it is in many cases implausible that a cognitively penetrated experience can justify— even only prima facie—a belief.

Siegel (2012) has described a way in which this intuition becomes palpable: cognitive penetration of perceptual experience seems to allow for the elevation of S from a worse epistemic position to a better one in cases in which such an elevation appears illegitimate or impossible. This epistemic elevation may occur when the penetrating state is unjustified or when it is justified. An instance of the first case is the one in which S gets support for an initially unjustified belief B entertained by her from B itself, through the mediation of an experience cognitively penetrated by B. This is what arguably happens to Jill in Angry Jack: Jill gets support for her initially unjustified belief (B) that Jack is angry from the very same belief B, thanks to the mediation of the perceptual experience as if Jack is angry, cognitively penetrated by B. An instance of the second case would be one where S gets additional support for a justified belief on the basis of a perceptual experience cognitively penetrated by that very same belief. Imagine that, before meeting Jack, Jill forms a justified belief (B) that Jack is angry, for she receives a furious email from him. This prior justified belief B makes Jill have the experience as if Jack is angry when she meets him later on. Thanks to this experience, Jill would get additional support for B.

To facilitate our discussion let us introduce the downgrade thesis (Siegel 2013a and Teng 2016). This thesis holds that a badly cognitively penetrated perceptual experience as if P provides less prima facie justification for believing P than a non-penetrated perceptual experience sharing the same content P. Precisely, if the whole content of the experience is badly cognitively penetrated, the experience as a whole is downgraded; and if only a part of it is badly cognitively penetrated, only that part of the experience is downgraded. For example, suppose S has a badly cognitively penetrated experience as if there is a red car before her. If what is badly cognitively penetrated is just the part of S’s experience that represents the car’s color, S’s experience is downgraded only with respect to the color. Thus, S has prima facie justification for believing that there is a car before her, but less or no prima facie justification for believing that the car is red (Teng 2016).

There is an interesting similarity between the cognitively penetrated experiences of a subject S and the experiences that S would have if she were a victim of a skeptical scenario (such as the Matrix scenario or the evil demon scenario envisaged by Descartes). In both cases, S’s experiences would have anomalous etiologies. In the first case, some mental state of S would interfere with S’s normal causal chains that produce experiences of a certain type. For example, the novice prospector’s craving for gold interferes with his normal visual processes. In the second case, the distal causes of S’s perceptual experiences would be unnatural. For example, if S were in the Matrix, the external cause of her visual experience of a cat would be the Matrix rather than a cat. Despite this similarity, many internalists tend to treat the cases of bad cognitive penetration and the cases of skeptical scenarios differently.

Internalists generally agree that when S is in a skeptical scenario, the anomalous etiologies of S’s perceptual experiences do not downgrade these experiences, so they do not affect their justifying power. The reason being that the segments of the etiologies of the perceptual experiences that make S a victim of a skeptical scenario are neither accessible to nor mental sates of S, which means they could not affect S’s perceptual justification. Internalists agree that if S were in a skeptical scenario, her perceptual beliefs would be at least prima facie justified when based on appropriate experiences. Internalists have long been using this argument to attack externalists about justification. Externalists seem in fact to be committed to holding that S’s perceptual beliefs would be all unjustified if S were deceived by the Matrix or a Cartesian demon. These beliefs would therefore be all false, which would entail that they are produced by unreliable processes (Poston 2018).

When it comes to cognitive penetrability, nevertheless, many internalists and externalists agree that if a perceptual experience of S were badly cognitively penetrated, it would be downgraded to the effect that S would lack prima facie justification for believing its content (Siegel 2012 and Tucker 2013). Externalists could defend this view by insisting that the anomalous etiologies of these perceptual experiences make the processes producing the correlated perceptual beliefs unreliable. Nevertheless, it is not immediately clear why the etiologies of cognitively penetrated experiences and the etiologies of experiences in skeptical scenarios should be considered to be so relevantly different from an internalist point of view. As we see later in the article, certain responses to the epistemic problem of cognitive penetration aim to illuminate this issue too.

2. Responses to the Epistemic Problem of Cognitive Penetrability

The debate on cognitive penetrability and perceptual justification has at least three basic and influential sides. One is the internalist resolute side, which aims to reject the downgrade thesis. For the most part, this is the side of the advocates of phenomenal conservatism. Another side is the externalist reliabilist one, which rejects (PC), does subscribe to the downgrade thesis and explains the weakening or annihilation of the justificatory power of badly cognitively penetrated experiences in terms of unreliability. The third side belongs to the internalist camp, but it deviates from the resolute one. This third side—called here the internalist concessive side—accepts the downgrade thesis but attempts to explain why perceptual justification is undermined in bad cognitive penetration cases, with the aim of, simultaneously, respecting internalist principles. The epistemologists belonging to this side all reject (PC), but some propose views that could be described as variants of phenomenal conservatism. Beyond these three fundamental sides, there are accounts that offer solutions to the problem of cognitive penetrability that do not fit the internalism-externalism dichotomy. The following sub-sections are dedicated to the presentation of key arguments that have been developed within all the aforementioned approaches, as well as to important objections to them.

a. Internalist Resolute Solutions

There are at least three distinct but not incompatible approaches adopted by internalists who reject the downgrade thesis: (i) the defeasibility approach, according to which cognitive penetration does not affect prima facie justification but can only influence all things considered justification; (ii) the intuitive plausibility approach, which rejects the downgrade thesis by heavily relying on internalist intuitions about the irrelevance of etiology as a justificatory factor and intuitions about the justifying power that perceptual experiences have thanks to their intrinsic features; and (iii) the different epistemic status approach, according to which in bad cognitive penetration cases the subject lacks not epistemic justification but rather some other epistemic property or status.

i. The Defeasibility Approach

According to the defeasibility approach, all cases of bad cognitive penetration can be construed as situations where S does have defeating evidence; namely, S suspects, believes or is in some other sense aware that (1) her perceptual experience would have been different if her prior mental state had been different; or S suspects, believes or is in some other sense aware that (1) and that (2) her prior mental state was unjustified or an unreliable guide to truth (see Siegel 2012 and Huemer 2013b). For instance, in Expert and Novice, arguably, the novice is in some sense aware that (1) he would not have had the experience as if the pebble is gold if he had not had the desire to find gold; or he is in some sense aware of both (1) and that (2) one’s craving for gold can make one’s perceptual experience of gold unreliable.

The advocates of this strategy contend that in all cases of bad cognitive penetration, S’s prima facie justification remains untouched. S would instead lack all things considered justification in virtue of having an evidential defeater. These epistemologists emphasize that this is coherent with the account of prima facie justification based on (PC) (Huemer 2013b).

An expected criticism says that in many cases of bad cognitive penetration, S is not actually aware that her perceptual experience is cognitively penetrated or that her cognitively penetrated experience is an unreliable guide to truth, though S could become aware of it (McGrath 2013b and Markie 2013). In response one might appeal to a weaker notion of evidential defeater. One might contend that S would have an evidential defeater even if one were just able to become aware of it, without being actually aware of it (see Siegel 2012). But this would not resolve all problems because the mental state that should work as an evidential defeater might be such that S could not possibly become aware of it (Siegel 2012 and Markie 2013). For example, think of a variant of Angry Jack in which Jill, because of inborn or induced cognitive deficiencies, is incapable of coming to believe that her perceptual experience would have been different if she had had a different prior cognitive state.

The main reason of concern about the defeasibility approach, however, stems from the intuition, which some epistemologists have, that in the case of bad cognitive penetration the subject would lack even prima facie justification (Markie 2005, Huemer 2013b and Tucker 2014).

ii. The Intuitive Plausibility Approach

Phenomenal conservatives may try to defend the contention that in the case of bad cognitive penetration, S would at least have prima facie justification by highlighting its plausibility against a background of internalist intuitions. A key thesis adduced in this context is that perceptual experiences have justifying power in virtue of being experiences, rather than in virtue of having a particular sort of etiology (see Lyons 2016). In accordance with this view, perceptual experiences can differ in their epistemic power only in virtue of their intrinsic factors, not because of their etiologies.

Let us see how this response can be developed. The intuitive plausibility approach aims to support the claim that (i) reflectively inaccessible etiologies of perceptual experiences in cognitive penetration cases play no role in determining whether or not perceptual experiences provide prima facie justification, and the claim that (ii) perceptual experiences possess intrinsic justificatory force. (i) and (ii) are two sides of the same coin.

A way to support (i) is to appeal to the absence of essential differences between bad cognitive penetration cases and zap-like cases (Siegel 2012). ‘Zap-like’ is the expression used by Siegel (2013a) to refer indifferently to scenarios involving bump-on-the-head situations (that is, cases in which S has a hallucination caused by a knock or bump on her head) and skeptical scenarios (involving, for instance, evil demons or the Matrix). Internalists may insist that cognitive penetration cases are not substantially different from zap-like cases. After all, the etiologies of perceptual experiences in cognitive penetration cases are processes reflectively inaccessible to the subject S, just as the etiologies of zap-like cases. Furthermore, the etiologies of perceptual experiences in cognitive penetration cases are processes that do not seem to be subject to S’s rational control, just as the etiologies of zap-like cases. It may appear plausible that the etiology of S’s perceptual experience in a zap-like scenario plays no role in determining whether or not S’s perceptual experience provides S with prima facie justification for her beliefs. (For instance, it may appear plausible that if an evil demon causes Jill’s perceptual experience as if Jack is angry, this fact cannot interfere with the prima facie justification for believing that Jack is angry, which Jill possesses in virtue of her experience. For the evil demon’s actions are reflectively inaccessible to Jill and are not subject to Jill’s rational control.) Since the cases of cognitive penetration are not relevantly different from the zap-like cases in terms of their etiologies, it can be argued that the latter play no role in determining whether or not S’s perceptual experience provides S with prima facie justification for her beliefs.

Although internalists may welcome this defense of (i), many externalists will not concede at the outset that justification is not negatively affected in zap-like cases. They will contend that since the relevant perceptual experiences are misleading in these cases, the correlated belief-formation processes are unreliable. These externalists would conclude that if we appeal to absence of essential differences, we must accept that prima facie justification is negatively affected in cases of bad cognitive penetration too.

A different criticism of this defense of (i) targets the claim that the etiologies of perceptual experiences in cognitive penetration cases are not subject to S’s rational control, just as the etiologies of zap-like cases. The claim is that whereas S may in certain cases be able to avoid bad cognitive penetration by controlling known factors that lead to it, S could not by assumption control the factors that make her a victim of zap-like cases (Siegel 2012 and 2013a). But even if it were established that the etiologies of perceptual experiences in cases of cognitive penetration are not subject to S’s rational control, there could be a debate about whether the etiologies of perceptual experiences in cases of cognitive penetration are in some sense attributable to S in a way that the etiologies of experiences in zap-like cases are not (Siegel 2013a). Internalist accessibilists can nevertheless insist that despite these complications, it is the shared inaccessibility of the etiologies of zap-like cases and cognitive penetration cases that make these cases homologous. S0 the claim would be that if S is unaware of the defective etiology in bad cognitive penetration cases, just as it happens to S in zap-like cases, the etiology must be irrelevant to S’s justification in those cases.

A more direct way to defend (i) is adducing the phenomenology (or subjective features) that a cognitively penetrated perceptual experience shares with a non-penetrated perceptual experience with the same content (see Siegel 2012). For instance, Jill’s perceptual experience as if Jack is angry looks the same when it is the effect of cognitive penetration and when it is not. The perceptual experiences in these two cases are identical in terms of what is introspectively accessible. It could therefore be argued that whether or not an experience is the effect of cognitive penetration is irrelevant to what one has prima facie reason to believe or not. Only evidence of a distorting etiology could be a defeater and affect all things considered justification (Huemer 2013a, see also Silins 2016).

Another way to support (i) is appealing to the intuition that it is implausible that S’s justification for an attitude A could depend on reasons that S could not adduce to explain whether A is justified or not. For instance, an argument by Huemer in defense of (i) considers a case in which S is unable to draw an epistemically significant distinction between the penetrated part and the non-penetrated part of the content of one and the same perceptual experience. Imagine I have one partly cognitively penetrated perceptual experience as if there is a gun and a box with eggs in the fridge. The gun-like part of my perceptual experience is cognitively penetrated, whereas the box-like is not.

I accept E [that there is a box with eggs in the fridge] on the basis of my visual experience. G [that there is a gun in the fridge] also appears to be equally well supported by my visual experience, and I have no reason for thinking the experience representing G to be any less reliable, nor epistemically inferior in any manner whatsoever, to the experience representing E. Nor have I any other grounds for doubting G. Nevertheless, while I accept E, I refuse to accept G, for no apparent reason . . . This attitude . . . strikes me as obviously irrational. I conclude that . . . [I] epistemically ought to accept G . . . If S would have no rational way of explaining why she believed E while refusing to accept G, then S would be irrational to believe E while refusing to accept G (Huemer 2013a, pp. 745–746).

This argument assumes that whether S is justified or unjustified in believing P depends on whether S can potentially appeal to the reasons that make herself justified or unjustified (Siegel 2013b). Given this assumption, S is not unjustified in believing P unless she can rationally explain why she is so. According to this line of thought, justification depends only on reflectively accessible factors. For S’s being in principle able to appeal to the reasons that determine whether she is justified or not in believing P requires S to be able to reflectively access those reasons. Given this, the etiology of perceptual experiences in cognitive penetration cases is irrelevant to S’s justification insofar as it is reflectively inaccessible to S. Setting aside general criticism of accessibilism, a concern about this strategy is that it is not uncontroversial that S can be justified or unjustified in adopting an attitude A only if S is potentially able to rationally explain why she is justified or unjustified in adopting A. (See two apparent counterexamples in McGrath 2013a and in Siegel 2013b).

We have considered ways of supporting or questioning (i)—the thesis that reflectively inaccessible etiologies of perceptual experiences in cognitive penetration cases are irrelevant to prima facie justification. Let us turn to (ii)—the thesis that perceptual experiences possess intrinsic justificatory force. (ii) is directly supported by an apparently straightforward argument resting on an intuition about what attitude S is rationally supposed to adopt, from her point of view, when S entertains a given mental state (McGrath 2013a). If S has an experience as if P and no evidence against P, the most reasonable attitude to take from S’s point of view is belief, rather than disbelief or a suspension of judgment. A parallel argumentative line interprets perceptual experiences as evidence (McGrath 2013a). Considering that S, as a rational believer, has to match her belief to the evidence E available to her, S should form only beliefs that fit E, whatever E might be. Even if, unbeknownst to S, E were acquired through a biased search or flawed method of evidence-gathering, E would constitute the evidence available to S. So, S should adjust her doxastic attitude in a way to fit E, independently of its etiology.

A further way of defending (ii) might be appealing to coherence requirements derived from an experience as if P. Suppose S does not have justification for believing P, but nevertheless S does believe P. In this case it is rational for S to believe, say, P-or-Q and disbelieve, say, Not-P. In general, if S is in a mental state M, S is rationally required to think in a particular way in virtue of coherence requirements derived from being in M, regardless of the credentials of M. One could argue that, in the same way, S has prima facie justification for believing R if S has a perceptual experience as if R, in virtue of coherence requirements and independently of the credentials of the experience—so independently of its etiology (see McGrath 2013a).

However, a reply would be that even if it is rational for S to believe P-or-Q when S believes P, in this case S does not necessarily have justification for believing P-or-Q. For S may not have justification for believing P in the first instance (McGrath 2013a and Ghijsen 2016). The intuition that this reply exploits is that the kind of rationality that would provide S with justification for believing P-or-Q is not reducible to coherence requirements. The rationality resting solely on coherence is a sort of conditional rationality: it can provide S with justification for P-or-Q only if S has justification for believing P in the first instance.

An illuminating distinction is the one between rational commitment and justification. If S believes P without justification, she is rationally committed to, for instance, disbelieving not-P and believing P-or-Q, but she does not have justification for disbelieving not-P and believing P-or-Q. Rational commitment is a mere coherence requirement (Tucker 2013 and McGrath 2013a, 2013b).

iii. The Different Epistemic Status Approach

This approach aims to substantiate the thesis that if S is in a case of bad cognitive penetration, ordinarily S does not lack (prima facie) justification but some other epistemic status. Various epistemic statuses have been proposed.

A popular candidate is knowledge, or else warrant—namely, the additional property that a true belief needs to have in order to become knowledge (Tucker 2010 and Huemer 2013a). The no knowledge/warrant approach says that in bad cognitive penetration cases S does not lack justification. Rather, S possesses justification without having knowledge or warrant. For instance, S could have justification for believing P without her belief tracking the truth, or without her belief arising from a reliable belief-forming mechanism, or without her belief arising from a belief-forming mechanism that works properly (Huemer 2013a). This is what presumably happens in evil demon cases or Gettier-style scenarios (see Siegel 2013a for a formulation of cognitive penetration cases as Gettier cases). A general concern about this strategy stems from the mentioned impression that there are substantial differences between perceptual experiences badly cognitively penetrated and the perceptual experiences of a victim of a skeptical scenario or a Gettier-style scenario (Tucker 2010 and Markie 2013). In all these cases, the subject S basing her beliefs on her perceptual experiences lacks knowledge and warrant. Nevertheless, in bad cognitive penetration cases, S may also appear to be blameworthy for having her experiences in a way that the victim of a skeptical scenario or a Gettier-style scenario may not (Tucker 2010). If justification essentially depended on the absence of blameworthiness, the fact that S lacks knowledge or warrant in bad cognitive penetration cases would be redundant or insufficient to explain our intuitions.

To dispel this concern Tucker (2010) adduces the Weirdo thought experiment. Weirdo successfully begs a demon to turn himself into a victim of a skeptical scenario and erase this request from his memory. Tucker insists that it is intuitive that when Weirdo becomes a victim of a skeptical scenario, though he is blameworthy (or lacks blamelessness) for having his deceptive perceptual experiences and he lacks knowledge and warrant, Weirdo is nevertheless justified in his beliefs about the external world (Tucker 2010, 2011). This suggests that S’s being blameworthy (or lacking blamelessness) plays no role in determining whether S is justified in bad cognitive penetration cases (assuming that there is no principled distinction between Weirdo’s blameworthiness and S’s blameworthiness due to cognitive penetration).

To question the no knowledge/warrant approach, Markie (2013) uses a different thought experiment. Suppose a novice gold prospector and an expert are in the same skeptical scenario. The expert’s experience as if the nugget before him is gold is a non-penetrated perceptual experience or a case of good cognitive penetration (given the external stimuli provided by the demon), whereas the novice’s perceptual experience as if the nugget is gold is partly caused by his “wishful seeing,” so it is a case of bad cognitive penetration (see also Tucker 2010 and McGrath 2013b). Markie stresses that the novice’s epistemic status appears worse than the expert’s despite their both lacking knowledge and warrant due to the skeptical scenario. This suggests that what explains the intuitive inadequacy of the epistemic status of the novice, and the intuitive inadequacy of the epistemic status in any bad cognitive penetration case, must be something different from knowledge and warrant.

Tucker (2010) observes that Markie’s case does not necessarily show that bad cognitive penetration affects justification. He suggests that although both the novice and the expert in the skeptical scenario lack knowledge and warrant, what renders them different from an epistemic point of view is simply this: only the novice is epistemically blameworthy in having his experience. Tucker thus proposes a novel candidate for rescuing justification: a victim of bad cognitive penetration does not lack epistemic justification but epistemic blamelessness. She is both justified and blameworthy.

Epistemologists have considered appealing to the absence of other candidates to explain why bad cognitive penetration cases are epistemically defective; for instance: epistemically virtuous belief or proper function of the cognitive faculty (McGrath 2013b); positive evaluation of the subject’s cognitive character (Tucker 2013 drawing from Skene 2013); practical appropriateness of belief-formation (Fumerton 2013).

b. Externalist Concessive Solutions

Externalist reliabilists—like Lyons (2011, 2016) and Ghijsen (2016)—typically agree with concessive internalists (which we consider in Section 2.c) on the truth of the downgrade thesis (Teng 2016). The major point of departure of the concessive reliabilists from the concessive internalists regards the explanation of why prima facie justification is negatively affected by bad cognitive penetration. Concessive reliabilists offer a traditional externalist account, which adduces the unreliability of the processes that produce bad cognitive penetration.

Cognitive penetration is epistemically bad—when it is bad—because and when it cuts us off from the world around us, when it makes us less sensitive to our environments, when it makes us more likely to believe p whether or not p is actually true (Lyons 2016, p. 3).

Bad cognitive penetration of perceptual experience can be construed as a phenomenon that renders the process of belief-formation unreliable with respect to its statistically tracking the truth, or as a phenomenon that makes a perceptual experience as if P an inappropriate ground for S’s belief that P (see Lyons 2011, 2016).

The contemporary debate of cognitive penetration and epistemic justification typically presupposes that cognitive penetration may either worsen or enhance the epistemic status of perceptual experience (see Section 1.a). A virtue of concessive reliabilism is the illuminating explanation that it offers for distinguishing the cases of bad cognitive penetration from the cases of good cognitive penetration (Ghijsen 2016). According to Lyons (2011, 2016), whereas the cases of bad cognitive penetration are those that affect reliability negatively, the cases of good cognitive penetration are those that affect reliability positively. And this is so regardless of the penetrating states being a (justified or unjustified) belief or a non-doxastic state like a desire or a fear.

Another asserted virtue of the concessive reliabilist account is that it offers a unitary solution to the problem of cognitive penetration and the problem of why perceptual experiences can have or lack justificatory power when experience is unpenetrated. In particular, it explains the cases in which S is affected by bad cognitive penetration and the cases in which S is a victim of a skeptical scenario by claiming that both situations are essentially cases in which S’s belief-production processes are unreliable (Ghijsen 2016). As we see in Section 2.c, the responses to the cognitive penetration problem by concessive internalists do not offer unitary solutions of this type. One might adduce this consideration to argue that the reliabilist accounts are preferable (see Ghijsen 2016).

A way to question this reliabilist response to the cognitive penetrability problem is raising standard objections to reliabilism about justification (see Becker 2018). Moreover, Tucker (2014) has argued that this reliabilist response fares no better than internalist resolute solutions. Suppose S’s perceptual experience as if P is cognitively penetrated by her desire that P but P happens to be actually true most of the times when this cognitive penetration obtains. To accommodate suppositions of this type, reliabilists might need to bite the bullet and claim that the output-beliefs of such processes would be actually justified, though this may appear counterintuitive. In a similar fashion, resolute internalists insist that justification is safe from the threat of cognitive penetration. For further criticism see, for instance, Vahid (2014).

c. Internalist Concessive Solutions

This section surveys the principal internalist concessive solutions to the cognitive penetrability problem. As previously mentioned, these accounts accept the downgrade thesis and reject (PC), but they might be described as modifications of phenomenal conservatism that confine the existence of the justificatory power of perceptual experiences to particular circumstances: when certain enabling factors are present or some disabling factors are absent (Chudnoff 2019).

We first examine three versions of what Lyons (2016) calls inferentialism: Siegel’s process inferentialism, McGrath’s receptivity approach, and Markie’s knowledge-how account. Inferentialism rests on the assumption that the proper way to assess epistemically a perceptual experience of S (and S’s beliefs based on it) is checking the way in which S has produced the perceptual experience, roughly in the same way in which we epistemically assess a belief B of S by checking the way in which S has inferred B from other beliefs. A key assumption is that in any case of bad cognitive penetration, the epistemic status of the relevant experience is downgraded as a result of the experience having a rationally assessable etiology but failing to meet certain standards of epistemic rationality. Whether a perceptual experience has justificatory power thus depends on its causal history (Lyons 2011, 2016). Since the factors that determine S’s perceptual justification—the etiologies of S’s perceptual experiences—are thought of as mental processes of S which are possibly reflectively inaccessible to S, inferentialism is typically considered to be an internalist mentalist view (Lyons 2016).

At the end of this section we examine Chudnoff’s presentational conservatism, an internalist (partly) concessive account that does not qualify as inferentialist.

i. Process Inferentialism

Siegel (2013a, 2013b) maintains that a perceptual experience gets epistemically downgraded whenever it has a checkered past; namely, its etiology is similar with respect to its psychological elements to the etiology of a (possible) belief that has the same content and proves unjustified. Consider this example that draws an analogy between wishful seeing and wishful thinking. John’s wishfully seeing that Jack is angry consists of John’s visual experience as if Jack is angry, produced by an etiology involving cognitive penetration by John’s desire that Jack is angry. John’s experience has a checkered past because its etiology is similar with respect to its psychological elements to the etiology of an unjustified belief that Jack is angry, which John could have out of his wishful thinking.

Note that a cognitively penetrated perceptual experience may not have a checkered past. Nevertheless, all beliefs based on cognitively penetrated experiences with checkered past are ill-formed, and so unjustified (Siegel 2013a).

The internalist who—like Siegel—endorses the downgrade thesis must explain why a perceptual experience may lose its justificatory force because of cognitive penetration, but it does not when the subject is simply in a zap-like state. Siegel (2013a) maintains that the etiology of a perceptual experience when the subject is in a zap-like state results from an arational process, whereas the etiology of a perceptual experience badly cognitively penetrated results from a rationally assessable but irrational process. People might find it counterintuitive that these processes are rationally assessable. A process inferentialist may insist, however, that rationally assessable etiologies are those that lie within the cognitive system of the subject, whereas arational etiologies are external to the subject’s cognitive system. Another possibility is that rationally assessable etiologies are those on which the subject has some type of rational control, which is impossible in zap-like cases (Siegel 2012, 2013a).

Process inferentialism has further problems. It is to a good extent indeterminate, by this account, which etiologies of perceptual experiences are defective and why. For it is unclear in what precise respects and to what extent the etiologies of perceptual experiences should share similarity in structure with the etiologies of ill-formed beliefs to qualify as defective (Lyons 2016). Furthermore, although there are paradigmatic instances of ill-formed beliefs (for example, those based on wishful thinking or jumping to conclusions), the distinction between well-formed and ill-formed beliefs is not always clear-cut. So, the only way to draw these distinctions might ultimately be by relying on people’s intuitions, which might diverge (Siegel 2013a). If bad etiologies cannot be identified by means of an effective criterion, process inferentialism is ineffective in distinguishing good cognitive penetration cases from bad ones. If the only way to draw this distinction with precision were appealing to a reliabilist criterion, process inferentialism would not fulfill its internalist ambitions (Lyons 2016).

Another possible source of difficulty for process inferentialism turns on relevant dissimilarities between experiences and beliefs. All perceptual experiences possess—many epistemologists contend—a distinctive phenomenology capable of turning them into justification-providing states; but this phenomenology is not to be found in any belief. This might indicate that the features of the etiologies of perceptual experiences are irrelevant to their justificatory power, and that drawing epistemological conclusions from analogies between perceptual experiences and beliefs is ultimately misguiding (see Vance 2014 and Silins 2016).

For responses to these and other concerns, and an updated defense of process inferentialism, see Siegel (2017, 2018).

ii. The Receptivity Approach

McGrath’s (2013a, 2013b) receptivity approach puts emphasis on the relation between perceptual experiences and their bases. Beliefs can be based on other mental states. In this account, perceptual experiences can do so too. McGrath maintains that one’s seemings can produce other seemings in one’s mind, and draws a distinction between receptive and nonreceptive seemings. A receptive seeming is the input and a non-receptive seeming is the output of a quasi-inference—a process that constitutes the transition from one seeming to another. More precisely,

A transition from a seeming that P to a seeming that Q is “quasi-inferential” just in case the transition that would result from replacing these seemings with corresponding beliefs that P and Q would count as genuine inference by the person (McGrath 2013b, p. 237).

Receptive seemings are unconditional justification-providing states of a subject S, whereas non-receptive seemings give S justification only if the relevant quasi-inference is good. Receptive seemings are given to S, whereas non-receptive seemings arise after S’s own doing. The former seemings provide S with justification without being epistemically assessable. The latter seemings are epistemically assessable due to their stemming from S’s own making (McGrath 2013b).

A good quasi-inference can be characterized by a comparison with a good inference between beliefs. A good inference is one that results in a justified output-belief. Assuming for simplicity that only two beliefs participate in the inference, what is involved in a good inference is a transmission of justification from one belief to another. This happens only if the first belief is justified and sufficiently supports the second. Furthermore, a good inference requires for the subject S some sort of appropriate rationalization (which need not involve higher-order thinking or justification)—for example, S’s correct grasp of the epistemic relation of support between the two beliefs, S’s correct use of background information stored in S’s cognitive system as relevant knowledge-how, or a mix of these two. This rationalization would not be appropriate, for instance, if it depended on factors that would make S jump to conclusions, such as expectations, desires and moods (McGrath 2013b). Analogously, in a good quasi-inference between seemings, what is involved is the transmission of the property, which a seeming might possess or lack, of making S have justification for believing its content. Only receptive seemings have this property by default. In a good quasi-inference, the receptive seeming transmits this property to the non-receptive seeming. As a result, S can be justified in believing the content of the non-receptive seeming. Yet, if the non-receptive seeming is not sufficiently supported by the receptive seeming—because an output-belief with the content of the first seeming would not be sufficiently supported by an input-belief with the content of the second seeming—the non-receptive seeming does not receive the relevant epistemic property. In this case, the quasi-inference is not good, and S does not wind up having justification for believing the content of the non-receptive seeming (McGrath 2013a, 2013b).

The receptivity approach explains the downgrade of perceptual experience affected by bad cognitive penetration by adducing the features of a correlated quasi-inference: the downgrade happens when the quasi-inference is bad (McGrath 2013a, 2013b). Take Angry Jack. In the receptivity approach, Jill initially entertains a receptive seeming about Jack’s face that has the intrinsic property of giving Jill justification for believing that Jack is not angry. Under the influence of cognitive penetration by her unjustified belief that Jack is angry, this receptive seeming is replaced in Jill’s mind with a non-receptive seeming that Jack is angry. This is a bad quasi-inference because the receptive seeming does not support the non-receptive seeming, as belief in the content of the first would not support belief in the content of the second. Hence, Jill is not justified in believing that Jack is angry.

It is unclear whether this approach can accommodate a disunified view of perception—one that distinguishes between sensations (low-level and non-conceptual) and seemings (high-level and conceptual) (Lyons 2016). What McGrath calls non-receptive seemings are states with conceptual content—so proper seemings. However, McGrath seems to concede that receptive seemings are not necessarily states with conceptual content—they may be sensations. This means that, for McGrath, a perceptual experience may arise from a quasi-inference whose input—the receptive seeming—is constituted by mere sensations. Yet a quasi-inference requires all seemings involved to have believable contents, and thus conceptual contents (see Lyons 2016). Moreover, suppose that perception is actually disunified and that the proponent of the receptivity approach denies that mere sensations can be the inputs of quasi-inferences. They should conclude that, for example, the transition in Jill’s mind leading to her perceptual experience that Jack is angry is not a quasi-inference. A consequence would be that this perceptual experience would be a receptive seeming, and thus a justification-provider. Many would find this counterintuitive (see McGrath 2013b and Lyons 2016).

Another concern is that the receptivity approach does not address what might actually be at stake in cases of bad cognitive penetration: the cognitive penetration of receptive seemings, rather than non-receptive seemings (Lyons 2016). Take again Angry Jack. Suppose the correct description of what happens is this: because of her unjustified belief that Jack is angry, Jill has a cognitively penetrated receptive seeming that Jack’s face has anger features. This receptive seeming produces in Jill’s mind, via a quasi-inference, a non-receptive seeming that Jack is angry. If this were the correct description of what happens in Angry Jack, the proponents of the receptivity approach should conclude that Jill is justified in believing that Jack is angry on the basis of her non-receptive seeming that Jack is angry. For this non-receptive seeming is actually supported by Jill’s receptive seeming that Jack’s face has anger features.

Lyons (2016) complains that the receptivity approach treats cognitively penetrated non-receptive seemings as personlevel phenomena, though it is intuitive that perceptual experiences do not result from our own doing. According to Lyons, transitions between seemings cannot be controlled by the subject and could at best be thought of as produced by unconscious inferential mechanisms—this would explain the impression that all seemings are given to us. Advocates of the receptivity approach might concede that all seeming-to-seeming transitions are produced by sub-personal mechanisms. An unpalatable consequence for the receptivity approach (which claims that all seemings produced by sub-personal mechanisms are receptive seemings) would be, however, that all seemings should be thought of as receptive, and thus as always capable of conferring prima facie justification.

Ghijsen (2016) notes that it is hard to find a coherent characterization of the background knowledge that the subject must have to carry out good quasi-inferences. Suppose the background knowledge required to appropriately rationalize the transition from a receptive seeming that this nugget is yellowish in a given way F to a non-receptive seeming that this nugget is gold is the propositional knowledge that whatever looks yellowish in a way F is gold. How could this knowledge be acquired by the subject? It could not be acquired via quasi-inferences from receptive seemings of objects looking yellowish in a way F to non-receptive seemings of objects looking gold. For these quasi-inferences presuppose the background knowledge that we want to characterize. If this background knowledge were conceived of in terms of knowledge-how, it would have better prospects for helping. However, what exactly would this knowledge-how consist of? If this account is meant to be internalist, it cannot coincide with the subject’s mere ability to reliably recognize gold when she comes across it. Thus, the problem remains open.

iii. The Knowledge-How Account

The last inferentialist account we survey, developed by Markie (2013), holds that S’s perceptual experience as if P is epistemically appropriate—namely, it provides S with prima facie justification for believing P—if it results from S’s knowledgehow about the proposition that P. This knowledge-how consists of S’s being disposed to have the perceptual experience as if P in response to S’s attending to particular features of her overall experience and S’s being disposed to do so in virtue of her having background knowledgethat these particular features of her experience indicate that P is true (Markie 2013). Consider an expert orthopedic who has a perceptual experience as if (P) the X-ray shows a knee suffering from osteochondritis. The experience provides the orthopedic with prima facie justification for believing P, for the experience is epistemically appropriate. This is so because the experience results from her knowledge-how about P. This knowledge-how involves both her being disposed to entertain that specific perceptual experience in response to her attending to the particular features of her overall experience, and her having that disposition in virtue of having background knowledge that these particular features of her experience indicate that P is true.

More accurately, Markie analyzes S’s knowing-how as being constituted by (i) S’s disposition to have a perceptual experience as if P after her shift of attention to relevant features of her overall experience, (ii) S’s possession of background information that anything displaying those features is appropriately connected in some factual sense with P (for example, background evidence or justification that any object provided with these features is actually gold), and (iii) the character of S’s disposition being at least partly determined by S’s background information.

For Markie, S’s knowledge-how about P need not be accompanied by S’s reliable practice. (In the evil demon scenarios, the expert knows how to identify gold, though he fails to identify it reliably.) Furthermore, even when S’s practice is reliable, this alone does not provide S with the relevant knowledge-how. S’s reliable practice must be accompanied with S’s understanding that the right object or type of object (for example gold) has been identified by her.

Markie himself acknowledges that both the method of S’s acquiring the relevant knowledge-that and the latter’s relationship with S’s knowledge-how require further specification. One might also doubt that knowledge-how always coexists with knowledge-that, and that knowledge-how depends on knowledge-that in case of coexistence (Lyons 2016). Furthermore, the knowledge-how account of cognitive penetration is afflicted by a problem analogous to one that affects McGrath’s. Markie’s account requires all epistemically appropriate perceptual experiences to depend on S’s understanding and doing. For it is S’s knowledge-that which determines S’s disposition to form appropriate perceptual experiences in response to given features of her experience. But this knowledge-that is an agent-level factor. So, the knowledge-how account holds that the formation of appropriate perceptual experiences happens at personal level, which is implausible (Lyons 2016).

Another difficulty of McGrath’s receptivity account seems to afflict also the knowledge-how account. Markie’s account might not address what is really at stake in cases of bad cognitive penetration. For bad cognitive penetration might directly affect the features of S’s experience that S attends to and in response to which she forms her perceptual experiences (Lyons 2016). Markie considers this criticism and bites the bullet: for him, if cognitive penetration directly affected these features, S’s experiences would still be capable of conferring justification, provided they were produced through the exercise of S’s relevant knowing-how.

iv. Presentational Conservatism

Chudnoff’s (2019) presentational conservatism is a restrained version of phenomenal conservatism that is both accessibilist and mentalist. Presentational conservatism imposes the following additional condition necessary for a perceptual experience to supply immediate justification: the experience must have a presentational phenomenology.

Suppose you see a picture of a dog with an occluded middle part. Your perceptual experience is presentational with respect to the left part of the dog, its right part, but not with respect to the middle part of the dog. This is so even though the middle part of the dog is somehow represented in the picture.

According to Presentational Conservatism it is only those contents with respect to which an experience has presentational phenomenology that prima facie justifies on its own, that is, immediately. If it justifies other contents, then it does so mediately. That the justification is mediate does not mean that it is remote or difficult to attain. Your experience of the partly occluded dog, for example, justifies you in believing various things about the dog’s middle both because they are made likely by the propositions about the dog’s rightward and leftward parts that it immediately justifies, and even entailed by some of the propositions about the whole dog that it immediately justifies (Chudnoff 2019, p. 6).

Chudnoff suggests three different ways in which presentational conservatism can account for cases of bad cognitive penetration, depending on what proposition is taken to be the target and what part of one’s experience cognitive penetration is taken to affect. Chudnoff focuses on the Angry Jack example. Let us consider all three accounts in turn.

Here is the first. Consider the proposition (a) Jack’s eyes and mouth are neutrally shaped, and the proposition (b) Jack is angry.

Jill’s experience immediately justifies her in believing (a) because it is both represented and presented; Jill’s experience doesn’t immediately justify her in believing (b) because though represented it isn’t presented; Jill’s experience would mediately justify her in believing (b) if she had reason to think that if (a) is true then (b) is true; but she doesn’t; so it doesn’t (Chudnoff 2019, p. 10).

Chudnoff suggests that Jill’s experience does not have presentational phenomenology with respect to (b) because anger is a mental state and, as such, is invisible. So, it cannot presentationally seem to Jill that Jack is angry

This account could be extended to other cases of cognitive penetration in which the penetrated perceptual experience results in a mental state without presentational phenomenology. In all these cases the perceptual experiences would be downgraded (see Brogaard 2018 for a similar strategy).

Epistemologists and philosophers of mind who believe that high-level properties are genuinely presented in our experiences might deny, however, that Jill’s experience that Jack is angry does not have presentational phenomenology. These philosophers might raise similar objections to analogous accounts of experience downgrade. This exposes a general weakness of presentational conservatism: since it is somewhat controversial what things and features can genuinely be presented in perceptual experience (Siegel 2016), if presentational conservatism is endorsed, it becomes equally controversial what sort of beliefs can be immediately justified by our perceptual experiences.

This is Chudnoff’s second explanation. Consider again proposition (a) and the proposition (c) Jack’s eyes and mouth express anger. Chudnoff thinks that although anger is not visible, one can see facial organs expressing anger. Facial organs expressing anger is something that can presentationally seem to one to be the case. By these lights, a presentational conservative can claim that Jill’s experience has presentational phenomenology with respect to both (a) and (c). Hence,

Jill’s experience immediately justifies her in believing (a) because it is both represented and presented; Jill’s experience immediately justifies her in believing [c] because it is both represented and presented; but Jill’s justification for believing (a) defeats Jill’s justification for believing [c] because she knows that if (a) is true, then [c] is not true . . . Though Jill’s experience prima facie justifies her in believing that Jack’s eyes and mouth express anger, all things considered Jill does not have justification for believing that Jack’s eyes and mouth express anger because she has justification for thinking that Jack’s eyes are horizontal, as is his mouth and she knows that horizontal eyes and mouth do not express anger (Chudnoff 2019, pp. 10–11).

What is affected in this case is only all things considered justification. Chudnoff suggests that the justification for (a) defeats the justification for (c), and not the other way around because Jill’s experience has stronger presentational phenomenology with respect to (a). Had Jill’s experience stronger presentational phenomenology with respect to (c), the justification for (c) would defeat that for (a).

Both explanations above assume that cognitive penetration does not change Jill’s experience with respect to the low-level neutral characteristics of Jack’s face. Chudnoff’s third explanation assumes that cognitive penetration causes Jill’s experience of Jack to have low-level, angry-face features. Chudnoff acknowledges that in this case Jill’s experience would have presentational phenomenology with respect to the proposition that the features of Jack’s face express anger. Therefore, her perceptual experience would provide immediate justification for (c) and, indirectly, for (b). Some epistemologists would find this result counterintuitive.

d. Other Options

This section presents four miscellaneous responses to the epistemic problem of cognitive penetrability that do not clearly fit the internalism-externalism dichotomy.

i. Sensible Dogmatism

Brogaard’s (2013) sensible dogmatism holds that experiences are mere collections of sensory impressions. Brogaard calls phenomenal contents of an experience the sensory impressions that constitute the experience. Furthermore, Brogaard calls phenomenal seemings the “interpretations” of experiences—that is to say, the conceptual or propositional ingredients of perception.

Sensible dogmatism is a special version of phenomenal conservatism that implies the downgrade thesis. This is its core principle:

If it seems to S as if [P] and the seeming is grounded in the content of S’s . . . experience, then, in the absence of defeaters, S thereby has at least some degree of justification for believing that [P] (Brogaard 2013, p. 278).

S’s seeming that P is grounded in a phenomenal content Q of an experience E that S has just in case (i) reliably, if Q is a content of S’s experience E, it seems to S as if P and (ii) reliably, if it seems to S as if P, P is true. (i) can be understood as: in most ‘hypothetical situations’ closest to the actual one in which Q is a content of S’s experience E, it seems to S as if P. (ii) prevents seemings from being grounded in the content of experiences by ‘sheer’ coincidence. (ii) does not require P to be actually true; it just requires P to be true in most of the closest ‘hypothetical situations’ where S has the seeming that P (Brogaard 2013).

Sensible dogmatism can explain the novice prospector case as follows: the novice is not justified in his belief that P because (i) is not met. Since the desire to find gold is not present in most of the closest possible situations where the novice has the same sensory experience of the pebble, this sensory experience does not lead him, in those situations, to have a seeming that the pebble is gold (Brogaard 2013). Another way in which sensible dogmatism can explain the novice case is this: suppose the novice’s desire is present in most or all of the closest possible situations where he has the sensory experience of the pebble, leading him to having the seeming that the pebble is gold even in cases where it is not so. Then, (ii) is not satisfied. For the content of his seeming that the pebble is gold would not be true in most of the closest possible situations where it would seem to him that the pebble is gold (Brogaard 2013). In conclusion, since the novice’s seeming that this pebble is gold is not grounded in the content of his experience, his seeming does not justify his belief that the pebble is gold. It is easy to see, on the other hand, that the expert prospector’s seeming is grounded in the content of his own experience, so this seeming justifies his belief (Brogaard 2013).

Given the reliabilist component of Brogaard’s position, sensible dogmatism appears to be an externalist view. Yet Brogaard insists that it is a weak internalist position, for the mental states that provide S with justification are accessible to S, though the factors that determine whether those mental states are justification-providing are not.

The reliabilist components of Brogaard’s position make it inherit problems from externalist reliabilism. Think for instance of the consequence of sensible dogmatism that the seemings of a Matrix’s victim would not provide her with justification because (ii) would not be met in the Matrix scenario (see Vahid 2014).

ii. The Imagining Account

Teng’s (2016) imagining account bases her defense of the downgrade thesis on a possible psychological explanation of how cognitive penetration is produced in a subject S presented in Macpherson (2012). Suppose S entertains a perceptual experience. According to Macpherson, one possible cognitive-penetration-causing mechanism involves the interaction of imagination and perceptual experience. In particular, it involves (i) the production of an imaginative experience by some mental state of S, and (ii) the interaction of this imaginative experience with S’s perceptual experience. The upshot is a novel phenomenal state of S with both the perceptual experience and the imaginative experience as contributors. As Teng emphasizes, since imaginative experiences are experiences in a sense fabricated by S, the phenomenal states resulting from a combination of an imaginative experience and a perceptual experience of S are to be considered to be partly fabricated by S as well. Cognitively penetrated experiences could be states of this type.

Teng finds it intuitive that an experience of S supplies S with prima facie justification for believing its content only if S does not fabricate (consciously or unconsciously) the experience. She infers from this that no imaginative experience of S could be a prima facie justification-provider. Teng concludes that since any cognitively penetrated experience of S is partly fabricated by S, it must be epistemically downgraded with respect to the fabricated part (Teng 2016).

A potential difficulty of this account concerns the explanation of the cases of good cognitive penetration. Teng submits that these cases might be explained by mere attentional shifts of S involving no imagining and capable of rendering certain objective features of the world more salient to S. She also suggests that S’s imagining might explain some specific cases of good cognitive penetration. For imagining could occasionally facilitate the perception of independent reality rather than interfering with it. Consider for instance the following experiment:

J. Farah (1985 and 1989) asked her participants to detect the presence of a faint letter H or T in a square while the participants projected a mental image of H or T onto the same location. It turned out that their detection was more accurate when they were imagining the same letter than a different one (Teng 2016, p. 25).

iii. The Analogy with Emotions

Vance’s (2014) account explains why a perceptual experience can be downgraded by its inappropriate etiology through drawing an analogy between cognitively penetrated experiences and cognitively penetrated emotional states.

Suppose S has an unjustified background belief that all foreigners are dangerous. One day S meets some foreigners and her background belief causes S to feel fear. Had she not had her unjustified belief, she would not have felt fear. On the basis of her fear, she forms the belief that the people before her are dangerous. Her fear is in this case downgraded: it cannot provide justification for her belief that those people are dangerous because it is grounded in a belief constituting a defective reason for her feeling. When emotions are grounded in such a defective way, their justificatory power decreases or ceases (Vance 2014). An emotional state with an etiology starting with a non-defective reason for the emotion could nevertheless be a justification-provider. For instance, S’s fear of a snake that S spots in her trail caused by her justified background belief that snakes are dangerous can provide S with justification for believing that walking on the trail is unsafe (Vance 2014).

Vance stresses that emotional states and perceptual experiences share extrinsic properties—such as psychological and epistemic features of their etiological structure—and intrinsic properties—such as their intentional character and distinctive phenomenology. From this, he derives that perceptual experiences, as well as emotions, can be downgraded with respect to their justificatory power. He submits that, in analogy with emotional states, this typically happens when perceptual experiences are grounded in unjustified beliefs.

A possible criticism of Vance’s account is that it is controversial whether the similarities between emotions and experiences could outweigh their differences in such a way that they both turn out to be rationally assessable states and in a similar way (Silins 2016).

iv. The Sensorimotor Theory of Perception

Vahid’s (2014) account of the cognitive penetrability problem and defense of the downgrade thesis rely on a conception of perceptual experience different from the traditional ones that conceive of perception as something given to us. Vahid’s conception is part of the extended cognition view of mental processes, which maintains that mental processes are partly constituted by environmental components situated out of the subject’s body. Think of Otto—a memory-impaired man—who uses his notebook to take notes that help him remember things he would otherwise forget. Otto’s cognition can be said to have been extended to his notebook.

While, on the received view, the notebook is not part of Otto’s cognitive processes, [the extended cognition thesis] takes Otto and his notebook to form a cognitive system where the information stored in the notebook functions as Otto’s non-occurrent, dis-positional beliefs. Cognitive processes are not, thus . . . purely in the head (Vahid 2014, p. 453).

Similarly, perceptual experiences may not be only in the subject S’s head. The sensorimotor theory of perception—one of the extended perception accounts—turns on the thought that perceptual experience is not just produced by S’s brain processes but is constituted by the ways in which these processes enable S to interact with her environment. In this account, S’s perceptual experience depends on both the features of S’s perceptual apparatus and those of the world to which this apparatus is sensitive.

[W]hen looking at a red apple, the sensation of seeing the apple . . . merely consists in our understanding or knowledge of a class of relevant counterfactuals, e.g., that if one were to move one’s eyes or body with respect to the apple, the sensory signals change in a way characteristic of red, rather than green, apples. One’s experience of seeing a red apple just is the knowledge of the class of the relevant sensorimotor contingencies (Vahid 2014, pp. 454–455).

In this view, perceptual experiences result from S’s expectations, assumptions, suppositions, understanding or implicit knowledge about what would happen in terms of new inputs from the world if S interacted in specific ways with the things the perceptual experiences are about (see Vahid 2014). (This theory is closely related to a model of the mind called predictive coding—see Hohwy 2012 and Clark 2013.)

To understand Vahid’s account of the cognitive penetrability problem, let us go back to Expert and Novice and Angry Jack. Vahid maintains that only the expert has implicit knowledge of the counterfactuals describing the perceptual consequences of his interaction with the nugget—or, at least, that the expert’s knowledge of them is more thorough than the novice’s. So, when faced with a gold nugget, the two prospectors actually have different cognitively penetrated experiences. For the expert’s experience is constituted by more numerous and detailed perceptual expectations than those of the novice’s experience. This enables us to distinguish the good cognitive penetration of the expert’s perceptual experience and the bad cognitive penetration of the novice’s perceptual experience. Angry Jack is interpretable along similar lines. Jill’s initial unjustified belief that Jack is angry penetrates her experience of Jack’s face by producing in Jill all the typical perceptual expectations that constitute perception of anger. In this case, we can say that Jill’s perceptual experience is badly penetrated because most of her expectations are mistaken (Vahid 2014).

Why is the novice’s belief that the nugget is gold not justified by his perceptual experience? And why is Jill’s belief that Jack is angry not justified by her experience? To answer these questions Vahid appeals to an explanationist conception of epistemic justification according to which a proposition is justified as long as it is the best available explanation of the subject’s evidence.

In the version of the angry-looking Jack case . . . the truth of Jill’s belief is not the best explanation of her incorrect expectations and assumptions that constitute her experience of seeing Jack’s face. Only correct expectations and suppositions reflect the facts about the external world . . . Likewise, in the gold-digging case, the truth of the novice’s belief that the pebble is gold is not the best explanation of his (thin) class of sensorimotor knowledge constituting his output experience as [the] less complex and simpler hypothesis [that the novice does desire to find gold] can discharge this function (Vahid 2014, p. 457).

See Ghijsen (2018) and Macpherson (2017) for discussion and criticism.

3. Conclusion

This article has provided an introductory map to the contemporary debate on the problem of cognitive penetrability of perception for epistemic justification. Internalist accessibilists typically do not concede that justification is hostage to cognitive penetration and put forward resolute responses to the cognitive penetration problem. On the other hand, externalist reliabilists together with some internalists from the mentalist camp concede that cognitive penetration may affect justification negatively and attempt to provide explanations of why and how this can happen. There are a few alternative accounts of the cognitive penetration problem that cannot easily be classified within the internalism-externalism framework.

4. References and Further Reading

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  • Brogaard, Berit. 2013. “Phenomenal Seemings and Sensible Dogmatism.” In Chris Tucker (ed.), Seemings and Justification. Oxford: Oxford University Press.
  • Brogaard, Berit. 2018. “Bias-Driven Attention, Cognitive Penetration and Epistemic Downgrading.” In Christoph Limbeck and Friedrich Stadler (eds.), Philosophy of Perception. Publications of the Austrian Ludwig Wittgenstein Society. De Gruyter.
  • Chudnoff, Elijah. 2019. “Experience and Epistemic Structure: Can Cognitive Penetration Result in Epistemic Downgrade?” https://philpapers.org/archive/CHUEAE-2.pdf (accessed on 1/5/2019).
  • Clark, Andy. 2013. “Whatever Next? Predictive Brains, Situated Agents, and the Future of Cognitive Science.” Behavioral and Brain Sciences 36: 3, 181–204.
  • Connolly, Kevin. 2017. “Perceptual Learning”. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/sum2017/entries/perceptual-learning/.
  • Farah, Martha J. 1985. “Psychophysical Evidence for a Shared Representational Medium for Mental Images and Percepts.” Journal of Experimental Psychology 114:1, 91–103
  • Farah, Martha J. 1989. “Mechanisms of Imagery-Perception Interaction.” Journal of Experimental Psychology: Human Perception and Performance 15:2 pp. 203–211.
  • Fumerton, Richard. “Siegel on the Epistemic Impact of “Checkered” Experience.” Philosophical Studies 162:3, 733–739
  • Ghijsen, Harmen. 2016. “The Real Epistemic Problem of Cognitive Penetration.” Philosophical Studies 173:6, 1457–1475
  • Ghijsen, Harmen. 2018. “Predictive processing and foundationalism about perception.” Synthese. Open access. https://doi.org/10.1007/s11229-018-1715-x
  • Goldman, Alvin I. 1979. “What is Justified Belief?” In George Pappas (ed.), Justification and Knowledge. Dordrecht: Reidel.
  • Hansen, Thorsten., Olkkonen, Maria., Walter, Sebastian and Gegenfurtner, Karl R. 2006. “Memory Modulates Color Appearance.” Nature Neuroscience 9:11, 1367–1368.
  • Hohwy, Jakob. 2013. The Predictive Mind. Oxford: Oxford University Press.
  • Huemer, Michael. 2001. Skepticism and the veil of perception. Lanham, MD: Rowman and Littlefield.
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  • Macpherson, Fiona. 2017. “The relationship between cognitive penetration and predictive coding.” Consciousness and Cognition 47, 6–16
  • Markie, Peter J. 2005. “The mystery of direct perceptual justification.” Philosophical Studies 126, 347–373.
  • Markie, Peter J. 2006. “Epistemically appropriate perceptual belief.” Noûs 40:1, 118–142.
  • Markie, Peter J. 2013. “Searching for true dogmatism.” In Chris Tucker (ed.), Seemings and Justification. Oxford: Oxford University Press.
  • McGrath, Matthew. 2013a. “Siegel and the Impact for Epistemological Internalism.” Philosophical Studies. 162, 723–732
  • McGrath, Matthew. 2013b. “Phenomenal Conservatism and Cognitive Penetration: The “Bad Basis” Counterexamples.” In Chris Tucker (ed.), Seemings and Justification. Oxford: Oxford University Press.
  • Pappas, George. 2014. “Internalist vs. Externalist Conceptions of Epistemic Justification.” In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/fall2017/entries/justep-intext/.
  • Payne, Keith B. 2001. “Prejudice and Perception: The Role of Automatic and Controlled Processes in Misperceiving a Weapon.” Journal of Personality and Social Psychology 81:2, 181.
  • Poston, Ted. 2018. “Internalism and Externalism in Epistemology.” Internet Encyclopedia of Philosophy. https://www.iep.utm.edu/int-ext/
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  • Raftopoulos, Athanassios and Zeimbekis, John. 2015. “Cognitive Penetrability of Perception: An Overview.” In Athanassios Raftopoulos and John Zeimbekis (eds.), The Cognitive Penetrability of Perception: New Philosophical Perspectives. Oxford University Press.
  • Siegel, Susanna. 2012. “Cognitive penetrability and perceptual justification.” Noûs 46, 201 –22.
  • Siegel, Susanna. 2013a. “The Epistemic Impact of the Etiology of Experience.” Philosophical Studies 162:3, 697–722.
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  • Siegel, Susanna. 2015. “Epistemic Evaluability and Perceptual Farce.” In Athanassios Raftopoulos and John Zeimbekis (eds.), The Cognitive Penetrability of Perception: New Philosophical Perspectives. Oxford University Press.
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Author Information

Christos Georgakakis
Email: c.georgakakis@abdn.ac.uk
University of Aberdeen
United Kingdom

and

Luca Moretti
Email: l.moretti@abdn.ac.uk
University of Aberdeen
United Kingdom

Simone Weil (1909—1943)

Weil photoThe French philosopher Simone Weil is a confronting and disconcerting figure in modern philosophy. This is not simply because she was so many things at once—ascetic and mystic, teacher and factory worker, labour activist and political militant, social thinker and piercing moral psychologist, critical Marxist and heterodox Christian theologian—but because of the striking “untimeliness” of her thought. For unlike philosophers in the analytic tradition, she insisted that life and philosophical reflection are connected on the deepest ethical level; and, unlike those in the postmodern tradition, she felt free to draw on terms like “truth,” “reality,” “the sacred,” “justice,” “soul,” and “God.”

Weil, of course, was not an analytic philosopher, nor a proto-postmodernist. She came to philosophy in the interwar years in a philosophical milieu of political radicalism, phenomenology, and emerging existentialism. As did most of her contemporaries, she saw philosophy in terms of the nature and challenges of the human condition, though she differed from the existentialists as to what this meant.

Whereas Jean-Paul Sartre and Simone de Beauvoir saw things in terms of the individual’s radical freedom to choose their values in a Godless world, Weil took a different path. Her concern was not to perfect herself as a replacement God figure, creating values out of a supposed absolute freedom, but to face up to, to have attended to, the real existence of other people. Whereas the existentialism of Sartre saw him faced with the challenge of showing how morality was even possible, Weil took the possibility of morality as a given—as an essential and fundamental modality of human life and experience, however partial and flawed its manifestations—and sought to show what it was to take morality seriously.
Taken that way, moral life rested on our capacity to care for others, where this meant to care for them as they were, and not as a means or obstacle to any end of our own, even that of our moral perfection or virtue. To refuse this attention was to read the world so that nothing and no-one was sacred, not even oneself. This reading gave us the world of power and so the sovereignty of force, and it was the ultimate logic of force “that it turn[ed] anyone subject to it into a thing.”
Such a reading of the world denied the ethical, yet equally it was precisely this denial the ethical sought to overcome. Here, for Weil, was a fundamental contradiction at the heart of ethical life. It was not a contradiction that meant the impossibility of that life, rather it showed us that the ethical was, ultimately, and at its foundations, something supernatural.
This article looks at Weil as a moral philosopher in a tradition that runs through Plato to Kant: one who took morality with a seriousness, with an utter commitment, alien to those philosophers tempted by scepticism or, in reaction, by a desire to find some rational foundation on which to securely rest an otherwise threatened edifice.

Table of Contents

  1. Life
  2. Writings
  3. Suffering, Oppression, Liberty
  4. Affliction, Detachment, the Impersonal, and the Sacred
  5. Uprootedness and the Needs of the Soul
  6. The Moral Ground
  7. References and Further Reading
    1. Primary
    2. Biographical
    3. Secondary

1. Life

Simone Weil was born in Paris on February 3, 1909, the second of two children born to comfortably off agnostic and secular Jewish parents. Her father was a medical doctor, and her brother, the 3-year older Andre, would become one of the most renowned mathematicians of the 20th century.

From the start Weil was both intellectually precocious and morally disconcerting. The intellectual capacity ran in the family (indeed, at 14, Weil would have a personal crisis in the face of what she considered her brother’s far superior abilities), but the moral sensitivity was her own and showed itself in various ways (for instance, refusing at age 5 to accept a necklace as a present on grounds of the discriminatory nature of luxury, and the very next year refusing to eat more sugar than that allotted to French troops as they battled the Germans).

She was educated at a number of schools and by private tutors before attending the Lycée Henry-IV as a pupil of the greatest philosophy teacher of the period, Émile Chartier (“Alain”). In 1928, and at her second attempt, she gained admission to the Ecole Normale Superieure, beating Simone de Beauvoir into second place in the Exam for General Philosophy and Logic. She studied philosophy there, graduating in 1931 with a diplome d’etudes superieures on the basis of her thesis “Science et perfection dans Descartes.” The same year, she passed the French Civil Service Examination (the agregation) and was appointed to a girls’ secondary school in the regional centre Le Puy, where she taught until 1936, with many breaks to pursue union activities, investigate Communist labour organizations in Germany, and fight on the Republican side in the Spanish Civil War.

After burning her foot badly stepping into a camouflaged pot of hot cooking oil, she left Spain and spent time in Portugal, then Italy, where she had her first mystical experiences.

The outbreak of World War II saw her in Paris, then, after the German invasion, in Marseille, publishing essays and doing what she could for those, often Jews like herself, seeking escape from Vichy France and the Nazi threat. In 1942, she accompanied her parents first to Morocco, then to New York, though she herself, determined to contribute to the Free French cause, soon returned to Europe, now to London. Weakened by inadequate nutrition and anguish, she died of tuberculosis on the evening of August 24, 1943, and, while not a baptised Catholic, was buried in a pauper’s grave in the Catholic Section of Bybrook Cemetery in Ashford, Kent.

2. Writings

Weil’s writings (collected now in 20 volumes) were produced in a mere 15 years. Much—including much of that which is most widely known—was published posthumously. Most of the work published in her lifetime was in the form of short essays for small political and literary journals, addressed to particular audiences. Such writings form only a small part of her collected work.

During her short life, she was most widely known as a political writer of the Left, an unorthodox and critical Marxist. Her most important work in this genre (though unpublished until 1955) was Reflections Concerning the Causes of Liberty and Social Oppression (1934). Around 1935, and especially after her first mystical experience in 1937, her writings took what many believed to be a new, religious direction. These writings, essays, notebooks, and letters she entrusted to the lay Catholic theologian Gustave Thibon in 1942, when, with her parents, she fled France. With the editorial help of Weil’s spiritual consultant (and sparring partner) Fr. Perrin, selections of these writings first made Weil widely known in the Anglo-American world. The serious effort for a complete publication of all Weil’s writings was largely the result of Albert Camus’ discovery of Weil’s writings while an editor at Gallimard (in 1951, he called her “the only great mind of our time.”) In 1988, Gallimard completed publication of her writings.

3. Suffering, Oppression, Liberty

In Memoirs of a Dutiful Daughter, de Beauvoir reports her first and perhaps only personal interaction with Weil in, most likely, 1929. “A great famine had just begun to devastate China,” she writes, and:

I was told on hearing the news she [Weil] had wept; these tears commanded my respect even more than her philosophical talents. I envied her for having a heart that could beat right across the world. One day I managed to approach her. I don’t remember how the conversation began; she declared in no uncertain terms that one thing alone mattered in the world today: the Revolution that would feed all the people on earth. I retorted, no less peremptorily, that the problem was not to make men happy, but to find a meaning for their existence. She looked me up and down: “It is easy to see you have never gone hungry,” she said. Our relationship stopped there. (239)

In this small exchange we see much of that which would shape Weil’s thought. What was basic for human life, and so a philosophy that dealt with the concerns of such a life, was not a quest for meaning, but rather a search for sustenance, for food. The food required was, in the end, both physical and spiritual, for there were needs of the body and needs of the soul. First there was, however, the need for physical sustenance. It followed that the primordial caring constitutive of the ethical must look always and first to the physical needs of other human beings. “It is an eternal obligation toward the human being not to let him suffer from hunger when one has a chance of coming to his assistance.”

This eternal obligation (eternal because constitutive) placed us as human beings into a shared community of mutual obligations.

For the early Weil, this eternal ethical obligation seemed, as it did at the time to many others, to be clearly and equally a political obligation (“revolution”). The task was to comprehend and, so far as possible, to deliver a social order that, because it enabled us to attend to the material needs of others, allowed those needs to be met.

It was here she found Karl Marx essential. “Marx’s truly great idea,” she wrote, was “that in human society as well as in nature nothing takes place otherwise than through material transformations.” It followed that to effectively meet our fundamental obligation required we uncover “the material conditions which determine our possibilities of action… conditions… defined by the way in which man obeys material necessities in supplying his own needs, in other words, by the method of production.”

For Weil, Marx could be understood as attempting to bring about a social order that enabled all in it to live, and so to be treated as ends-in-themselves. As such, it had to be a society free from oppression; and so a society in which all could (and did) attend to others, rather than viewing them indifferently, or as facilitating or hindering some personal or sectional interest or goal.

The trouble with Marx was not his failure to see this, it was his failure to understand the ultimate roots of oppression, and so what it would mean to overcome it. Thus, he thought that what we had to do was encourage the productive forces of capitalism so that they broke asunder the chains of labouring necessity; and he thought that the way to do this was to banish private property and so the drive for surplus value extraction.

However, as she saw it, this was not enough, and she pointed out that Marx himself at times seemed clearly to appreciate this. For the roots of the oppression that diminished, even sometimes obliterated, our capacity to attend to the basic needs of others did not lie solely, even mainly, in the fact of private property. She made the point this way:

“In the factory”… [Marx] writes in Capital, “there exists a mechanism independent of the workers, which incorporates them as living cogs… The separation of the spiritual forces that play a part in production from manual labour, and the transformation of the former into power exercised by capital over labour, attain their fulfilment in big industry founded on mechanization. The detail of the individual destiny of the machine-worker fades into insignificance before the science, the tremendous natural forces and the collective labour which are incorporated in the machines as a whole and constitute with them the employer’s power.” Thus the worker’s complete subordination to the undertaking and to those who run it is founded on the factory organization and not on the system of property [emphasis added]. (OL 9-10)

For Weil, the logic of “the factory system” that Marx had pointed to, even as he had missed its importance, was not limited simply to that system. It was, rather, a matter of the division—inherent to any social order above the most rudimentary—between intellectual and physical labour. This division was, at the same time, a division between people, dividing the human world into “two categories of men: those who command and those who obey.” This division undermined the foundations of ethical life because those who commanded could not avoid “reading” those they ordered about as—in the light of their being ordered about—means (or obstacles) to the desired ends. Such power over others as instruments or obstacles did two things to those who wielded it: it “intoxicated” them so that they no longer saw their own vulnerability before the necessities and contingencies of the world (their “ultimate fragility”), nor did they see, because of this intoxicated blindness, the humanity (and so the suffering) of those they lorded it over.

Still, as she saw it at this stage (before her discovery of the “enigma” of affliction), this did not mean that the capacity to attend to, and to care for, the suffering of others demanded “a miracle,” and so was something “supernatural.” What it demanded was, rather, a certain technique of compassion. “Human beings,” she wrote, “are so made that the ones who do the crushing feel nothing; it is the person crushed who feels what is happening.” If, in such a world—that is to say, in our world—ethical life was to find its footing, the challenge was clear: “unless one has placed oneself on the side of the oppressed,” she wrote, unless one “feel[s] with them, one cannot understand.”

4. Affliction, Detachment, the Impersonal, and the Sacred

At this point, for all its elegance and clarity, Weil’s moral philosophy was, ultimately, nothing out of the ordinary. Ethical life presupposed caring for others; and caring for others counted most essentially when others were in need, and so when they were suffering. The moral task was to let it register as it registered in and on the suffering one. It demanded an attentive compassion, understood as “the rarest and purest form of generosity.”

As an intellectual or theoretical stance, all this was unobjectionable, even admirable. However, it could not be simply and completely an intellectual or theoretical stance, for ethical life was also and fundamentally, a practical matter. Marx himself had insisted on this. He said, “the philosophers have only interpreted the world in various ways; the point, however, is to change it.” To change it in an ethical direction and from an ethical stance, however, one had to do more than simply say or think that one understood the oppression, and so the suffering, one sought to identify, alleviate, and eliminate. This was the problem with “the major Bolshevik leaders,” for they pretended “to create a free working class and yet none of them—definitely not Trotsky, and neither I think, Lenin… have… stepped foot into a factory and therefore have the least idea of the real conditions which determine the servitude or freedom of the workers.”

Obligations might be acknowledged, even fought for in revolutionary struggle, but to be truly recognised as the obligations, they had to penetrate. The point was particularly clear with suffering. For to acknowledge suffering as an ethical reality, it was not enough to endorse the description “so and so is suffering,” for that might be done by an entirely disinterested or impartial observer; rather, one needed to be penetrated by that suffering, and, out of the practical necessity involved in that penetration, to do what one could to meet the obligation that suffering imposed.

Here lay the real problem, and one that only came home to Weil when, in an effort to live up to and to live out her ethical vision, she went to work with those she saw at the time as most clearly as of the class of those “who obey”: oppressed, menial, piece-working factory labourers. In this decision and project, she meant to place herself “on the side of the oppressed,” to “feel with them,” and so to understand and to act. Here she would live—and in living, demonstrate—the fundamental penetrative point of the ethical, of obligation, in (and into) the realm of force.

What happened, however, was that she found—in others and in herself—something that seemed to tear the realm of force and the ethical life irretrievably apart: she discovered that suffering that is affliction (malheur, literally “calamitous misfortune”). The suffering “seared the soul.”

It was affliction that turned her moral philosophy away from the conventional and that led her to speak of ethical life in religious terms; and it was affliction that made, or allowed, her to see that what made a human being sacred, what made them the kind of being whose suffering counted, was no ascriptive empirical fact about them, no matter how essential to their “personality,” but was, rather, the impersonal in them.

Affliction was suffering that robbed its bearer of all dignity, both in the eyes of others and in their own eyes. It left them “mutilated,” valueless, worthless. It involved the twinned and catastrophic impact of physical pain (which might be simply the fear of such pain), and social humiliation, social degradation. Affliction, she wrote in a letter to Father Perrin, “takes possession of the soul and marks it through and through with its own particular mark, the mark of slavery,” and it was what she found, in her co-workers and so in herself, as they laboured for Alsthom and Renault. “The affliction of others entered into my flesh and my soul… There I received forever the mark of slavery” (WG 66-67).

What this experience showed her was that her initial political reading of the conditions essential to the morality of attentive caring was ultimately a superficial one: one that did not take morality and its demands on us seriously enough. While there was no doubt that things could be done to reduce the opportunities and occasions for suffering, affliction showed us that human identity, and so the human sense of self dignity and the dignity of others, was inherently fragile, able to be shattered at any time by the unforeseen contingencies of necessity and force that left “the victim writhing on the ground like a half-crushed worm,” “like a butterfly pinned alive into an album.” Unless this terrible and eternal fact had been allowed to penetrate us, even the best-intentioned reforms, even especially those driven by revolutionary righteousness, would produce, in due course, their own half-crushed worms, their own pinned-alive butterflies.

To take morality seriously meant taking affliction seriously, for if suffering mattered at all, it certainly mattered here. It was just at this point, however, where everything was in the balance, that the inadequacy of her previous understanding revealed itself, for with affliction caring attention—being penetrated by the object—was “impossible.” In the essay “The Love of God and Affliction”, she wrote that the afflicted:

…have no words to express what has happened to them. Among the people they meet, even those who have suffered much, those who have never had contact with affliction (properly defined) have no idea what it is. It is something specific, irreducible to any other thing, like sounds we cannot explain at all to a deaf-mute. And those who themselves have been mutilated by affliction are in no state to bring help to anyone at all, and nearly incapable of even desiring to help. (WG 120)

In fact, it was not simply that those who had never experienced affliction could not comprehend it, it was that any normal, “healthy” human being naturally fled from such recognition, from such penetration: “thought flees from affliction as promptly, as irresistibly, as an animal flees death,” and it did so for a like reason—for affliction manifested that force that turns a human being into a thing. It might not do so by killing outright, but—in a way even more shocking—it managed the paradoxical horror of “turn[ing] a human being into a thing while he is still alive.”

To care for the afflicted, to have been penetrated by affliction, and so to have enacted and lived that point where ethical life meets force (and—the same thing—to make real the point where justice meets and condemns slavery), was to love “where there is nothing to love.” This was why “when compassion truly produces itself, it is a miracle more astonishing than walking on water, healing the sick or even the resurrection of the dead.”

To understand the miracle that gave ethical authority power in a world of amoral force and necessity meant understanding what it was “to love human beings in so far as they come to be “read” by themselves and others “as nothing.”

This idea of attending to, of caring for, and so being penetrated by, a suffering that removed from its bearers “everything that makes us human” meant for Weil two things.

First, that what grounded our attention, our love, did not rest on or presuppose any positive (“valuable”) ascriptive fact about a person (for instance, their sense of rights, of freedom, their dignity or demand for respect, even their sense of hope or longing for the good). All these things, as she saw it, were matters merely of our “personality,” and it was our personality that, in affliction, was destroyed and annihilated. If there was to be any moral connection here, what was crucial could not be anything personal and individuating; as it were, something that stood there, able, as Eric O. Springsted put it, to “overcome circumstances, no matter how bad they are.” To the contrary, and as affliction showed us and the intoxication of power blinded us, “We possess nothing in the world—a mere chance can strip us of everything.”

And second, that to be penetrated by such suffering, such affliction, and so to recognise and respond to it, meant losing one’s own “personality,” one’s own individuality (“the power to say ‘I’”), and so to oneself experience the “void” of the living non-existence that is affliction. This was to be “de-created.” It was to accept the death, the absence, of all that made up our personality, and so to all that was particular in us that “attached” us to the world, and so made of it a kind of fantasy world, focally arrayed, and not something independent, impartially available, and so real. She wrote:

The reality of the world is the result of our attachment. It is the reality of the self which we transfer into things. It has nothing to do with independent reality. That is only perceptible through total detachment. Should only one thread remain, there is still attachment. (G&G 14)

Affliction destroyed the “I” of attachment, but it did not destroy or extinguish the possibility of ethical life and so the obligation to attend to such affliction. How could it? The void was real, as the necessity of avoiding, of fleeing, from it, brought home. It followed that the ultimate ground of value in us—the one that survived affliction insofar as it grounded an absolute obligation to meet and alleviate that personality annihilating suffering—was the “impersonal” in us, not the “personal.” In the 1933 essay “Human Personality,” she wrote:

Neither the person nor the human person in him or her is holy to me… Far from it: it is that which is impersonal in a human being. All that is impersonal in humankind is holy, and that alone. (SE 10,13)

Weil found it natural, even necessary, to speak of the impersonal in terms of our “soul,” and so of that which was “holy” in us, that which was “sacred,” and to view the de-creative capacity to attend to the impersonal in terms of “grace.” She found it equally natural, even necessary, to see the paradigm instance of this impersonality and its recognition, in the caring, afflicted, sacrifice of the Christ of the Crucifixion. However, just as often she spoke of the impersonal in terms of truth and (for her an aspect of the same thing) beauty, and it is this way of speaking that is perhaps the most instructive for philosophers, deriving as it does, and in her own unique way, from the philosopher she most valued, Plato.

For Weil, the pursuit of truth and our receptivity to beauty demanded, and so exhibited, the same kind of open, loving attention to the impersonal that was constitutive of the ethical life and its justice bringing gaze. She pointed, as she often did, to mathematical truth to explain the point. “If a child is doing a sum and does it wrong,” she wrote, “the mistake bears the stamp of his personality. [But] if he does the sum exactly right, his personality does not enter into it at all.” Her idea was that any error here would have to be explained in terms of something individual to the child calculator—for obviously a sum, being mistaken, could not explain itself. However, a sum done “exactly right” just was explained, and completely explained, by itself; it is what, by arithmetical necessity, emerged in an act of attention filled with, penetrated by, the relevant numbers and (so) their relationships. Here there was nothing essentially personal, as there was in any mistaken calculation, only the impersonal—and so universal—truth of the sum as revealed in an act of pure attention.

Of course, a sum done rightly possessed a beauty that one done wrongly lacked, and it was here truth and beauty came together. Not only because the perception or awareness of the beautiful demanded just that impersonal attention ethical life demanded, but—and this was the astounding and contradictory, indeed the redeeming aspect of affliction—because that which we selflessly attended to, that which we allowed to penetrate us as it was in itself, and so in all its truth, was, for that very reason, seen and experienced, even in the horrors of affliction, as (also, at the same time, eternally) beautiful. This, for Weil, was just how it was when it came to loving attention.

For Weil the internal tie between truth and beauty and loving attention—the tie that was constitutive, so “eternal,” in ethical life—found expression in the occasional miracles of compassionate awareness we might come across in life. However, we could find it expressed, too, in two works of supreme beauty: Homer’s Iliad, and the Gospels. In the authors of both, as they shaped their texts, we find expressed “the sense of human misery [that] was the precondition for justice and love.” Here was to be found “the incredible bitterness” of detached, sacred, justice as it penetrated into ethical void of the world of force.

In the Iliad, Weil wrote, this bitter justice:

proceeds from tenderness and that spreads over the whole human race, impartial as sunlight. Never does the tone lose its coloring of bitterness; yet never does the bitterness drop into lamentation. Justice and love, which have hardly any place in this study of extremes and of unjust acts of violence, nevertheless bathe the work in their light without ever becoming noticeable themselves, except as a kind of accent. Nothing precious is scorned, whether or not death is its destiny; everyone’s unhappiness is laid bare without dissimulation or disdain; no man is set above or below the condition common to all men; whatever is destroyed is regretted. Victors and vanquished are brought equally near us; under the same head, both are seen as counterparts of the poet, and the listener as well. (25)

Homer, in the Iliad, saw the infinite value and fragility of human life with a loving, “impersonal,” and (so) unsentimental compassion. He was penetrated by all—Greek and Trojan, defeated and momentarily victorious, Achilles and Priam—and, bathed in his impersonal love, fashioned from their lives an object of supreme, eternal, beauty.

5. Uprootedness and the Needs of the Soul

In December 1942, Weil arrived in London from New York, desperate to contribute to the cause of the Free French. In nine months, she would be dead.

In those months, she returned to the political concerns first broached in Oppression and Liberty. She did so reluctantly, and only because her proposal to train and lead a corps of front-line nurses had been rejected (de Gaulle, on reading her proposal, had exclaimed, “but she’s mad!”). Instead she was set to work analysing political documents sent to London from Resistance Committees in France, many of which concerned the reconstruction of France after the hoped-for Allied victory.

Weil’s contributions to this literature—Draft for a Statement of Human Obligation and The Need for Roots: Prelude towards a declaration of duties towards mankind—were never finally completed, but what was completed lets us see how she brought the moral seriousness she had developed and explored in the years since 1934 to those political concerns she had always had. While she may not have sought the task, she embraced it as a necessity. That was because while it was one thing, and a great thing, to have attended to the suffering and affliction of others, much of that suffering was the result of “social force,” and so the obligation to respond to that suffering had to address those forces. After all—as she had acknowledged from the start—morality at any stage beyond the socially rudimentary led inevitably to politics.

The very titles brought out, in a way only implicit in Oppression and Liberty, the untimeliness of her moral and political thought. For she did not begin with rights, nor with the ideal of liberal freedom encapsulated in Hobbes’ remark that a free man “is he that… is not hindered to do what he has a will to.” She built, rather, on the internal ethical connection between need and obligation:

Obligation is concerned with the needs in this world of the souls and bodies of human beings, whoever they may be. For each need there is a corresponding obligation: for each obligation a corresponding need. There is no other kind of obligation, so far as human affairs are concerned. (SE 21)

Needs and obligations were more fundamental than rights of any kind. Indeed, to think rights fundamental to “social conflicts” was itself a grave moral error, for it “inhibit[ed] any possible impulse of charity on both sides.” She continued:

Relying almost exclusively on this notion [“rights”], it becomes impossible to keep one’s eyes on the real problem. If someone tries to browbeat a farmer to sell his eggs at a moderate price, the farmer can say ‘I have the right to keep my eggs if I don’t get a good enough price.’ But if a young girl is being forced into a brothel she will not talk about her rights. In such a situation the word would sound ludicrously inadequate. (SE 21)

For Weil, rights were “middle level” moral concepts. They were not, and could not be, fundamental or “eternal.”

An obligation which goes unrecognised by anybody loses none of the full force of its existence. A right which goes unrecognised by anybody is not worth very much… Rights are always found to be related to certain conditions. Obligations alone remain independent of conditions. They belong to a realm situated above all conditions, because it is situated above this world. (NR 18)

The fundamental political obligation imposed equally on all of us, and just because of our shared humanity, was the obligation, according to our responsibilities and the extent of our power, to work to reduce to the barest minimum “all the privations of soul and body which are liable to destroy or damage the earthly life of any human being whatsoever.”

Her early claim, as de Beauvoir reported it, “that one thing alone mattered in the world today: the Revolution that would feed all the people on earth,” had deepened and ramified through her discovery of affliction. Affliction may have been grounded in our physicality, but it was much more than that. True affliction arose from “an event that grasps a life and uproots it attacks it directly or indirectly in all its parts—social, psychological, physical.”

Thus, to counter affliction it was not enough to propose a politics that met humanity’s bodily needs (food, shelter, warmth, rest, exercise, breathable air, and potable water), though all this was essential and basic; there had, too, to be a politics that met those needs of the soul crushed, violated, and extinguished, in the deracinated degradation of the afflicted. For while it was the “impersonal” in us that was sacred, this sacredness found its sacramental expression in just that concern for the attachments of the “I” that soul-wearing affliction obliterated. If affliction involved the uprooting of life, then countering it politically meant respecting the human need for roots.

“A human being,” Weil wrote, “has roots by virtue of his real, active and natural participation in the life of a community which preserves in living shape certain particular treasures of the past and certain particular expectations for the future.” This meant that the political challenge we faced—insofar as we concerned ourselves with justice, and not merely the demands, challenges, and threats of force—was immense. This was because “in an epoch like ours”—ruled by the worship of money, driven by a false (because force-centred) conception of greatness, and committed to an assertive, individualistic, “rights”-based (mis)conception of justice in the context of the loss of any living sense of “the sacred”—we were all of us uprooted. This is something that Marx and Weber had noted, too, but without understanding it as an ethical, and so a spiritual, sickness.

Weil had, by this time, no faith in revolutionary politics as the path to a more just, more rooted, human world. Indeed, she had come to see the hope, even the pursuit, of revolution as “the opium of the people.” A politics that recognised and so opposed affliction had to be a moral politics, and ultimately therefore a supernatural politics, for it was “only what comes from heaven that can make a real impress on the earth.” What was required—as an ideal, if never, here in the material domain, as a fully achievable actuality—was a politics, so a shared political vision, that embodied and expressed “poignantly tender feelings” for the “beautiful, precious fragile and perishable object” that is a human being.

This, for Weil, was a politics of equality, not the assertive competitive equality of rights (“to place the notion of rights at the centre of social conflicts is to inhibit any possible impulse of charity on both sides”). It was the political equality of the universal, the eternal, mutual community of needs-based human obligations. Equality, she wrote, “consists in a recognition, at once public, general, effective and genuinely expressed in institutions and customs, that the same amount of respect and consideration is due to every human being because this respect is due to the human being as such and is not a matter of degree.”

Such a world, such a political society, was not, nor could it be, a world entirely without force, a world without those who give orders and those who obey. The very point of the ethical life, of justice, was to bring that life, that justice, to the recalcitrant material world of force and power; it was not to annihilate it in its own orgy of affliction producing, because affliction is blind, power.

What mattered was that the division between order and obedience, between intellectual and physical labour, was absolutely minimised, and that the division that remained rested in the real consent of those who, here, obeyed. A clear and instructive instance of such consent was, she felt, to be found in friendship, for friendship was alive and real and meaningful only when “each wished to preserve the faculty of free consent both in himself and in the other.”

Placed on the level of politics, such a demand, Weil insisted, could only ever be answered in and from the contingencies of real political history. However, as a general point, and one deeply relevant to the modern centralising state and its uprooting capitalist economics, what was called for, what was demanded, was just that she had first pointed to in Oppression and Liberty: the cooperative and systematic decentralisation of society in such a way that no human being was deprived of the “relative and mixed goods (home, country, traditions, culture, etc.) which warm and nourish the soul and without which, apart from sanctity, a human life is impossible.”

Such a cooperative and systematic decentralisation would open up the possibility of our becoming rooted in the world, so in place and in history, in a way that linked and balanced particularity and universality, the local and the global.

That possibility, if it were to be real one, depended on our capacity to shape social force in ways that encouraged the conditions of mutual and attentive human respect, and so human self-respect. On one level, that simply meant organising our lives so as to facilitate the mutual and universal provision of our physical needs, but to be completed (and so to comprehend affliction), it had too to meet the needs of the soul. That, for Weil, meant balancing and harmonising what were, considered in themselves, antithetical needs. Indeed, it was just this antithetical character that allowed us to see the essential challenges for any politics of attention. Human beings, as beings free from the annihilating horrors of affliction, needed to organise themselves in such a way that they found an ordered world in which there was also individual freedom, a world in which there was true equality but also (for it was essential to any non-rudimentary social order) hierarchy, a world in which there was both the responsibility of command and necessity for freely provided consensual obedience, a secure world, but one that allowed for a certain level of risk, a world shaped by an absolute and fundamental concern for truth, but also one that allowed for a real freedom of opinion, and a world that had a place for both private and collective property. These antithetical but also complementary needs of the soul constituted the principles and the challenges of political wisdom. Only through their having real effect might we have any hope for a “flowering of fraternity, joy, beauty and happiness.”

6. The Moral Ground

In one crucial sense, Weil had no time for traditional philosophical concerns for a “foundation” or a “ground” of morality and the ethical life. Any such efforts—like Kant’s attempt to ground the absolute obligation to treat people as ends-in-themselves in their “reverence for the [rational] Law,” or Aristotle’s attempt to ground our ethical concerns in the individual’s drive for self-development, or Hume’s attempt to derive ethical life from our “limited sympathies” in the context of more general prudential and utilitarian calculations—did not work and could not work. Any individual-centred account went astray from the start, for moral life was, at its heart, a matter of inter-human attention and care, while any account that, like Hume, viewed the essential inter-human aspect in terms of limited sympathies and local concerns was focally individualistic, and so provided no basis on which the “supernatural” universal mutuality of moral obligation might have arisen.

However, there was another sense in which Weil was concerned to find a ground for morality. For if she could not give an account of how the capacity for selflessly receptive attention to the suffering of others arose in and from the human condition, and so from human nature, then her moral vision would simply hang there, a fantasy interesting, if at all, only for what it revealed of its author’s personality.

Weil’s morality might invoke the supernaturalness of eternally binding human obligation, but it could only do this and avoid fantasy if that supernatural aspect had its origins in human nature, as indeed, Weil thought, it clearly did.

On what natural foundation then, on what natural primitive fact, did the human capacity, such as it was, to attend to the suffering, ultimately the affliction, of other people arise and (to the extent it did) develop? For Weil, the crucial point was that human beings—primitively, and all things being equal—reacted differently to “things” than they did to other human beings, and that this was the case because of a certain basic or fundamental “power” we exercised over each other. As she wrote in her early essay, “The Iliad or The Poem of Force”:

Anybody who is in our vicinity exercises a certain power over us by his very presence, and a power that belongs to him alone, that is, the power of halting, repressing, modifying each movement that our body sketches out. If we step aside for a passer-by on the road, it is not the same thing as stepping aside to avoid a billboard; alone in our rooms we get up, walk about, sit down again quite differently from what we do when we have a visitor. (5)

Consider the case of the passerby; and assume a primitive situation—one where we what we have is simply a passer-by, not (say) someone we already “read” as an enemy, means, or obstacle. When we see the other person, headed towards us and our path, we “hesitate” in a way we do not if we see, instead, a billboard in the way. There is, with the person, but not the billboard, a certain reciprocal power that modifies “each movement our body sketches out.” Here, in this primitive, “impersonal,” but reciprocity recognising reaction of human to human, is found “that interval of hesitation, wherein lies all our consideration for our brothers in humanity.”

For Weil, such impersonal recognition of the human is the primitive ground of that attention that fills the space “between the impulse and the act,” and in doing this makes the other real for us, one with us, and so one of us. It was, indeed, just this hesitation and the capacity for attention it expressed and opened up for further elaboration that embedded in our (inter)relationship that fundamental equality that meant consent was essential to justice between us. And—perhaps even more fundamental—it was an impersonal hesitation before the human that presupposed and acknowledged that which—through the de-creative powers of affliction—could be destroyed and annihilated by the impact of the “empire of force.” This primitive human perception/reaction, this attentive hesitation that recognised our reciprocity and (so) mutuality, expressed the eternal moral fact on which all of obligation arose and rested. For in our hesitation in the face of the passer-by, in their power to halt, repress, and modify each movement “our body sketches out,” lies an implicit recognition: the recognition of the “supernatural” fact that:

…at the bottom of the heart of every human being, from earliest infancy until the tomb, there is something that goes on indomitably expecting, in the teeth of all experience of crimes committed, suffered, and witnessed, that good and not evil will be done to him. It is this above all that is sacred in every human being. (SE 10)

It was here, “beyond space and time,” and as revealed in our primitive natural history, that Justice, that the Good, revealed itself in its eternal purity. It was here that Weil finally brought together her two most influential historical interlocutors, Kant and Plato. For the ground of our duty to treat others always and never merely as means, but ends in themselves, arose, not from “reverence for the (moral) law,” but from our primitive and reciprocal expectation that in the world, and so “in the teeth of all experience of crimes committed, suffered, and witnessed,” “good and not evil” will be done to us. This “indomitable expectation” is where morality enters the world of force and necessity. It is where the supernatural and the natural world make contact in the sacredness of the impersonal obligation to meet human needs.

7. References and Further Reading

a. Primary

  • Waiting on God. tr. Emma Cruwfurd, (Harper & Row, New York, 1973.)
  • Formative Writings: 1929–1941. eds. Dorothy Tuck McFarland and Wilhelmina Van Ness, (University of Massachusetts Press, 1987.)
  • Intimations of Christianity Among the Greeks. tr. Elisabeth Chas Geissbuhler, (Routledge Kegan Paul, London, 1957.)
  • Letter to a Priest. tr. Arthur Wills, (G. P. Putnam’s Sons, New York, 1954.)
  • The Need for Roots. tr. Arthur Wills, (Routledge Classics, London, 2002.)
  • Gravity and Grace. tr. Emma Crawford and Mario van der Ruhr, (Routledge Classics, London, 2002.)
  • The Notebooks of Simone Weil. tr. Arthur Wills, (Routledge, London, 2003.)
  • On Science, Necessity, & The Love of God. tr. Richard Rees, (Oxford University Press, 1968.)
  • Oppression and Liberty. tr. Arthur Wills and John Petrie (Routledge Classics, London, 2001.)
  • The Iliad, or the Poem of Force. tr. Mary McCarthy, Chicago Review 18:2 1965.
  • Simone Weil: First and Last Notebooks. tr. Richard Rees, (Oxford University Press, 1970.)
  • Simone Weil: Lectures on Philosophy. tr. Hugh Price, (Cambridge University Press, 1978.)
  • Simone Weil—Selected Essays: 1934–1943. tr. Richards Rees, (Oxford University Press, 1962.)
  • Simone Weil: Seventy Letters. tr. Richard Rees, (Oxford University Press, 1965.)
  • On the Abolition of All Political Parties. tr. Simon Leys, (Black Inc., Melbourne, 2013.)

b. Biographical

The deep connection between Weil’s thought and life has seen many authors explore her philosophy through her biography. Here are some of those.

  • Cabaud, Jacques, Simone Weil, (Channel Press, New York, 1964.)
  • Fiori, Gabriella, Simone Weil: An Intellectual Biography. tr. Joseph R. Berrigan, (University of Georgia Press, 1989.)
  • Gray, Francine Du Plessix, Simone Weil, (Viking Press, New York, 2001.)
  • McLellan, David, Utopian Pessimist: The Life and Thought of Simone Weil, (New York: Poseidon Press, 1990.)
  • Perrin, J.B. and Thibon, G., Simone Weil as We Knew Her. tr. Emma Craufurd, (Routledge & Kegan Paul, 1953.)
  • Pétrement, Simone (1976) Simone Weil: A Life. tr. Raymond Roenthal, (Pantheon, New York, 1977.)
  • White, George A., ed. (1981). Simone Weil: Interpretations of a Life, University of Massachusetts Press (1981.)
  • Yourgrau, Palle, Simone Weil, Critical Lives Series, (Reaktion Press, London, 2011.)
  • Weil, Sylvie, At Home with André and Simone Weil. tr. Benjamin Ivry, (Northwestern University Press, 2010.)

c. Secondary

  • Allen, Diogenes, Three Outsiders: Pascal, Kierkegaard, Simone Weil, (Wipf and Stock, Eugene, 2006.)
  • Blanchot, Maurice, The Infinite Conversation. tr. Susan Hanson, (University of Minnesota Press, 1993.)
  • Bell, Richard H., Simone Weil, (Rowman & Littlefield,1998.)
  • Chenavier, Robert, Simone Weil: Attention to the Real. tr. Bernard E. Doering. (University of Notre Dame Press, 2012.)
  • Dietz, Mary, Between the Human and the Divine: The Political Thought of Simone Weil, (Rowman & Littlefield, 1988.)
  • Doering, E. Jane, Simone Weil and the Specter of Self-Perpetuating Force. (University of Notre Dame Press, 2010.)
  • Doering, E. Jane, and Eric O. Springsted, eds. The Christian Platonism of Simone Weil, (University of Notre Dame Press, 2004.)
  • Finch, Henry Leroy, Weil and the Intellect of Grace, (Continuum International, New York, 1999.)
  • Irwin, Alexander, Saints of the Impossible: Bataille, Weil, and the Politics of the Sacred, (University of Minnesota Press, 2002.)
  • McCullough, Lissa, The Religious Philosophy of Simone Weil, (I. B. Tauris, London, 2014.)
  • Morgan, Vance G., Weaving the World: Simone Weil on Science, Mathematics, and Love, (University of Notre Dame Press, 2005.)
  • Moulakis, Athansios, Simone Weil and the Politics of Self-Denial. tr. Ruth Hein, (University of Missouri Press, 1998.)
  • Plant, Stephen, Simone Weil: A Brief Introduction, (Orbis Books, 2007).
  • Radzins, Inese Astra, Thinking Nothing: Simone Weil’s Cosmology, (Vanderbilt University, 2005.)
  • Rhees, Rush, Discussions of Simone Weil, (SUNY Press, 2005.)
  • Rozelle-Stone, Rebecca A., and Stone, Lucien, Simone Weil and Theology, (Bloomsbury, New York, 2013.)
  • Springsted, Eric O. (2010) Simone Weil and the Suffering of Love. Wipf and Stock Publishers.
  • Veto, Miklos, The Religious Metaphysics of Simone Weil. tr. Joan Dargan, (State University of New York Press, 1994.)
  • von der Ruhr, Mario, Simone Weil: An Apprenticeship in Attention, (Continuum, London, 2006.)
  • Winch, Peter, Simone Weil: “The Just Balance,” (Cambridge University Press, 1989.)

Author Information

Tony Lynch
Email: alynch@une.edu.au
University of New England
Australia

Haskell Brooks Curry (1900-1982)

Curry photoHaskell Brooks Curry was a mathematical logician who developed a distinct philosophy of mathematics. Most of his work was technical: he was the major developer of combinatory logic, which nowadays plays a role in theoretical computer science. This formalism was originally intended to be a basis for a system of symbolic logic in the usual sense, but the original system turned out to be inconsistent, and the core which was consistent later became a formalism that is a kind of prototype of the computer languages called functional, in which programs are allowed to apply to and change other programs. It is essentially equivalent to the lambda-calculus-calculus) of Alonzo Church. (See the article on λ-calculi in this encyclopedia.)

Curry’s work on combinatory logic led him to a notion of formal system which is different in some respects from the one which has since become standard. In addition, Curry became interested in proof theory, especially the work of Gerhard Gentzen. Curry wanted to use these ideas in his search for a consistent system of logic based on combinatory logic. Curry also did some work on computing in the early days, including work on the ENIAC (one of the first electronic computers) immediately after World War II. Finally, he also became known for a philosophy of mathematics that he called formalism, which he originally considered as denying mathematics as the science of formal systems (in his sense), but which he later extended to include formal methods in general. This idea of formalism is probably better thought of today as a form of structuralism.

Table of Contents

  1. Biography
  2. Combinatory Logic
    1. Beginning Period
    2. The Kleene-Rosser Paradox and its Aftermath
    3. Late Period (after World War II)
  3. Gentzen-style Proof Theory
  4. War Work and Computing
  5. Formalism: the Philosophy of Mathematics
  6. References and Further Reading
    1. Primary Sources
    2. Secondary Sources

1. Biography

Haskell Brooks Curry was born on September 12, 1900 at Millis, Massachusetts. His father was Samuel Silas Curry, president of the School of Expression of Boston, Massachusetts. The School of Expression was originally founded by Anna Baright in 1879 as the School of Elocution and Expression. It was renamed in 1885, after Anna Baright married Samuel Silas Curry. It became Curry College in 1943. His mother was Anna Baright, who was Dean of the School of Expression. He graduated from high school in 1916 and entered Harvard University with the intention of going into medicine. During his first year, he took a mathematics course at the suggestion of his advisor and did very well. In the Spring of 1917, the United States entered World War I, and Curry responded by enlisting in the army, becoming a member of the Student Army Training Corps on October 18, 1918. He felt he would never play a direct role in the war if he continued with his pre-medical course, so he changed his major to mathematics with the idea of going into the artillery. The war ended on November 11, 1918, and Curry left the army on December 9, 1918, but he kept on in mathematics, receiving his A. B. degree in 1920.

For the next two years he studied electrical engineering at MIT in a program that involved working half-time at the General Electric Company. Because he was usually interested in why an answer was correct when the engineers seemed interested only in the fact that it was correct, he decided that he would be better off pursuing a degree in pure science, and in 1922 he switched to physics. He returned to Harvard, where for the year 1922–23 he was a half-time research assistant to P. W. Bridgman, who later won the Nobel prize in physics. In 1924 he received his A.M. in physics (from Harvard). But by this time his interests had shifted still further, and he now switched to mathematics. (During this period, both of his parents died, his father dying in 1921 and his mother in 1924.)

He continued to study mathematics at Harvard until 1927, where he was a half-time instructor during the first semester of 1926-27 but otherwise studied full-time. He was also involved in the business affairs of his family, the School of Expression.

During this period, Curry had become interested in logic. Originally, all of his logic was reading on the side, and at one point he was supposed to be working on a dissertation on a topic in differential equations assigned to him by George D. Birkhoff. Furthermore, he was getting advice from various faculty members at Harvard and elsewhere to stay away from logic. This advice was especially strong from Norbert Wiener, who was at MIT and who was a member of the same birdwatching club as Curry. But Curry had become too interested in logic to stop thinking about it. He was especially interested in the first chapter of Principia Mathematica [Russell and Whitehead 1910-1913], which he started reading in 1922 when he was 21 years old, and where a system of propositional logic is defined by means of axioms and two primitive rules. The first one is detachment, which says that from not -p or q and from p to deduce q (this is equivalent to modus ponens, which says that from pq and p to deduce q). The second one is substitution, which says that given any formula, any formula obtained by substituting another formula for a variable can be deduced; for example, if from the formula pp, one can substitute ¬qr for p to get ¬qr¬qr. Curry noticed when he first saw this that the rule of substitution is much more complicated than detachment in the sense that today we would find it more complicated to implement in a computer language. In 1926-27, as a result of trying to analyze substitution down to its simplest elements, Curry had the idea for using operators which he called combinators, the term we still use today. He used these operators to analyze this rule of substitution, and he concluded that this idea might lead to a dissertation. When he took this idea to several professors, he got a different reaction than he had previously had about staying away from logic. This was especially true of Norbert Wiener at MIT, who said that his opinion had been that logic was a subject to be avoided “unless you had something to say,” and since Curry clearly had something to say, “strength to your right arm!”

However, there was no faculty member at Harvard who could supervise a dissertation on this topic. So Curry decided that it would be useful to teach for a year, and, after getting a recommendation for the position from George D. Birkhoff, assumed an instructorship at Princeton for the year 1927-28. During a library search there he found the paper by Moses Schönfinkel, [Schönfinkel 1924], a report of a talk given at Göttingen in 1920, which had clearly anticipated his ideas. Curry was shocked at this anticipation because he had thought his ideas were completely original, and he ran to the office of Oswald Veblen, who, although primarily a geometer, was interested in the foundations of mathematics and who was also the PhD supervisor of Alonzo Church, to tell him about the anticipation. Veblen calmed Curry down by saying, “Good, I am always glad when somebody has one of my ideas, for it shows that I am on the right track.” To find out more about Schönfinkel, Veblen then took Curry to see the Russian topologist Pavel Alexandroff, who was visiting Princeton that year. Alexandroff reported that Schönfinkel was in a mental hospital and was unlikely to resume his mathematical work, but that at Göttingen were several mathematicians, including Paul Bernays, who were probably betteer paced to discuss these topics. It was thus decided that Curry should go to Germany.

As part of an application for financial support for that trip, Curry wrote his first published paper, [Curry 1929]. Before leaving for Germany, Curry married, on July 3, 1928, Mary Virginia Wheatley of Hurlock, Maryland. (Virginia had been a student at the School for Expression, where they met.) After the wedding, the Currys left for Germany, where they spent the year 1928-29 at Göttingen. During that year, Curry first met the logician Alonzo Church, who was there for half the year.

That year at Göttingen was enough for Curry to complete his dissertation. His referee was David Hilbert, although he actually did most of his work with Paul Bernays, and he was examined on July 24, 1929. At this examination, Hilbert asked Curry a question on another topic (called automorphic functions), which Hilbert assumed that Curry would not know. As it happened, Curry had taken a course on that very subject at Harvard, and Curry was able to give a good answer. Hilbert responded by asking in great surprise, “Wo haben sie das gelernt?” (“Where did you learn that?”) The dissertation was published (in German) as [Curry 1930].

Curry now needed a job, and he took up a position as an Assistant Professor at the Pennsylvania State College (Penn State – Penn State became the Pennsylvania State University in 1953). Eventually, most people who knew Curry came to associate him with Penn State, but when he first went there he did not plan to stay long. He had been at Harvard, Princeton, and Göttingen, and at Penn State he felt cut off from most of his former academic community. Furthermore, in those days, Penn State did not support research. (Later, thanks partly to Curry’s influence, Penn State changed its policy, and it is now a major research institution.) But his arrival there coincided with the beginning of the great depression, and the demand for logicians in the academic world was not very high. So he remained and settled down at Penn State, staying there, with the exception of several leaves of absence, until his retirement in 1966. He progressed normally through the academic ranks, becoming an Associate Professor in 1933 and a full Professor in 1941.

Everybody who knew the Currys was aware of how friendly and helpful they always were. Curry always did more for colleagues and students than be a source of important ideas (although, of course, his ideas have been of tremendous importance). He was always willing to listen to anybody who wanted to talk to him, to discuss their ideas, and to give whatever encouragement he could. His office door was always open. Also well known wherever the Currys lived was the hospitality they both showed. There were always many parties and other, less formal, gatherings. Curry also had a playful sense of humor.

The first of his leaves of absence was a year at the University of Chicago in 1931-32 as a National Research Council Fellow. (The original award was supposed to extend into the following year, but the second year was cancelled for Curry because he had a job to go back to and there were other National Research Council Fellows who did not. It was, after all, the depths of the Great Depression.) In 1938-39, Curry was in residence at the Institute for Advanced Study in Princeton.

Otherwise, Curry spent the 1930s at Penn State teaching and carrying on his research. During this period he was on the reviewing staff of the Zentralblatt für Mathematik und ihre Grenzgebiete (1931-1939). In 1936, he became a founding member of the Association for Symbolic Logic; he was Vice President in 1936-37 and President in 1938-40 as well as being a member of the Council as ex-president during 1942-46.

During this period, the Currys also began their family: Anne Wright Curry (later Mrs. Richard S. Piper) was born on July 27, 1930, and Robert Wheatley Curry followed on July 6, 1934.

By the end of the 1930s, Curry was established as one of the most important mathematical logicians in the United States and, in fact, in the entire world. As such, he was asked to present his views on the nature of mathematics to the International Congress for the Unity of Science held at Cambridge, Massachusetts at the beginning of September 1939. The result was a long manuscript of which he presented a shorter version to the Congress, [Curry 1939]. A series of papers on the philosophy of mathematics began with this paper and continued for the rest of his life.

In the following year, 1940, Curry became a member of the Board of Trustees of Curry College, formerly the School of Expression, the institution of which his father had been president. He remained a member until 1951. Later, on June 5, 1966, the college presented him with the honorary degree of Doctor of Science in Oratory.

When the United States entered World War II, Curry decided to put logic aside for the duration of the war. From 1940 until 1942 he had been a member of the National Committee on War Preparedness of the American Mathematical Society and the Mathematical Association of America. On May 25, 1942, he left Penn State and went to the Frankford Arsenal, where he worked as an applied mathematician until January 1944; then he went to the Applied Physics Laboratory at Johns Hopkins University, where he remained until March, 1945. Next he went to the Ballistic Research Laboratories at the Aberdeen Proving Ground, where he stayed until September, 1946. During his last three months there, he was Chief of the Theory Section of the Computing Laboratory and for one month he was Acting Chief of the Computing Laboratory; it was during this period that he became involved with the ENIAC computer. As a result of this experience he was a consultant in the field of computing methods to the United States Naval Ordinance Laboratory from June 1, 1948 until June 30, 1949.

In September, 1946, Curry returned to Penn State. He wanted to pursue his work on electronic computers, and so he tried to interest the university in acquiring some computing equipment. He was unsuccessful in this. He persisted until a colleague pointed out to him that if he did succeed, he would probably be made head of the program without any increase in salary. He then decided that this colleague was right and gave up the attempt. This effectively limited him from pursuing computing theory.

He was, however, getting back to logic. In Amsterdam in the summer of 1948, during the Tenth International Congress of Philosophy, it was proposed to him that he write a little book of under 100 pages on the subject of combinatory logic for the new North-Holland series in logic. He felt that there was too much unpublished research on the subject to write such a short book, and so he sent them instead his philosophical manuscript from 1939 with a few minor revisions. This appeared as [Curry 1951]. But this idea did suggest to him the project that eventually led to his two volumes with the title Combinatory Logic [Curry and Feys 1958] and [Curry et al.1972]. Feeling that he needed a collaborator, especially one who was better than he was at exposition, he decided to work with Robert Feys, who had published some papers on combinatory logic. Curry thus obtained a Fullbright grant and spent the year 1950-51 at Louvain in Belgium. After his return to Penn State, he and Feys continued their work, and the manuscript of [Curry and Feys 1958] was completed in 1956. The book appeared in 1958, published by North-Holland.

Meanwhile, money finally became available at Penn State for graduate students. Edward J. Cogan first approached Curry before he left for Louvain, and worked with Curry after he returned in 1951, finishing his dissertation in 1955. Kenneth L. Loewen also studied with him during this period, but left to take an academic position elsewhere in 1954 and did not finish his dissertation until 1962.

After the completion of [Curry and Feys 1958] Curry turned his attention to Gentzen-style proof theory. He had done some previous work on this, including a series of lectures delivered at Notre Dame University in Indiana in April, 1948 (which resulted in his book [Curry 1950]), and he felt that it formalized the kind of reasoning used in the development of the part of combinatory logic as a system of logic in the usual sense, and so he felt that it should be settled before he began work on [Curry et al. 1972]. He thus began work on what became his book [Curry 1963]. This work was made easier when, in 1959, he became Evan Pugh Research Professor and was thus relieved of undergraduate teaching duties. The manuscript of [Curry 1963] was completed in 1961.

By this time, there were two more graduate students, Bruce Lercher and Luis E. Sanchis, both of whom completed their dissertations in 1963.

From February to September, 1962, the Currys took a trip around the world, visiting a number of universities where Curry gave lectures.

In 1964, Curry met two new future collaborators. J. Roger Hindley arrived at Penn State for a lectureship which served as something of a postdoctoral position after finishing his dessertation at Newcastle-upon-Tyne, and Jonathan P. Seldin arrived as a beginning graduate student. Curry was just beginning work on [Curry et al. 1972]. Unfortunately, Feys had died in 1961, and Curry, left to work alone, soon realized that he needed collaborators. In 1965, he invited Hindley to join him on the project.

In 1966, Curry retired from Penn State after being there for 37 years. He then went to Amsterdam, where for the next four years he was Professor of Logic, History of Logic, and Philosophy of Science, and also Director of the Instituut voor Grondslagenonderzoek en Philosophie der Exacte Wetenschappen, both at the university of Amsterdam. Seldin went to Amsterdam on a Graduate Fellowship from the United States National Science Foundation, and completed his dissertation in 1968, after which he joined Curry and Hindley as a co-author of the book they were then writing. Curry had one more graduate student in Amsterdam, Martin W. Bunder, who finished his dissertation in 1969.

The manuscript of [Curry et al. 1972], was completed in May, 1970, just before Curry retired from the University of Amsterdam. He returned to State College, Pennsylvania (the town in which Penn State is located), where he continued his mathematical work, writing reviews (especially for Mathematical Reviews) and occasional papers. John A. Lever wrote a master’s thesis with him there in 1977 after obtaining special permission from the university authorities to work under a retired professor. In 1971-72, Curry accepted a visiting position at the University of Pittsburgh. Otherwise, he and Virginia remained at State College, except for some occasional trips, until his death on September 1, 1982. Curry left his papers to the library at Penn State.

Curry’s hobby throughout his life was bird watching, and by the end of his life, Curry had a reputation as an amateur ornithologist.

2. Combinatory Logic

a. Beginning Period

Curry invented combinatory logic independently by analyzing the operation of the substitution of a well-formed formula for a propositional variable in the system of propositional logic of the first chapter of [Russell and Whitehead 1910-1913]. He intended combinatory logic to be a foundation for mathematical logic and perhaps also for all of mathematics. Much of the subject is extremely technical. This will be as non-technical an introduction as it is possible to write.

The basic idea here is that of a function, which is a mathematical operation which does something to an input. Thus, for example, there is the numerical function which squares its argument (i.e., multiplies it by itself). Mathematicians usually write that if f is the squaring function, then for each possible argument (input) x, f(x)=x2. Then, if this function is applied to the number 3, we get f(3)=32=9.

In combinatory logic, the application of a function to an argument, such as f(3), is written (f3) or f3. Also, the need for functions of more than one variable is avoided by allowing the value of a function to be another function. For example, suppose, in traditional notation, f(x,y)=xy. Then let g(x)=hx(y) where hx(y)=xy. Then f(3,y)=3y=h3(y). In combinatory notation, (gx)y=xy and (g3)y=3y. In this notation, we use association to the left for application, so that gxy=(gx)y.

This method of using only functions of one argument has come to be called currying, and the function g of the previous paragraph is often called (curryf). Curry himself learned of this use of his name in his last years, and he protested because he had gotten the idea from Schönfinkel, but this use of Curry’s name has stuck.

Other combinators are:

  1. The identity operator I, with the property that Ix=x.
  2. The constancy operator K with the property that Kxy=x. Thus, Cx is a constant function whose value for any argument is x.
  3. The compositor B, with the property that Bxyz=x(yz). This says that to apply Bxy to z, first apply y to z and then apply x to the result.
  4. The diagonalizer W with the property that Wxy=xyy.
  5. The distributor S with the property that Sxyz=xz(yz).

Note that I can be defined in terms of the other operators, since WKx=Kxx=x, so I=WK. Also, since SKKx=Kx(Kx)=x, I can be defined as SKK.

Now suppose we want to say that an operation, say addition, is commutative (i.e. the order of adding does not matter). The traditional way of writing this in mathematics is x+y=y+x. But this is not a property of x and y; it is a property of +. To say this in the language of combinatory logic, we would write +xy=+yx. Now suppose we have an operator C (for “commutator” with the property that (Cx)yz=xzy. Then +yx=(C+)xy, and we can say that + is commutative by writing (C+)=+. This operator C is called a combinator.

The defining rules for these combinators have been written above with the equality symbol, which is symmetric. But it is often useful to read these equations only from left to right. Then these equations would be called contractions, so that Ix contracts to x, Cxyz contracts to xzy, Kxy contracts to x, Bxyz contracts to x(yz), Wxy contracts to xyy, and Sxyz contracts to xz(yz). Terms are reduced to other terms by performing sequences of 0 or more contractions on subterms of the original term. For example, the reduction of SKKx to x is as follows:

SKKxKx(Kx)x.

(Here I am using the symbol ‘’ to indicate a reduction.) Note that there are some terms which cannot be reduced. These terms are said to be in normal form. On the other hand, some terms can lead to infinite reductions, for example

WWWWWW.

Curry decided to found mathematical logic on a system of combinators whose primitive combinators were B,C,K, and W. (He did not yet understand the role of S, which he got from Schönfinkel.) The part of combinatory logic that deals with the basic properties of the combinatory terms without reference to logical connectives and quantifiers is now called pure combinatory logic. He was going to add logical connectives and quantifiers until he had developed a complete system of logic; this part of the subject he called illative combinatory logic. This word “illative” is a word Curry coined himself, based on the Latin word illatum, the past participle of infero, which means “to conclude”.

He proved several important results in this context. First of all he proved that if X is any combination of combinators and the variables x1,x2,xn, there is a term F in which the variables x1,x2,xn do not appear such that Fx1x2xn=X. Curry used the notation [x1,x2,,xn]X for this F. For example, since SIIxIx(Ix)xx, we can take SII to be [x]xx. He also gave axioms for the system so that this F was uniquely determined by X and the variables in question. (The existence of such an abstract for every term X and all variables x1,x2,,xn is called combinatory completeness.) Another of the things he proved early on (in his dissertation) is that the basic system of combinators, without any axioms for any logical connectives or quantifiers, is consistent.

Using the notation of combinators, Curry wrote what is normally written (x)A as ΠX, where Xx=A. This operator Π was present in his dissertation, but none of its properties were developed there. Instead, Curry started writing a series of papers expanding combinatory logic to include not only this universal quantifier Π, but also P (for implication, so that PXY=XY, or if X then Y) and equality Q, so that Qxy means x=y. In 1934, Curry published [Curry 1934a] giving properties of P and Q.

b. The Kleene-Rosser Paradox and its Aftermath

In 1932, Curry learned of a paper by Alonzo Church, [Church 1932]. Church’s system was based on λ-abstraction, which forms terms from variables by application and abstraction: if x is a variable and M is a term, then (λx.M) is a term. (The outermost parentheses may be omitted if no confusion results.) For example, (λx.x2) is the squaring function, and (λx.x2)3=32=9. Here, (λx1x2xn.M), which is an abbreviation for (λx1.(λx2.(λxn.M))), plays the role of Curry’s [x1,x2,,xn]X. (For a complete introduction to both λ-calculus and combinatory logic, see [Hindley and Seldin 2008]. See also the article on λ-calculi in this Encyclopedia.) Also, the variables x in λx.M is called bound; variables not within the scope of a λ are called free.

Reduction for Church’s system is defined by a rule that Curry called (β): (λx.M)N contracts to [N/x]M, which is the result of substituting N for x in M, where other bound variables are changed to avoid capture. In ordinary predicate logic, this sort of change is made by changing (x)(x<y) to (z)(z<y) if a term in which x occurs free is substituted for y.

Note that reduction in Church’s system differs from reduction in combinatory logic in that if M reduces to N, then λx.M reduces to λx.N, but in combinatory logic the fact that X reduces to Y does not automatically imply that [x]X reduces to [x]Y, since subterms of X often do not really occur in [x]X.

In 1934, Curry received a letter from Rosser informing him that Kleene and Rosser had proved inconsistent the system of [Church 1932] and the system of [Curry 1934]. They did this by deriving Richard’s Paradox (See the article on Richard’s Paradox in this Encyclopedia.) in both systems.

Church and his students, Kleene and Rosser, then gave up on the idea of building a system of mathematical logic adequate for all of mathematics by basing the system on λ-terms. Instead, they took that part of Church’s system involving only λ-terms and treated it separately as the λ-calculus. (See the article on λ-calculi But Curry had a different reaction. He had always considered the possibility that some systems he would propose might be inconsistent, and so he reacted by beginning a careful analysis of the paradox with the idea of finding a way to define a consistent system.

This analysis lasted for several years, and by the time he took a leave of absence from Penn State to do applied mathematics for the U.S. government during World War II, he had developed a plan for research to look for consistent systems. He had already published [Curry 1941], and he had found a much simpler paradox (now known as Curry’s Paradox; see [Curry 1942b]). The plan he had developed was to look at three different kinds of systems, which differed in the logical connectives and quantifiers that were taken as primitive. The kinds of systems will be discussed here in the order Curry gave them in [Curry 1942a].

  1. Systems based on the theory of functionality. This was Curry’s idea, dating back to 1930, that led to type assignment. He wrote Fαβ for the predicate of functions which take arguments in α with values in β, and he intended FαβX to mean (x)(αxβ(Xx)). Nowadays, the category (or predicate) Fαβ is considered a type rather than a predicate, and is usually written αβ.
  2. Systems based on the theory of restricted generality. Curry had noted that most universal quantification is not absolute, but is over some restricted domain. (This seems obvious nowadays, but in the 1930s it ran counter to the generalising tendency of Frege and Russell.) He defined an operator Ξ to stand for this restricted quantification, so that ΞXY would stand for (x:X)(Yx), or (x)(XxYx) (where here x does not occur free in X or Y).
  3. Systems based on the theory of universal generality. These were systems based on Π and P, where ΠX meant (x)(Xx) (where x does not occur free in X) and PXY means XY.

In 1942, Curry assumed that these kinds of systems increased in strength in the order given above. The paper [Curry 1942a] was really an abstract of future research rather than a report on completed work.

In the late spring of 1942, Curry finally came to understand the combinator S. Rosser had published a paper on combinatory logic (based on different basic combinators from those Curry used), and he had shown how to define [x]X by induction on the structure of X. When Curry read this paper and translated the results into his own formalism, he realized why Schönfinkel had defined all combinators in terms of K and S, and he started to do the same. The use of S greatly increased the lengths of definitions of [x]X compared with Curry’s original definition, but greatly simplified the algorithm for building them. With computer implementation has come a reversal of values: an algorithm’s speed of action is now valued more than its simplicity or “beauty”.

c. Late Period (after World War II)

After World War II, when Curry returned to Penn State (For details, see the section of the Bibliography section of this article for Curry’s work during World War II.), he slowly got back into logic. He attended the Tenth International Congress of Philosophy in the summer of 1948, and as a result of a proposal made to him there, he decided to write a long work on combinatory logic, which he intended to include everything known on the subject. Feeling he needed a collaborator, he approached Robert Feys at Louvain in Belgium. Curry used a Fulbright which he was awarded for the year 1950-51 to start this work to start, and Curry and Feys continued to work on it after Curry returned to Penn State in 1951. Curry wound up working on this work and a second volume for most of the rest of his life.

The earliest work on this book was on the basic exposition. Curry and Feys completely revised the foundations of combinatory logic, and spent a lot of time explaining Curry’s approach to formal reasoning and formal systems. They then introduced Church’s λ-calculus, and gave a new proof and analysis of the Church-Rosser Theorem, which proves pure λ-calculus consistent. The book then took up combinatory logic itself, first pure combinatory logic and then illative combinatory logic. The book finishes with two chapters on the theory of fuctionality.

However, Curry soon began to start new research to be included. At first, this included work expanding the theory of functionality. There was always more than one such theory, and different theories depended on which terms could be what we would now call types, but which Curry called F-obs. There is the basic theory of functionality, in which types are formed from atomic types by the operation that forms Fαβ from α and β. (This is equivalent to forming the type αβ from α and β.) This system is easily proved consistent.

Then there is the full free theory of functionality, in which any combinatory term can be a type. Curry thought that this system was consistent, and in 1954 he tried to prove that consistency. He spent over four months at this attempt by trying to prove that if, from a set of typing assumptions ξ1X1,ξ2X2,,ξnXn (where X1,X2,,Xn may be any combinatory terms), one can prove ξX, then the deduction must take a certain specific form. After almost five months, he realized that if ξX is the conclusion of any deduction in this special form, then the term X is irreducible in some sense. But the sense involved was not the sense of reduction in combinatory logic, but rather the sense of λ-calculus. The difference is that in λ-calculus, if MN then λx.Mλx.N, which is what one would expect. But in combinatory logic, the fact that XY does not automatically imply that [x]X[x]Y, for subterms of X do not necessarily occur in [x]X.

For Curry, the fact that the term X in the conclusion of a deduction in the theory of functionality must be irreducible in the sense of λ-calculus was not very satisfactory. Curry usually thought in combinators rather than λ-terms. Thus, he set out to find a reduction among combinatory terms that would be more like λ-reduction. He began with λβη-reduction, which is λ-calculus in which the reduction rules include (α), the rule for changes of bound variables, (β), the basic reduction for λ-calculus, which says that (λx.M)N[N/x]M, the result of substituting N for x in M, and (η), the rule which says that if x is not free in M, then λx.MxM. He then defined strong reduction for combinatory logic that is equivalent to λβη-reduction. For technical reasons, he needed to take C as a primitive combinator instead of defining it as SKK as he had done previously, so now combinatory logic is usually defined by taking the three combinators I, K, and S as primitive combinators.

Curry soon managed to prove that the full free theory of functionality is, in fact, inconsistent. The book [Curry and Feys 1958] ends with a chapter including the proof that the full free theory is inconsistent and also some results that are true that were proved as part of the failed attempt to prove it consistent.

This volume also includes the first published proof of the Normal Form Theorem, which says that every term with a type has a normal form. (A term is said to be in normal form if it cannot be reduced. It is said to have a normal form if it can be reduced to a term in normal form.) This result has become more and more important in various systems of typed λ-calculi in the decades since this volume was published.

In the years immediately after the publication of [Curry and Feys 1958], Curry began to work on systems of restricted generality. But he only published a couple of papers on this before he began work on [Curry et al. 1972]. This volume begins with addenda to pure combinatory logic, most of which are highly technical. Curry did try to devise a general framework that would include both combinatory logic and λ-calculus by defining what he called C-systems. The idea was to set up a framework that could be used to prove results in illative systems that were based either on λ-calculus or on combinatory logic without having to give separate proofs for the two cases. But this attempt was not completely successful, since it was later found that many results still needed one proof for λ-calculus and another for combinatory logic.

Curry also extended the definition of illative combinatory logic to include any systems with new atomic constants that have special postulates associated with them, even if these new constants do not represent logical connectives or quantifiers. This allowed him to include systems of combinatory arithmetic. Arithmetic had first been represented by Alonzo Church in combinatory logic and λ-calculus by defining natural numbers as iterators: the number n is represented by λfx.f(f(f(fnx))), which applies f to x n times. But by the 1960s, other ways of representing numbers as combinators or λ-terms had appeared. For this reason, Curry suggested representing numbers by taking new atomic constants to represent 0 and the successor function (σ) and including a combinator that mapped one of these numbers to the corresponding iterator. With any of these representations, a function can be represented by a combinator or λ-term if and only if it is partial recursive, or, equivalently, Turing-computable. (This result was first proved for λ-calculus independently by Church, Kleene, and Turing in 1936; see, for example, [Kleene 1936c].)

Curry also considered extensions of the results on the theory of functionality, including the introduction of a new typing operator G with the rule that from GαβX and αY follows βY(XY), so that the type of the value of a function may depend on the argument as well as on the type of the argument. The type Gαβ is the type that is now usually denoted (Πx:α.βx), and is usually called the dependent function type. However, the type was only introduced, and no systems based on it were developed by Curry.

The rest of the book includes material on the theory of restricted generality and universal generality. It was shown that these kinds of systems are essentially equivalent. Systems were proved consistent that are essentially equivalent to first-order systems of logic by defining classes of canonical terms which are supposed to represent propositions and propositional functions. Attempts to find consistent systems in which the assumptions for terms to be canonical were stated as axioms of the logic were made, but most of the systems involved were later proved to be inconsistent. Finally, the theory of functionality was used to define systems of type theory in the traditional sense.

Curry spent the rest of his life continuing this work and other work he had done. The last problem he worked on was an attempt to find a reduction for combinatory terms that is equivalent to λβ-reduction, λ-reduction in which the contraction rules are only (α) and (β). As of this writing, this problem is not yet settled. See Seldin’s papers [Seldin 2011] and [Seldin 2017].

3. Gentzen-style Proof Theory

Curry read Gentzen’s work [Gentzen 1934] two years after it appeared, and it did not take him long to realize that the ideas of that paper could be useful in finding a system of logic based on combinatory logic that could be proved consistent.

Gentzen had introduced two new formulations of logical systems: natural deduction systems and sequent calculi (L-systems). Natural deduction systems are covered in the article Deductive-Theoretic Conceptions of Logical Consequence in this encyclopedia. Sequent calculi are equivalent to natural deduction systems and are designed to search for proofs.

The consistency of natural deduction systems for propositional calculus and first-order predicate calculus follows from what is called the normalization theorem (due originally to Prawitz, [Prawitz 1965]). This result is equivalent to a result of Gentzen on sequent calculi: the cut elimination theorem. Curry worked out his own proof of the latter theorem. He also used a version of it to give the first published proof of the normal form theorem for ordinary basic functionality. (A proof by Turing from 1941 was not published until 1980; see [Gandy 1980b].)

Curry became convinced that a system of formal logic is not properly formalized unless there is a sequent calculus for it for which the cut elimination theorem can be proven.

Another feature of Curry’s approach is that he considered these systems as formalizing the elementary metatheory of what he called an elementary formal system. An elementary formal system is one in which there are no rules which discharge assumptions. Curry had such a formal system for combinatory logic. He used the idea that he was formalizing the elementary metatheory of an elementary formal system to justify all the operational rules. This illustrates that Curry was concerned with semantics.

4. War Work and Computing

When Curry first left Penn State to do applied mathematics for the U.S. Government, he began working on the mathematics of aiming a projectile at a moving target, the so-called fire control problem. Curry had studied this kind of mathematics as a student, and so he had little trouble doing this work during World War II.

By 1945, when Curry was at the Aberdeen Proving Ground, there was word that an electronic computer, the ENIAC, was being built for the purpose of calculating firing tables for the artillery. Curry was named to the committee that was being set up to evaluate the ENIAC when it was delivered. This committee first met in July, 1945, and early that month Curry attended a lecture on the ENIAC by Herman Goldstine. The next day, he decided to write a program to calculate the digits of e, the base of the natural logarithms. He finished the program in early 1946, but whether it was ever run is uncertain. Curry later reported that nobody else that he knew at the time who was working on the ENIAC in 1946 could see the point of using a computer for a result assumed to be known.

In 1949, John von Neumann and some colleagues wrote and ran programs to calculate the digits of π and e. (See [Reitwiesner 1950a] and Reitwiesner et al. 1950b].) As a result, they discovered that the amateur mathematician William Shanks, who had spent over two decades starting in the middle of the 19th century calculating digits of π, and who had calculated to 707 digits, had made a mistake on digit number 528. The people who wrote the program in 1949 seem to have had no idea that Curry wrote such a program just a few years earlier. On the other hand, by 1949 there had been some changes in the ENIAC, and the program Curry wrote in 1945–46 might no longer have been compatible with the ENIAC.

Curry also became involved in writing programs to do inverse interpolation on the ENIAC, programs useful for dealing with firing tables. See [de Mol et al. 2010].

Curry’s work on programming inverse interpolation on the ENIAC led him to develop a theory of programming. Curry’s basic approach was very similar to the approach he had taken two decades earlier in analyzing the process of substitution. He broke programs down into the simplest possible elementary components and then proposed using program composition to put them together again. This approach has been compared to the later development of compilers for user languages. See [Curry 1954].

However, Curry was not able to continue to work on this development because he could not persuade Penn State to buy any computer equipment in the late 1940s.

5. Formalism: the Philosophy of Mathematics

Curry developed a distinctive philosophy of mathematics. His views developed considerably over the course of his career, but he is mostly known for his earlier works on the subject.

Curry’s earliest philosophical work, dating from 1939, proposed to define mathematics as the science of formal systems. But Curry’s approach to formal systems was not quite the same as that of most others in the field.

The usual definition of a formal system begins by defining the formal objects as words on an alphabet of symbols, or, to use the terminology more current in computer science today, strings of characters. But then some of these words are picked out as “well formed formulas” by an inductive definition with the property that each well formed formula has a unique construction from the “atomic formulas”. For example, for the propositional calculus, we are given a possibly infinite set of atomic formulas p1,p2,,pn,, and a typical definition of well formed formula goes as follows:

  • Every atomic formula is a well formed formula.
  • If P is a well formed formula, then ¬P is a well formed formula.
  • If P and Q are well formed formulas, then PQ, PQ, and PQ are well formed formulas.
  • Nothing else is a well formed formula.

If the logical system involved includes quantifiers, then the atomic formulas are themselves defined, and that definition may depend on inductive definitions. For example, if we are defining a formal system for first-order logic, we start with terms, which are built up out of atomic terms and individual variables by using basic functions, and then we have predicates, from which the atomic formulas are obtained by applying them to terms. If the first order system is a system of arithmetic, we start with the atomic term 0 and functions denoted by (as a superscript) and + and (as infixes), and then terms are defined as follows:

  • Every individual variable is a term.
  • 0 is a term.
  • If t is a term, then so is t. (This is intended to denote the number that is one more than t.)
  • If s and t are terms, then s+t and st are terms. (The term st is often abbreviated as st.)
  • Nothing else is a term.

Once terms have been defined, atomic formulas are defined as follows:

  • If s and t are terms, then s=t is an atomic formula.

And then the following clause is added to the definition of well formed formula:

  • If x is an individual variable and A is a well formed formula, then (x)A and (x)A are well formed formulas.

Curry noted is that although these definitions of term, atomic formula, and well formed formula say they are about strings of symbols on some alphabet, they do not really depend on that fact. For him, the crucial thing was that each term and well formed formula have a unique construction, whereas any word of three or more letters has more than one construction.(For example, the string abc can be formed in two ways: c can be added to ab on the right, or a can be added to bc on the left.) So while we obviously represent formal objects on a page or on a blackboard as strings of characters, it is not necessary that they actually be such strings. The strings may only be the names for these formal objects. It is only necessary that they are defined inductively so that each one has a unique construction.

Also, formal systems do not need to be systems of logic in the ordinary sense with logical connectives and quantifiers. It is possible to have a simpler formal system. An example Curry gave is what he called the “system of Sams” for natural numbers. (He got this name from the Hungarian word for number, which is szám.) In this system, the formal objects are interpreted as natural numbers. There is one primitive formal object, which I will name “0”. There is one operation, which forms X| from X. The rules for forming the sams are as follows:

  • 0 is a sam.
  • If X is a sam, then so is X|.
  • Nothing else is a sam.

There is one predicate, which forms X=Y from sams X and Y. Thus, the elementary statements are those of the form X=Y, where X and Y are sams. There is one axiom, namely

0 = 0

There is also one rule of inference: From X=Y to deduce X|=Y|. This is a very simple formal system, and it is easy to show that the theorems (provable elementary statements) are those of the form X=X, where X is a sam.

In saying that mathematics is the science of formal systems, Curry was claiming that (pure) mathematics does not really have a subject matter. It was not what he called a contensive topic. (The word contensive is a word Curry coined to express the idea of the German word inhaltlich.) Of course, mathematical statements do have subjects and therefore subject matter, but Curry claimed that the only subject matter any mathematical statements had was other mathematics.

Curry’s attitude towards truth was that truth comes in two kinds:

  1. Truth within a formal system (or within a given theory). This depends on how the system or theory is defined.
  2. The acceptability of a system (or theory) for some purpose. This depends on the purpose, and Curry took this pragmatically.

In his work on combinatory logic and Gentzen proof theory, he preferred to use only constructive logic in the metatheory, this would be accepted by more people than classical logic. (In this, he did not see that most mathematicians were not familiar with constructive mathematics.) On the other hand, he had no trouble accepting classical logic in the mathematics to be used in physics. In a sense, Curry did not really believe in one absolute notion of truth.

On the other hand, once formal systems (or any other kind of theories) are created, they have properties which can be investigated, and hence have objective existence. In this sense, Curry believed in the idea that Karl Popper introduced later of the third world. In fact, Popper presented this idea at a session of the Third International Congress of Logic, Methodology, and Philosophy of Science in Amsterdam in 1967, and as it happened Curry was the chair of the session. (See [Popper 1968].) After Popper’s presentation was over, Curry told his graduate student Jonathan P. Seldin, who was also present, that he thought that Popper had made a big deal out of something that was trivially and obviously true.

Over his career, Curry changed several times the words he used to denote the formal objects of a formal system. In his earliest work on combinatory logic, he called them “entities” (using the German word Etwas as a noun in his dissertation, which was written in German). However, in a discussion with a philosopher (whom he did not name in his later years), he was told that his use of that word implied some philosophical conclusions with which he disagreed. At that point, he decided to use the word “term” instead. It is now common to refer to “combinatory terms” and “λ-terms”. However, this caused him a problem when he was dealing with a formal system of logic with quantifiers, since the terms would be what are usually called “formulas”, and there are other formal objects called “terms”. So in the end, he coined his own word by taking the first syllable of the word “object”, and started calling them obs. To some people, the word ob appeared to refer specifically to combinatory logic, but in fact Curry used the word for formal objects of any kind of formal system.

In his later work, Curry extended his definition of formal system to allow for systems whose formal objects are strings of characters. He called such systems syntactical systems, and called his earlier kind of formal systems ob systems.

Also in his later work, Curry also extended his definition of mathematics from saying that mathematics is the science of formal systems to saying that mathematics is the science of formal methods. This definition should be sufficiently broad to include all of mathematics, since if we compare piles of apples and oranges by seeing if there is a one-to-one correspondence between them, we are looking at the forms of the piles rather than the content (apples or oranges).

Curry chose the name “formalism” for his philosophy of mathematics because of David Hilbert. However, Curry’s idea of formalism is very different from the idea of other philosophers of mathematics who call themselves formalists. It is probably better to think of Curry’s formalism as a kind of structuralism.

6. References and Further Reading

a. Primary Sources

  • [Curry 1929] Curry, Haskell B., An analysis of logical substitution”, American Journal of Mathematics 51, 363-384.
    • Curry’s first published paper, written as part of an application for a grant to go to Gottingen.
  • [Curry 1930] Curry, Haskell B., Grundlagen der kombinatorischen Logik”, American Journal of Mathematics 52 (1930) 509-536, 789-834.
    • Curry’s dissertation, written in German at Gottingen in 1928-1929. Republished with a translation into English and an introduction on Curry’s work by Fairouz Kamareddine and Jonathan P. Seldin as Foundations of Combinatory Logic by College Publications, 2016.
  • [Curry 1934a] Curry, Haskell B., Some properties of equality and implication in combinatory logic”, Annals of Mathematics (2) 34, 381-404.
    • This is the paper that gave Kleene and Rosser what they needed to prove inconsistent the systems of Church and Curry.
  • [Curry 1934b] Curry, Haskell B., Functionality in combinatory logic”, Proceedings of the National Academy of Sciences U.S.A., 20, 584-590.
    • An extended abstract of item 1936 below, which Curry had some trouble getting accepted for publication because the approach originally looked strange.
  • [Curry 1936] Curry, Haskell B., First properties of functionality in combinatory logic,” Tohoku Mathematical Journal 41 Part II, 371-401.
    • Curry’s first paper on functionality. He originally wrote it in 1932, but had trouble getting it accepted for publication. The version published in 1936 contains many misprints.
  • [Curry 1939] Curry, Haskell B., Remarks on the definition and nature of mathematics”, Journal of Unified Science 9, 164-169, and reprinted many times since.
    • Curry’s first work on the philosophy of mathematics.
  • [Curry 1941] Curry, Haskell B., The paradox of Kleene and Rosser”, Transactions of the American Mathematical Society, 50, 454-516.
    • Curry’s study of the paradox mentioned in the title.
  • [Curry 1942a] Curry, Haskell B., Some advances in the combinatory theory of quantication”, Proceedings of the National Academy of Sciences U.S.A. 28, 564-569.
    • This is the paper Curry wrote just before his leave of absence from Penn State to do war work in which he set out his plans to try to send consistent systems of logic based on combinatory logic.
  • [Curry 1942b] Curry, Haskell B., The inconsistency of certain formal logics”, Journal of Symbolic Logic 7, 115-117.
  • [Curry 1949] Curry, Haskell B., A simplication of the theory of combinators”, Synthese 7, 391-399.
    • The paper in which Curry published his understanding of the combinator S.
  • [Curry 1950] Curry, Haskell B., A Theory of Formal Deducibility, (Indiana University Press).
    • Curry’s first book on Gentzen-style proof theory.
  • [Curry 1951] Curry, Haskell B., Outlines of a Formalist Philosophy of Mathematics (Amsterdam, North-Holland).
    • This was mostly written in 1939 and is essentially the long manuscript from which the paper of 1939 was prepared as a shorter version.
  • [Curry 1954] Curry, Haskell B., The logic of program composition”, In Applications Scientiques de la Logique Mathematique, Actes du 2e Colloque International de Logique Mathematiques, Paris 25-30 Aout 1952, Institut Henri Poincare, (Paris: Gauthier-Villars and Louvain: Nauwelaerts). Curry’s summary of his theory of programming.
  • [Curry and Feys 1958] Curry, Haskell B. and Feys, Robert, Combinatory Logic, Volume I, (Amsterdam, North-Holland).
    • The first volume of Curry’s great work on combinatory logic.
  • [Curry 1963] Curry, Haskell B., Foundations of Mathematical Logic, (McGraw-Hill, and since reprinted by Dover).
    • Curry’s major work on Gentzen-style proof theory.
  • [Curry et al. 1972] Curry, Haskell B., Hindley, J. Roger, and Seldin, Jonathan P., Combinatory Logic, Volume II, (Amsterdam, North-Holland).
    • The second volume of Curry’s great work on combinatory logic.

b. Secondary Sources (by year)

  • [Russell and Whitehead 1910-1913] Russell, Bertrand and Whitehead, Alfred North, Principia Mathematica, 3 volumes (Cambridge University Press).
    • The first major work on logic that Curry read.
  • [Schönfinkel 1924] Schönfinkel, Moses, Über die Bausteine der mathematischen Logik”, Mathematische Annalen 92, 305-306.
    • A work that Curry first encountered in 1927-28 which, much to his surprise, had anticipated his own idea for combinators. The paper was written by Behman, and was a report on a seminar talk Schonnkel had given at Gottingen in 1920. An English translation has appeared as “On the building blocks of mathematical logic”, in From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, edited by Jean van Heijenoort (Harvard University Press, 1967), pp. 355-366.
  • [Hilbert 1925] David Hilbert, Über das Unendliche”, Mathematische Annalen 95 (1925) 161-190.
    • One of the most important papers Hilbert wrote on the foundations of mathematics. Reprinted (in German) in David Hilbert, Hilbertiana: Fünf Aufsätze (Darmstadt: Wissenschaftliche Buchgesellschaft, 1964), pp. 79-108. Translation into English published as “On the infinite” in Jean van Heijenoort (editor), From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, (Cambridge, MA and London, England: Harvard University Press 1967), pages 367-392.
  • [Heyting 1930] Heyting, Arend, Die formalen Regeln der intuitionistischen Logik”‘, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse 1930, 42-56.
    • The paper in which Heyting introduced his formal system of intuitionistic logic.
  • [Church 1932] Church, Alonzo, A set of postulates for the foundation of logic”, Annals of Mathematics (2) 33, 346-366.
    • The paper in which Church first introduced abstraction as part of a larger system.
  • [Gentzen 1934] Gentzen, G., Untersuchungen über das logische Schliessen”, Mathematische Zeitschrift 39, 405-431.
    • The paper in which Gentzen introduced his systems of natural deduction and his L-systems (sequent calculi).
  • [Kleene 1935] Kleene, Steven C. and Rosser, J. Barkley, The inconsistency of certain formal logics”, Annals of Mathematics (2) 36, 630-636.
    • The paper in which Kleene and Rosser published their proof of the contradiction in the systems of Church and Curry.
  • [Church and Rosser 1936a] Church, Alonzo and Rosser, J. Barkley, Some properties of conversion”, Transactions of the American Mathematical Society 39, 472-482.
    • The paper in which the Church-Rosser Theorem was first proved for lambda-calculus.
  • [Church 1936b] Church, Alonzo, An undecidable problem in elementary number theory’, American Journal of Mathematics 58, 345-363.
    • The paper in which Church proved that there is a problem in elementary number theory which cannot be decided by an algorithm. The paper includes a statement by Church that a function is partial recursive if and only if it can be represented by a -term, a result that he and Kleene obtained independently about the same time.
  • [Kleene 1936c] Kleene, Steven C., “-denability and recursiveness”, Duke Mathematical Journal 2, 340-353.
    • The paper in which Kleene first proved that a function is partial recursive if and only if it can be represented by a -term, a result he discovered independently at the same time Alonzo Church did. This formed part of the justication of the Church-Turing thesis, that a function is mechanically computable if and only if it is partial recursive if and only if it is Turing computable if and only if it is -denable.
  • [Rosser 1942] Rosser, J. Barkley, New sets of postulates for combinatory logics”, Journal of Symbolic Logic 7, 18-27.
    • Rosser’s paper that enabled Curry to understand the combinator S, although Rosser did not use that combinator.
  • [Reitwiesner 1950a] Reitwiesner, George W., An ENIAC determination of pi and e to more than 2000 decimal places”, Mathematical Tables and Other Aids to Computation, 4, 11-15.
    • A paper on the program run on the ENIAC to calculate digits of and e in 1949-1950. The paper shows no indication of any knowledge of the program Curry wrote to do this for e in 1945-46.
  • [Reitwiesner et al. 1950b] Metropolis, N. C., Reitwiesner, G., and von Neumann, J., Statistical treatment of the values of first 2,000 decimal digits of e and calculated on the ENIAC”, Mathematical Tables and Other Aids to Computation, 4, 109-111.
    • The statistical analysis of the results of the program run on the ENIAC as described by George W. Reitwiesner.
  • [Prawitz 1965] Prawitz, Dag, Natural Deduction: A Proof-Theoretical Study, Almqvist & Wiksell, 1965. Reprinted by Dover in 2006.
    • This was originally Prawitz’ doctoral dissertation, and introduced Prawitz’ ideas of proof reduction and proof normalization.
  • [Popper 1968] Popper, K. R., Epistemology without a knowing subject”, in van Rootselaar, B. and Staal, J. F. (editors), Logic, Methodology and Philosophy of Science III: Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science, Amsterdam 1967, (Amsterdam: North-Holland), pp. 333{373.
    • This is the paper in which Popper introduced his idea of the third world. The paper had been presented in the first session of the congress (11:15 a.m. to 12:00 noon, with H. B. Curry in the chair) under the title “Epistemology and scientic knowledge”. See the program of the congress on p. 543 of the proceedings.
  • [Hindley and Seldin 1980a] Hindley, J. Roger and Seldin, Jonathan P. (editors), To. H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, (Academic Press).
    • A collection of papers related to Curry’s work. Includes a short biography and a complete list of Curry’s publications.
  • [Gandy 1980b] Gandy, R. O., An early proof of normalization by A. M. Turing”, in [1980a], pp. 453{455.
    • This is Turing’s earliest proof of the normal form theorem for typed-calculus with an introduction by Gandy.
  • [Hindley and Seldin 2008] Hindley, J. Roger and Seldin, Jonathan P., Lambda-Calculus and Combinators, An Introduction, (Cambridge University Press).
    • A general introduction to lambda-calculus and combinatory logic.
  • [de Mol et al. 2010] de Mol, Liesbeth, Bullynck, Maarten, and Martin, Carle, “Haskell before Haskell. Curry’s contribution to programming (1946-1950)”, in Ferreira, F., Lowe, B, Mayordomo, E., and Gomes, L.M. (Eds.), Programs, Proofs, Processes, 6th Conference on Computability in Europe, CIE, 2010, Ponta Delgada, Azores, Portugal, June 30-July 4, 2010, Springer Lecture Notes in Computer Science, vol. 6158, pp. 108-117.
    • A paper on Curry’s theory of programming.
  • [Seldin 2011] Seldin, Jonathan P., “The search for a reduction in combinatory logic equivalent to -reduction”, Theoretical Computer Science 412, 4905-4918.
    • A paper describing the attempt to find a reduction in combinatory logic equivalent to -reduction, including a discussion of the technical problems involved.
  • [Seldin 2017] Seldin, Jonathan P., The search for a reduction in combinatory logic equivalent to -reduction, Part II, Theoretical Computer Science 663, 34-58.
    • A paper giving the proofs of the key properties of the proposals given in Seldin 2011.

Author Information

Jonathan P. Seldin
Email: jonathan.seldin@uleth.ca
University of Lethbridge
Canada

Cognitive Phenomenology

Phenomenal states are mental states in which there is something that it is like for their subjects to be in; they are states with a phenomenology. What it is like to be in a mental state is that state´s phenomenal character. There is general agreement among philosophers of mind that the category of mental states includes at least some sensory states. For example, there is something that it is like to taste chocolate, to smell coffee, to feel the wind in one´s hair, to see the blue sky and to feel a pain in one´s toe. Is there also something that it is like to consciously think, to consciously judge and to consciously believe something? Are such cognitive states, when conscious, phenomenal states? Is there a clear distinction between sensory states and cognitive states? Or, can our knowledge, thoughts and beliefs influence our sensory experiences? Is there a cognitive phenomenology?

It is challenging to give a clear characterization of the cognitive phenomenology debate, since different contributors conceive of the debate in different ways. Central for the debate is the question of whether conscious thoughts possess a non-sensory phenomenology. Intuitively, there is something that it is like to consciously think, consciously judge and consciously believe something. However, the debate about cognitive phenomenology is not, strictly speaking, about whether there is something that it is like to consciously think. Rather, the debate concerns the nature of cognitive phenomenology. Is the phenomenology of cognitive states reducible to purely sensory phenomenology? Or, is there an irreducible cognitive phenomenology? A sceptic about cognitive phenomenology claims that conscious cognitive states are non-phenomenal. But, conscious cognitive states may seem to be phenomenal because they are accompanied by sensory states. For instance, when one thinks that ´Paris is a beautiful city`, one´s thought may be expressed in inner-speech and an image of Paris may accompany it. These accompanying sensory states are phenomenal states, and not the thought itself. Contrary to this, the proponent of cognitive phenomenology claims that a conscious cognitive state can have a phenomenology that is irreducible to purely sensory phenomenology.

Other debates have also been placed under the ´cognitive phenomenology’ label. There is an ongoing debate within the philosophy of perception about how cognition influences our sensory experiences. Philosophers tend to agree that, for example, an expert ornithologist´s perceptual experience of a type of bird can differ from that of a novice, even if the viewing conditions for both expert and novice are the same. The expert´s knowledge of birds can influence her experience. However, what philosophers disagree about is how the expert´s knowledge influences her experience, and how her knowledge contributes to what her experience is like.

Table of Contents

  1. Background
    1. Terminological Clarifications
    2. Two Kinds of Mental States
    3. Phenomenal Intentionality
  2. The Nature of Cognitive Phenomenology
    1. Irreducible Cognitive Phenomenology
    2. Proprietary Cognitive Phenomenology
    3. Pure and Impure Cognitive Phenomenology
    4. Attitudinal Phenomenology and Content Phenomenology
    5. General, Particular and Individuative Cognitive Phenomenology
  3. Arguments for Cognitive Phenomenology
    1. Arguments from Examples
    2. Contrast Arguments
    3. The Self-Knowledge Argument
    4. An Argument for Pure Cognitive Phenomenology
    5. Individual Differences
  4. Implications of the Cognitive Phenomenology Debate
  5. References and Further Reading

1. Background

a. Terminological Clarifications

When this article talks about a state being conscious, being conscious should be understood as being phenomenally conscious. A phenomenal state is a mental state that is phenomenally conscious in that there is something that it is like for the subject of that state to be in that state. Phenomenal states are states with phenomenology. What it is like to be in a phenomenal state is that state´s phenomenal character. An example of a phenomenal state is a visual experience of the blueness of the sea. Another example is an auditory experience of the sound of waves. There is something that it is like to have these experiences. There is also something that it is like to simultaneously visually experiencing the blueness of the sea and auditorily experiencing the sound of the waves (Bayne & Chalmers 2003). Our everyday conscious experiences are often complex in that they involve simultaneously thinking, feeling and experiencing within different sensory modalities. Such a complex experience is referred to as an overall phenomenal state.

Examples of sensory mental states are perceptual states, proprioception, bodily feelings and pains. Examples of cognitive states are thoughts, judgments and beliefs. According to some views, emotions and categorical perceptual experiences (such as experiencing something as being a type of bird) should also be categorized as cognitive states, or as partly cognitive and partly sensory states (see Chudnoff 2015a, Montague 2017).

b. Two Kinds of Mental States

Traditionally, it was common to distinguish between two kinds of mental states, namely sensory states and propositional attitudes. Paradigmatic examples of propositional attitudes are cognitive states such as beliefs, desires, thoughts and judgements. Propositional attitudes are intentional states since they are about or represent objects, properties or states of affair. They are states with propositional contents that can be linguistically expressed by using a ´that-clause.Thecontentofmybelief´ is ´that it will rain tomorrow. When I believe ´that it will rain tomorrow I am having a certain attitude towards that content, namely the attitude of belief. I could have had a different attitude towards the same content, I could for instance desire ´that it will rain tomorrow`.

According to the traditional view, sensory mental states, unlike cognitive states, have qualia. On this view, qualia are seen as phenomenal properties that can be separated from intentional or representational properties. For example, my visual experience of a red rose in front of me is intentional in that it is about or represents ´that there is a red rose in front of me`, but it is also something that it is like for me to experience the red rose. The redness that I experience is a property of my experience, a quale. While conscious sensory states are regarded as phenomenal states with qualia, conscious cognitive states are said to lack qualia. They are seen as non-phenomenal states.

Lately, this traditional view has been challenged. Firstly, proponents of intentionalism argue that when I experience a red rose I experience the redness as a property of the rose itself, and not as a property of my experience of the rose. My experience of the red rose has a phenomenal character, but this phenomenal character is embedded in the intentional content of my experience. Secondly, proponents of cognitive phenomenology challenge the assumption that cognitive states are non-phenomenal states when conscious.

c. Phenomenal Intentionality

In their seminal paper from 2002 ‘The Intentionality of Phenomenology and the Phenomenology of Intentionality’, Horgan and Tienson argue against the traditional view and argue in favour of intentionalism and cognitive phenomenology. They also argue for a view about the relation between the intentional and the phenomenal that has recently gained popularity, Phenomenal intentionalism.

According to intentionalism, all mental states are intentional, including phenomenal states. A mental state is commonly regarded as intentional if it is about or directed towards some objects or states of affairs, and if it has a content.

Phenomenal intentionality is a kind of intentionality that is said to be grounded in phenomenal consciousness (Kriegel 2011, Mendelovici 2018). According to proponents of Phenomenal intentionalism, there is a Phenomenal intentionality and all other forms of intentionality are derived from Phenomenal intentionality. While other proponents of intentionalism hold that intentionality is primary to phenomenology (see for example, Tye 1995 and Dretske 1995), proponents of Phenomenal intentionalism claim that phenomenology or Phenomenal intentionality is primary to all other forms of intentionality (Horgan & Tienson 2002, Kriegel 2011, Mendelovici 2018).

While most proponents of Phenomenal intentionalism also claim that there is a cognitive phenomenology, the two views should not be intermingled. Phenomenal intentionalism is a view about what it is that grounds the relation between phenomenal consciousness and intentionality, while cognitive phenomenology is a view about the scope of phenomenal consciousness. A proponent of cognitive phenomenology needs not accept Phenomenal intentionalism, and it is not necessary for a proponent of Phenomenal intentionalism to hold that there is a cognitive phenomenology. However, since proponents of Phenomenal intentionalism claim that all intentionality is derived from Phenomenal intentionality, it is easier to explain the intentionality of cognitive states if one holds that conscious cognitive states are phenomenal states. If one denies that there is a cognitive phenomenology and accepts Phenomenal intentionalism, one needs to tell a story about how the intentionality of cognitive states is derived from the Phenomenal intentionality of sensory states. While if one holds that there is a cognitive phenomenology one can simply claim that the intentionality of non-conscious cognitive states (such as dispositional beliefs) is derived from the Phenomenal intentionality of conscious cognitive states.

2. The Nature of Cognitive Phenomenology

The debate about whether or not there is a cognitive phenomenology can seem bewildering since there are different claims about what cognitive phenomenology is, and these claims may vary in both strength and generality.

a. Irreducible Cognitive Phenomenology

According to Elijah Chudnoff (2015a), a proponent of cognitive phenomenology should minimally accept the irreducibility thesis.

Irreducibility: ‘Some cognitive states put one in phenomenal states for which no wholly sensory states suffices’ (Chudnoff 2015a: 15).

It follows from Irreducibility that some cognitive states are such that because one is in them one is in a phenomenal state for which no wholly sensory states suffice. That is, there is a phenomenal character that is over and above the phenomenal character that accrues for sensory states. Putting one in a phenomenal state should be understood as a non-causal explanatory relation that can alternatively be picked out by ´in virtue of or ´constitutively dependent on (see Chudnoff 2015b).

In order to get a better grip on the Irreducibility thesis we can contrast it with an alternative view on the relation between cognitive states and phenomenal states. It is uncontroversial to claim that cognitive states can make an impact on our sensory states. For instance, judging that the sum of the angles of a triangle is 180 degrees can lead one to visualize the triangle or to express sentences such as ´the sum of the angles of a triangle is 180 degrees` in inner speech. In this case, one is in a phenomenal state since one is in a certain cognitive state, but the phenomenal state one is in is not different from the phenomenal state various wholly sensory states can put one in (Chudnoff 2015a). What Irreducibility claims is that some cognitive states can put one in phenomenal states that are different from those phenomenal states that wholly sensory states can put one in. Chudnoff uses an example from mathematics to illustrate how Irreducibility differs from the view that cognitive states merely cause one to be in a certain phenomenal state. At first you read that ´If a < 1, then 2 – 2a > 0, and you wonder whether this is true (Chudnoff 2015a: 15). Then you realise how a´s being less than 1 makes 2a smaller than 2 and so 2 – 2a greater than 0. When you realise the truth of this mathematical proposition you might say to yourself in inner speech ´If a < 1, then 2 – 2a > 0 and you might visualize the variable ´a and the numeral ´1. You might also feel satisfied because you got it right. These states that you are put in are all sensory phenomenal states. However, if you believe Irreducibility and if you think that this case of realising the truth of this mathematical proposition involves cognitive phenomenology, then you also believe that these sensory states taken together cannot account for the overall phenomenal state you are in. You think that there is some phenomenal state that is left over which only the cognitive states of ´realising or ´intuiting can put you in.

Following Chudoff, Irreducibility is the thesis that a proponent of cognitive phenomenology must minimally accept. There are other theses figuring within the cognitive phenomenology debate that go beyond Irreducibility and make stronger and more specific claims about the nature of cognitive phenomenology.

b. Proprietary Cognitive Phenomenology

According to Irreducibility, some sensory states put one in phenomenal states for which no wholly sensory states suffice to put one in. However, it does not follow from Irreducibility that only cognitive states put one in these phenomenal states. Neither does it follow from Irreducibility that the phenomenal character of the phenomenal states that cognitive states put one in is cognitively grounded. That is, that their phenomenal character is different in kind from sensory phenomenal character (Levine 2011).

Many proponents of cognitive phenomenology hold that there is a proprietary cognitive phenomenology (See Horgan & Tienson 2002, Horgan 2011, Kriegel 2011, Kriegel 2015a, Kriegel 2015b, Pitt 2004, Pitt 2011, Siewert 1998, Siewert 2011). The kind of phenomenology that philosophers are talking about when they are talking about cognitive phenomenology must differ in kind form the kind of phenomenology one is familiar with through one´s sensory experiences. As David Pitt puts it:

I believe that the phenomenology of occurrent conscious thought is proprietary: It´s a sui generis sort of phenomenology, as unlike, say, auditory or visual phenomenology as they are unlike each other—a cognitive phenomenology. (Pitt 2011: 141)

There is something that it is like to be in a conscious cognitive state and/or to consciously entertain a cognitive content, and this phenomenology is distinct from the phenomenology one experiences when one is consciously perceiving something or feeling something. Cognitive phenomenology is, on this view, proprietary and sui generis.  

Proprietary: Conscious cognitive states have proprietary or sui generis phenomenal character.

Someone who accepts Proprietary also accepts Irreducibility, but one may accept Irreducibility and deny Proprietary. For example, one could claim that knowing a lot about sparrows may influence the way one visually experiences sparrows so that one can be put in phenomenal states for which no wholly sensory states suffice. One´s knowledge does not merely cause one to attend to sparrows in a particular way. Rather, one´s knowledge puts one in a phenomenal state that one could not have been put in by wholly sensory states. In such a case, cognitive states can make a constitutive contribution to one´s perceptual experience by, for example, structuring the experience, without thereby producing a phenomenal state that is non-sensory in kind (see Levine 2011, Nes 2011). However, most philosophers hold that cognitive states can cause one to be in certain sensory states by influencing attention. Carruthers and Veillet (2011) argue that it is not clear that the sparrow expert´s experience involves irreducible cognitive phenomenology, since it is possible that her knowledge simply causes her to attend to sparrows in a different way compared with a novice. She will notice certain properties of the sparrows that the novice fails to notice, but the phenomenal state she is in is a state that wholly sensory states suffice to put her in. How should we decide between these views?

If cognitive phenomenology is proprietary, it should in principle also be possible to pick it out via introspection. Holding that cognitive phenomenology is proprietary allows one to appeal to introspection in cases where there is a dispute about whether cognitive phenomenology is involved or not. This may serve as a motivation for holding that cognitive phenomenology is proprietary, and not merely irreducible.

c. Pure and Impure Cognitive Phenomenology

We can further distinguish between three different ways of characterizing the nature of a phenomenal state: 1) A phenomenal state is purely sensory in case wholly sensory states suffice to put one in that state; 2) A phenomenal state can be partly cognitive (and partly sensory) if no wholly sensory states suffice to put one in that state and no wholly cognitive states suffice to put one in that state; 3) A phenomenal state is purely cognitive in case cognitive states suffice to put one in that state (Chudnoff 2015b). A cognitive phenomenal state is an impure cognitive phenomenal state if 2 holds but not 3. A cognitive phenomenal state is a pure cognitive phenomenal state if 3 holds. In other words, a cognitive phenomenal state is a pure cognitive phenomenal state if it is independent of sensory states.

A proponent of cognitive phenomenology needs not accept that there is pure cognitive phenomenology. It is compatible with Irreducibility that there is merely impure cognitive phenomenology. Many of the cases that are commonly appealed to in arguments for cognitive phenomenology seem to involve impure cognitive phenomenology. For instance, the overall phenomenal state one is in when one suddenly grasps a mathematical proposition arguably depends on both sensory experiences and intuiting. Proposed candidates for pure cognitive phenomenology are imageless thoughts and beliefs.

It is compatible with Irreducibility to deny that there is pure cognitive phenomenology. However, if one holds Proprietary one seems committed to accept that pure cognitive phenomenology is, at least, possible. Following Proprietary, cognitive phenomenology is different in kind from other kinds of phenomenology, and it should in principle be possible to pick out this kind of phenomenology via introspection. When one is in a phenomenal state that involves different sensory modalities—such as the state one is in when watching a TV-show—one seems able, at least roughly, to pick out and separate visual phenomenology from auditory phenomenology. This is because visual phenomenology is quite unlike auditory phenomenology. Similarly, when one is consciously thinking that p, one should be able to separate the phenomenology of thinking from the auditory phenomenology involved when expressing the content in inner-speech. On this view, cognitive phenomenology is a sui generis kind of phenomenology, as unlike auditory and visual phenomenology as they are unlike each other (Pitt 2004, Pitt 2011).

d. Attitudinal Phenomenology and Content Phenomenology

Cognitive states such as thoughts, beliefs, judgements and inferences are propositional attitudes. One may think that conscious cognitive states have attitudinal cognitive phenomenology PA:

PA: There is something that it is like to have a conscious cognitive attitude towards a content, and no wholly sensory states suffice to put one in a state with this phenomenal character. 

PA is compatible with Irreducibility and Proprietary.

The claim that there is a cognitive phenomenology can also be a claim about the cognitive content that one is consciously entertaining when one is in a cognitive state. One may think that conscious cognitive states have content cognitive phenomenology CA:

CA: There is something that it is like to consciously entertain a cognitive content, and no wholly sensory states suffice to put one in a state with this phenomenal character.

A proponent of cognitive phenomenology can accept that there is an attitudinal cognitive phenomenology and deny that there is a content cognitive phenomenology. One can also hold that there is a content cognitive phenomenology, but not an attitudinal cognitive phenomenology. Or, one can accept that there is both an attitudinal cognitive phenomenology and a content cognitive phenomenology.

e. General, Particular and Individuative Cognitive Phenomenology

Cognitive phenomenology claims can be general claims such as the claim that conscious cognitive attitudes have attitudinal cognitive phenomenology, where this attitudinal cognitive phenomenology is common for all cognitive attitudes. Alternatively, cognitive phenomenology claims can be claims about there being a particular cognitive phenomenology involved when one is consciously believing, and this attitudinal cognitive phenomenology is different from the attitudinal cognitive phenomenology involved when one is having other conscious cognitive attitudes. One may also think of attitudinal cognitive phenomenology as even more fine-grained: for example, that there are different attitudinal cognitive phenomenologies involved in having different kinds of conscious beliefs.

The claim that there is a content phenomenology can be more or less general. The most general claim is that there is a content cognitive phenomenology that is common for all cognitive contents. A more particular view claims that the cognitive content phenomenology involved in consciously entertaining the content that p, say, differs from the cognitive content phenomenology involved in consciously entertaining that q. An even more particular view holds that the content cognitive phenomenology involved in consciously entertaining the content that p is different from the content phenomenology involved in consciously entertaining any other cognitive contents. Further, one could hold that the phenomenology involved in consciously entertaining the cognitive content that p may differ from person to person. For example, the content phenomenology involved when John consciously entertains the cognitive content that p, differs from the content phenomenology involved when Jane consciously entertains the cognitive content that p.

Particular claims about either attitudinal cognitive phenomenology and content cognitive phenomenology are often motivated by the view that phenomenology is individuative. That is, in virtue of having the phenomenal character it has, my belief is a belief as opposed to a judgment, a thought or an intuition. And, in virtue of having the phenomenal character it has, the content that I am entertaining, the content that p, is the very content that p as opposed to the content that q. By claiming that phenomenology is individuative one can elegantly explain how one can determine the content of one´s own phenomenal state. One knows which phenomenal state one is in, and its content, because it has the phenomenal character that it has. For instance, when I am having a visual experience of a red rose I come to know—via introspection—that I am having a visual experience of a red rose. Similarly, I come to know that I am consciously believing that p due to the phenomenal character belief that p has (Pitt, 2004, Horgan 2011, Kriegel 2011, Kriegel 2013).

3. Arguments for Cognitive Phenomenology

We can distinguish between different types of arguments for cognitive phenomenology. These arguments are generally arguments for Irreducibility, but some of them also defend stronger claims about the nature of cognitive phenomenology. This section presents the types of arguments that are most commonly used and common responses to them.

a. Arguments from Examples

Arguments from examples appeal to cases or circumstances where one seems to be in phenomenal states that involve cognitive phenomenology. For instance, there is something that it is like for me to suddenly remember that I have an appointment with a student in 5 minutes. The state that I am in when I suddenly remember something is a cognitive state. There can be sensory states involved as well; a visual image of my student may pop-up, or I may feel annoyed because I almost forgot about the appointment. The cognitive state I am in when I suddenly remember my appointment puts me in a phenomenal state, and no wholly sensory states suffice to put me in that state.

Another argument from example appeals to tip-of-the-tongue experiences, the kind of experiences one has when searching for a word that one knows but fails to retrieve (Goldman 1993). There is something that it Is like to have such experiences, and cognitive states play a role in putting one in that state, and no wholly sensory states suffice to put one in that state.

A sceptic about cognitive phenomenology may agree with the proponent of cognitive phenomenology in that the states that these arguments appeal to are phenomenal states, while denying that they are cognitive phenomenal states. According to the sceptic there is always some sensory states involved when one suddenly remembers something. When I remember that I have an appointment with my student in 5 minutes, I may visualize my student and feel annoyed by myself for almost forgetting about the appointment. The sensory states that I am in can, according to the sceptic, fully account for the phenomenal character of the state that I am in.

One can make a similar response to the tip-of-the-tongue example. When having a tip-of-the-tongue experience I am making an effort to retrieve a word, and it is the sensory feeling of making an effort that accounts for the phenomenal character of the experience.

A proponent of cognitive phenomenology can insist that if one carefully introspects one´s phenomenal states, it becomes apparent to one that these states involve cognitive phenomenology. However, such appeals to introspection are problematic because a sceptic may simply claim that she is carefully introspecting the phenomenal state she is in when she suddenly remembers something, but she finds only sensory phenomenology. Nevertheless, it seems wrong to completely dismiss appeals to introspection, as some such appeals appear more convincing than others. Charles Siewert (1999) argues that the sensory states involved in cases where one suddenly remembers something occur after the state of suddenly remembering. The state that one is in when suddenly remembering something needs not involve any sensory phenomenology at all. Following Siewert, the state of suddenly remembering is a pure cognitive phenomenal state (Siewert 1999).

b. Contrast Arguments

One of the most commonly used type of argument for cognitive phenomenology is contrast arguments. Contrast arguments for cognitive phenomenology appeal to two contrasting phenomenal states, s1 and s2, where there appears to be a difference in the phenomenal character of s1 and s2, and where this difference is best explained as a difference in cognitive phenomenology. Contrast arguments can be used when arguing for attitudinal cognitive phenomenology, content cognitive phenomenology, pure and impure cognitive phenomenology. The expert/novice argument that is introduced earlier in this article can be seen as a contrast argument.

When contrast arguments are used as argument for attitudinal cognitive phenomenology one typically appeals to cases where there is a slight change in one´s attitude towards a content. An example is the change of attitude one experiences when one suddenly grasps a mathematical proof. There is something that it is like to grasp a mathematical proof, and the state one is in when one suddenly grasps it differs from the state one was in before grasping it.

When contrast arguments are used as arguments for content phenomenology one typically appeals to a pair of situations where one is attending to the meaning of an ambiguous utterance in natural language, and where there appears to be a phenomenal difference in the states one is in depending on which proposition one takes the utterance to express (Horgan & Tienson 2002).

Contrast arguments can be more or less convincing, depending on how easy it is to give an alternative explanation of the contrast, and on whether the claim that there is a contrast is convincing.

´The foreign language argument’, due to Galen Strawson (1994), is maybe the most famous contrast argument for cognitive phenomenology: Jack is a native English speaker who does not understand French, while Jacques is a native French speaker. Both Jack and Jacques hear the same instance of the utterance ´La vie est belle. There is something that it is like for both Jack and Jacques to hear the utterance, though what it is like for Jacques differs from what it is like for Jack. So, Jack and Jacques are put in different phenomenal states. The difference in the phenomenal character of their states can be explained by the fact that Jacques, unlike Jack, understands what is being said. Jacques, unlike Jack, has an attitude of understanding towards the content, and he is able to consciously entertain the content that is being expressed. In the case of Jacques, unlike Jack, cognitive states of understanding and entertaining a content put him in a phenomenal state, and this explains why the phenomenal state he is in differs from the phenomenal state Jack is in. In order to make the foreign language argument into an argument for cognitive phenomenology one needs to add that the phenomenal difference between Jacks and Jacques` states is a difference in cognitive phenomenology.

However, in this case, at least some of the differences between the two phenomenal states involve differences in sensory phenomenology. From phonetic studies, we know that a sentence expressed in a language sounds different for a person who understands that language, compared to what it sounds like for a person who does not understand the language (Pinker 1995). This difference is at least partly auditory. The person who understands the language attends differently to the phonemes and prosody of the utterance compared with the person who does not understand the language. A sceptic about cognitive phenomenology may therefore agree that there is a phenomenal difference between the states that Jack and Jacques are in, but claim that the difference is a difference in purely sensory phenomenology (Lormand 1996). The proponent of cognitive phenomenology may insist that though the phenomenal states of Jack and Jacques also differ in sensory phenomenology, the differences in sensory phenomenology do not sufficiently explain the whole phenomenal difference.

A different type of contrast argument that appeals to ambiguous utterances in a familiar language has been proposed by, among others, Kriegel 2011, Horgan 2011, Horgan & Tienson 2002 and Siewert 1999. For example: it is something that it is like to hear the ambiguous utterance ´I am going to the bank` where one understands this utterance as being about the financial institution, as opposed to what it is like to hear the same instance of the utterance and understand it as being about the river bank. One is in different phenomenal states depending on which proposition one consciously entertains. Arguably, given that one accepts that there is a phenomenal difference between these states, this difference is best explained as a difference in cognitive phenomenology.

In this case, the argument is appealing to the same instance of utterance in a language that one does understand. A sceptic who agrees that there is phenomenal difference between the two states may possibly claim that the different understandings cause one to be in different sensory states, and that the phenomenal difference is due to this. However, it is less easy, compared with the foreign language argument, to see what candidates for such states would be. Surely, hearing the utterance and understanding it as ´I am going to the financial institution` may cause some emotional responses in someone who has financial problems, but it needs not have such an effect. Apparently, one needs not respond emotionally to either of the two understandings of the utterance. Also, one may, but one needs not visualize the financial institution or the river bank when hearing the utterance. Arguably, one´s sensory states can remain the same, regardless of which of the two understandings one consciously entertains, and still there is a phenomenal difference. Therefore, if there is a phenomenal difference in this contrast case, the most plausible candidate for explaining the difference is that there is a difference in cognitive phenomenology. One is put in different phenomenal states, and no wholly sensory states suffice to put one in these phenomenal states. Contrast arguments involving ambiguous utterances of this type have the virtue that if there is a phenomenal contrast in these cases, this contrast is difficult to explain away as a contrast in sensory phenomenology. One way of responding to such contrast arguments is to deny that there is a phenomenal contrast. That is, one is not in different phenomenal states in such cases.

c. The Self-Knowledge Argument

The self-knowledge argument that was originally presented by David Pitt (2004) is a very complex argument, and this article presents only a rough version of it.

The argument from self-knowledge differs from the types of arguments introduced above in that it explicitly supports a strong cognitive phenomenology claim: the claim that there is a proprietary, distinctive and individuative cognitive phenomenology. According to the argument, we can have immediate knowledge of the content of our own conscious thoughts, and the only way we can explain how such knowledge is possible is by assuming that there is a proprietary, distinctive and individuative cognitive phenomenology of thought. From this it follows that one is able to consciously do three distinct things: a) to distinguish one´s occurrent conscious thoughts from one´s other occurrent conscious mental states (cognitive phenomenology is proprietary); b) to distinguish one´s occurrent conscious thoughts from each other (cognitive phenomenology is distinctive); c) to identify each of one´s occurrent conscious thoughts as the thought it is (cognitive phenomenology is individuative).

According to the self-knowledge argument (Pitt 2004):

P1: It is possible immediately to identify one´s occurrent conscious thoughts: one can know by acquaintance (via introspection) which thought a particular occurrent thought is: but

P2: It would not be possible immediately to identify one´s conscious thought unless each type of conscious thought had a proprietary, distinctive, individuative phenomenology, so

C: Each type of conscious thought—each state of consciously thinking that p, for all thinkable contents p—has a proprietary, distinctive, individuative phenomenology.

The argument is valid. Before questioning the premises, we should say something about what it is that motivates them.

Intuitively, one does know the content of one´s conscious thoughts, and one has a privileged introspective access to one´s own thoughts that other people lack. I know when I am thinking ´that pizza is good`, and I know that the mental state I am in is a thought and not a perceptual state. So, I am able to identify my thought as a thought, and I am able to identify the content of my thought and distinguish it from other thoughts.

However, according to the premises of the argument, it is possible to ´immediately` identify one´s occurrent conscious thoughts (P1). This premise relies on a particular view on introspection of phenomenal states—the acquaintance theory—that is controversial. On this view, introspection makes one directly or immediately aware of one´s phenomenal states and their contents. No inferences are made and no causal processes are involved. If one holds a different view on introspection one can simply deny P1 and the argument for self-knowledge. In his article, Pitt strongly defends the acquaintance theory of introspection. For further reading consult Pitt 2004 and Pitt 2011.

d. An Argument for Pure Cognitive Phenomenology

Contrast arguments and arguments from examples are generally neutral when it comes to whether they are arguments for pure or impure cognitive phenomenology.

However, Kriegel´s cognitive zombie argument is an argument for pure cognitive phenomenology (see Kriegel 2015b and Chudnoff 2015b). A philosophical zombie is a being that acts and talks like a phenomenally conscious being, but who completely lacks phenomenal states. In other words, there is nothing that it is like to be a zombie (see Chalmers 1996).

Imagine a partial zombie, Zoe, who is an expert mathematician. Zoe is also a sensory zombie, in that there is nothing that it is like for her to have sensory experiences. Still, there is something that it is like for her to gain new mathematical insights. Since Zoe is a sensory zombie the phenomenal states she is in when gaining new mathematical insights are purely cognitive phenomenal states.

A sceptic may respond to this thought experiment by claiming that since Zoe is a sensory zombie, there is nothing that it is like for her to gain these insights. One may insist that cognitive states do not suffice to put one in the phenomenal states that one is normally put in when one grasps something or gains a new insight. The sceptic can either claim that the phenomenology involved in being in such phenomenal states is purely sensory, or she could hold that it is impurely cognitive phenomenal.

In order to strengthen the appeal of this thought experiment, one can turn it into a contrast-argument. Imagine that Zoe turns into a full zombie. As a full zombie, there is nothing that it is like for her to gain mathematical insights. Intuitively, there is a phenomenal contrast between the states of sensory zombie Zoe, and the states of full zombie Zoe. While there is something that it is like for the sensory zombie Zoe to gain mathematical insights, there is nothing that it is like for the full zombie Zoe to do so. If we share the intuition that there is such a contrast between the two zombies, we should also accept that pure cognitive phenomenology is possible.

Interestingly, the cognitive zombie argument appears as more challenging for proponents of impure cognitive phenomenology who deny that there is pure cognitive phenomenology, than for a sceptic who denies that there is cognitive phenomenology. Sensory states within different sensory modalities can put one in certain phenomenal states. We can imagine a zombie who lacks sensory phenomenology in all sensory modalities apart from audition. Intuitively, since she has auditory phenomenal states there is something that it is like for her to watch a movie though her experience is clearly not as rich as that of an ordinary person. Similarly, even if it is normally the case that the phenomenal state one is in when grasping a mathematical proof is a phenomenal state that both sensory and cognitive states puts one in, still there is something that it is like for Zoe the sensory zombie to grasp mathematical proofs. Though Zoe´s phenomenal states may not be as rich as that of a normal person. (For further reading, consult Kriegel 2015b and Chudnoff 2015b.)

e. Individual Differences

Philosophers of mind generally agree that conscious sensory states have phenomenal characters. We come to know what it is like to be in a certain conscious sensory state simply by being in that state. But, when it comes to irreducible cognitive phenomenology, philosophers strongly disagree about whether it exists or not. Why do they disagree?

Maybe the reason why philosophers disagree so strongly is that people simply differ? That is, some people have cognitive phenomenal states, while others do not (see Schwitzgebel 2008)? If this is the case, it can explain why highly competent philosophers on both sides of the debate come to different conclusions when introspecting their own conscious states. However, most philosophers seem to dismiss this possibility. What are the reasons for thinking that people differ so greatly in their phenomenal states? Why are there no similar controversies when it comes to disputes about sensory phenomenology?

4. Implications of the Cognitive Phenomenology Debate

What are the implications of the cognitive phenomenology debate? Why should we care about cognitive phenomenology?

One issue that arises from the cognitive phenomenology debate concerns the trustworthiness of introspection. If there is a cognitive phenomenology, then the opponents have overlooked a range of phenomenal states that they enjoy. On the other hand, if there is no cognitive phenomenology, the proponents have been positing a range of phenomenal states that they do not enjoy (Bayne & Montague 2011). Such considerations may lead us to question the reliability of introspection (Schwitzgebel 2008).

The cognitive phenomenology debate also has implications for the general debate about consciousness, since there are certain theories of consciousness that are at odds with the existence of cognitive phenomenology. For example, accounts that identify phenomenal states with intentional states with non-conceptual contents (see Tye 1995). Such views are not compatible with thoughts having a distinctive phenomenal character, since the content of a thought is conceptual.

Further, the cognitive phenomenology debate has implications for our view on the relationship between phenomenology and intentionality. Proponents of phenomenal intentionalism take phenomenology to be the source of intentionality (Kriegel 2013, Mendelvici 2018). Most proponents of phenomenal intentionalism hold that there is a cognitive phenomenology. If phenomenology is the source of intentionality, cognitive phenomenology is the source of the intentionality of cognitive states. If there is no cognitive phenomenology, the proponents of phenomenal intentionalism need to tell a different story of how phenomenology can be the source of the intentionality of cognitive states.

The cognitive phenomenology debate also has implications for the debate about whether consciousness can be naturalized. If only sensory states are phenomenal states, naturalizing cognition is part of what Chalmers (1996) labels ´the easy problem of consciousness, while naturalizing conscious sensory states is part of ´the hard problem of consciousness. The easy problems of consciousness are those that can be solved (in the future) by using the standard methods of cognitive science. Whereas the hard problem is that of explaining phenomenal consciousness (see “The Hard Problem of Consciousness”). If there is a cognitive phenomenology, the hard problem of consciousness becomes more expansive as it will include both sensory and cognitive phenomenal states. Arguably, therefore, if there is a cognitive phenomenology, naturalizing consciousness becomes harder. However, the hard problem remains ´hard` whether we accept that there is a cognitive phenomenology or not. If arguments convince us that there is a cognitive phenomenology, we should accept these independently of the fact that it has the consequence of expanding the hard problem.

5. References and Further Reading

  • Bayne, T & Chalmers, J. L. 2003. “What is the Unity of Consciousness”. In Cleeremans, A (ed.) The Unity of Consciousness. Oxford University Press.
  • Bayne, T. 2009. “Perception and the Reach of Phenomenal Content.” Philosophical Quarterly 59 (235): 385-404.
  • Bayne, T and Montague, M. 2011. “Cognitive Phenomenology: An Introduction”. In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Carruthers, P and Veillet, B. 2011. “The Case against Cognitive Phenomenology”. In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Chalmers, D. 1996. The Conscious Mind. Oxfords University Press.
  • Chudnoff, E. 2015a. Cognitive Phenomenology. Routledge.
  • Chudnoff. E. 2015b. “Phenomenal Contrast Arguments for Cognitive Phenomenology.” Philosophy and Phenomenological Research 90 (2): 82-104.
  • Dretske, F. 1995. Naturalizing the Mind. MIT Press.
  • Goldman, A. 1993. “Consciousness, Folk Psychology, and Cognitive Science.” Consciousness and Cognition 2 (4):364-382.
  • Horgan, T. 2011. “From agentive phenomenology to Cognitive Phenomenology: A guide for the perplexed”. In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Horgan, T and Graham, G. 2012. “Phenomenal Intentionality and Content determinacy”. In Richard Schantz (ed.) Prospects of Meaning. De Gruyter.
  • Horgan, T and Tienson, J L. 2002. “The Intentionality of Phenomenology and the Phenomenology of Intentionality”. In Chalmers, D (ed.) Philosophy of Mind: Classical and Contemporary readings. Oxford University Press.
  • Kriegel, U. 2011. The Sources of Intentionality. Oxford University Press.
  • Kriegel, U. 2013. “The Phenomenal Intentionality Research Program”. In Kriegel, U (eg.) Phenomenal Intentionality. Oxford University Press.
  • Kriegel, U. 2015. “The Character of Cognitive Phenomenology” In Breyer, T and Gutland, C (eds.) Phenomenology of Thinking. Routledge.
  • Kriegel, U. 2015. The Varieties of Consciousness. Oxford University Press.
  • Levine, J.2011. “On the Phenomenology of Thoughts” In Bayne & Montague (eds.) Cognitive Phenomenology. Oxford University Press.
  • Lormand, E. 1996. “Nonphenomenal Consciousness” Nous 30(2): 242-261.
  • Mendelovici, A. 2018. The Phenomenal Basis of Intentionality. Oxford University Press
  • Montague, M. 2017. “Perception and Cognitive Phenomenology” Philosophical Studies 174: 2045-2062.
  • Nes, A. 2011. “Thematic Unity in the Phenomenology of Thinking” Philosophical Quarterly 62: 84 -105.
  • Pitt, D. 2004. “The Phenomenology of Cognition, or What it is Like to Think That P?” Philosophy and Phenomenological Research 69(1): 1-36.
  • Pitt, D. 2011. “Introspection, Phenomenality, and the Availability of Intentional Content”. In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press
  • Prinz, J. 2011. “The Sensory Basis of Cognitive Phenomenology”. In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Schwitzgebel, E. 2008. “The unreliability of naïve introspection” The Philosophical Review 117 (2): 245-273.
  • Siegel, S. 2010. The Contents of Visual Experience. Oxford University Press.
  • Siewert, C. 1998. The Significance of Consciousness. Princeton University Press.
  • Siewert, C. 2011. “Phenomenal Thought”. In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Smithies, D. 2013a. “The Significance of Cognitive Phenomenology” Philosophy Compass 8(8): 731-743.
  • Smithies, D. 2013b. “The Nature of Cognitive Phenomenology” Philosophy Compass 8(8): 744-754.
  • Spener, M. 2011. “Disagreement about Cognitive Phenomenology.” In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Strawson, G. 1994 Mental Reality. MIT Press.
  • Strawson, G. 2011. “Cognitive Phenomenology: Real life” In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.
  • Tye, M. 1995. Ten Problems of Consciousness: A Representational Theory of the Phenomenal Mind. MIT Press.
  • Tye, M and Briggs, W. 2011. “Is there a Phenomenology of Thought?” In Bayne, T and Montague, M (eds.) Cognitive Phenomenology. Oxford University Press.

Author Information

Mette Kristine Hansen
Email: Mette.Hansen@uib.no
University of Bergen
Norway

Sigmund Freud: Religion

This article explores attempts by Sigmund Freud (1850-1939) to provide a naturalistic account of religion enhanced by insights and theoretical constructs derived from the discipline of psychoanalysis which he had pioneered. Freud was an Austrian neurologist and psychologist who is widely regarded as the father of psychoanalysis, which is both a psychological theory and therapeutic system. As a theory, psychoanalysis conceptualizes the mind as a system composed of three constituent elements: id, ego, and superego. It focuses on the interaction between those elements, and includes such key concepts as infantile sexuality, repression, latency and transference. Psychoanalytic therapy is an application of this conceptual schema, in which the interaction of the mind’s conscious and unconscious elements in individual cases is explored using the techniques of dream interpretation, free association and the analysis of resistance to identify repressed conflicts and bring them into the conscious mind.

Freud’s thought on religion is, perhaps fittingly, rather complex and ambivalent: while there can be little doubt as to its roundly skeptical, and at times hostile, character, it is nonetheless clear that he had a firm grounding in Jewish religious thought and that the religious impulse held a life-long fascination for him. This article charts the evolution of his views on religion from Totem and Taboo (1913), through The Future of an Illusion (1927) and Civilization and its Discontents (1930) to Moses and Monotheism (1939), focusing in particular on the parallels drawn by him between religious belief and neurosis, and on his account of the role which the father complex plays in the genesis of religious belief. The article concludes with a review of some of the main critical responses which the Freudian account has elicited.

Table of Contents

  1. Psychoanalysis and Religion
  2. Freud’s Jewish Heritage
  3. Philosophical Connections
  4. The Orientation of Freud’s Approach to Religion
  5. Totemism and the Father Complex
  6. Religion and Civilization
  7. The Moses Narrative: The Origins of Judaic Monotheism
  8. Critical Responses
    1. The Anthropological Critique
    2. Myth or Science?
    3. Lamarckian vs. Darwinian Evolutionary Principles
    4. The Primordial Religion: Polytheism or Monotheism?
    5. Religion as a Social Phenomenon
    6. The Projection Theory of Religion
    7. Moses and Monotheism: Interpretive Approaches
  9. References and Further Reading
    1. References
    2. Further Reading

1. Psychoanalysis and Religion

 At the heart of Freud’s psychoanalysis is his theory of infantile sexuality, which represents individual psychological human development as a progression through a number of stages in which the libidinal drives are directed towards particular pleasure-release loci, from the oral to the anal to the phallic and, after a latency period, in maturity to the genital. He thus saw the psychosexual development of every individual as consisting essentially of a movement through a series of conflicts which are resolved by the internalization, through the operation of the superego, of control mechanisms derived originally from an authoritative, usually parental, source. In infancy, such a progression entails a process whereby parental control involves the introduction to the child of behavioral prohibitions and limitations and necessitates the repression, displacement or sublimation of the libidinal drives.

Central to this account is the idea that neuroses, which may include the formation of psychosomatic symptoms in the individual, arise essentially either out of external trauma or through a failure to effect a resolution of the internal conflict between libidinal urges and the key psychological control mechanisms. Symptomatically, these often present as compulsive and debilitating patterns of behavior—as in hysteria, repetitive ceremonial movements or an obsession with personal hygiene—which make a normal healthy life impossible, requiring psychotherapeutic intervention in the form of such techniques as dream analysis and free association. Of particular importance, he held, is the resolution of the Oedipus complex, which arises at the phallic stage, in which the male child forms a sexual attachment with the mother and comes to view the father as a hated and feared sexual rival. That resolution, which Freud saw as essential to the formation of sexuality, entails the repression of the drive away from the mother as libidinal object and the male child’s identification with the father. The cluster of associations relating to the multifaceted relationship between son and father Freud termed “the father complex” (1957, 144) and, as we shall see, viewed it as central to a correct understanding both of the developmental psychology of human beings and to many of the central and most important social phenomena in human life, including religious belief and practice.

In his account of religion Freud deployed what Paul Ricoeur (1913—2005) terms a hermeneutic “of suspicion” (Ricoeur 1970, 32), a reductive and demystifying style of interpretation that repudiated what he saw as a masquerade of conventional meanings operating at the level of common discourse in favor of deeper, less conventional truths relating to human psychology. He sought to demonstrate by this means the true origins and significance of religion in human life, in effect utilizing the techniques of psychotherapy to achieve that goal. Freud’s general position on religion stands firmly in the naturalistic tradition of projectionism stretching from Xenophanes (c.570—c.475 B.C.E.) and Lucretius (c.99—c.55 B.C.E.) through Thomas Hobbes (1588—1679) and David Hume (1711—76) to Ludwig Feuerbach (1804—1872) in holding that the concept of God is essentially the product of an unconscious anthropomorphic construct, which Freud saw as a function of the underlying father complex operating in social groups. “The psycho-analysis of individual human beings,” he thus stated boldly in Totem and Taboo, “teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father” (Freud 2001, 171).

The following sections examine the considerations which led him to this view, to the manner in which it found articulation in his writings on religion and to the main criticisms which it has encountered.

2. Freud’s Jewish Heritage

 Freud was born to Jewish parents in the town of Freiberg, then in the Austro-Hungarian Empire. His father Jacob was a businessman descended from a long line of rabbinical scholars; a textile merchant, he went bankrupt when Sigmund was four years of age and the family were forced to move to Vienna, where they lived in genteel poverty for many years, dependent in part upon the generosity of relatives. The young Sigmund found it difficult to come to terms with the new urban surroundings and family’s reduced financial circumstances. Experience of the latter left him with a life-long fear of poverty, his overweening ambition to establish psychoanalysis as a new science and successful treatment for hysteria was as a result partially motivated by the desire to achieve financial security for his family.

In the preface to the Hebrew edition of Totem and Taboo, published in 1930, Freud described himself as being “in his essential nature a Jew and who has no desire to alter that nature,” but one who is “completely estranged from the religion of his fathers—as well as from every other religion” (Freud 2001 Preface, xiii). This phrasing marks Freud’s recognition that, notwithstanding his skepticism regarding religion, his character had largely been formed by a Judaic cultural heritage passed on to him by his father Jacob, with whom he had a rather fraught relationship. Freud’s ancestors were affiliates of Hasidic Judaism going back many generations, and included several rabbis and distinguished scholars among their number (Berke 2015, xii). While Jacob was liberal and progressive in his outlook, he retained a deep reverence for the Talmud and the Torah and had overseen Sigmund’s childhood study of the Philippson family Bible, which generated in the young Sigmund a life-long fascination with the story of Moses and his connection with Egypt. He also ensured that the boy had a traditional Jewish schooling in which he was steeped in Biblical studies in the original Hebrew. In that connection the young Freud developed a deep admiration for, and friendship with, one of his religion teachers, Rabbi Samuel Hammerschlag, who was a strong proponent of humanistic Reform Judaism. Such was his admiration for his teacher that Freud ultimately named his fifth and sixth children, Sophie and Anna, after Hammerschlag’s niece and daughter; commentators now generally agree that the patient referred to as ‘Irma’ in Freud’s pivotal The Interpretation of Dreams was in fact Anna Hammerschlag. It was Rabbi Hammerschlag’s deep humanism, more than any other feature of his character, which Freud found inspiring, inculcating in him a lasting commitment to the universality of Enlightenment values. It is notable that, in seeking to pay Hammerschlag the highest compliment possible in the obituary which he wrote for him in 1904, Freud compared him to the Hebrew prophets, but also highlighted the extent to which that aspect of his character was integrated with humanistic ideals: “A part from the same fire which animated the great Jewish seers and prophets burned in him … but the passionate side of his nature was happily tempered by the ideal of humanism of our classical German period, which governed him and his method of education” (Freud 1976 IX, 256).

Notwithstanding the positive impact of such religious influences, from adolescence onwards Freud apparently found the observances and strictures required by orthodox Jewish belief increasingly burdensome and he became overtly hostile to the religion of his forefathers and to religion in general (Goodnick 1992, 352); it is likely that this was the principal cause of the estrangement between Sigmund and his father Jacob. That the estrangement ran deep and was a source of distress to Jacob became evident on the occasion of his son’s 35th birthday, when, in a gesture conforming with an established Jewish custom, he presented Sigmund with the family Bible which he had studied so closely as a child, newly rebound in leather. This was accompanied by a richly lyrical dedication in Hebrew, written in the style of melitzah, a literary tradition of Biblical allusion (Alter 1988, 23), referencing the relationship between them and their shared Jewish heritage. In part, the verse ran:

Son who is dear to me, Shelomoh. In the seventh in the days of the years of your life the Spirit of the Lord began to move you and spoke within you: Go, read in my Book that I have written and there will burst open for you the wellsprings of understanding, knowledge, and wisdom… For the day on which your years were filled to five and thirty I have put upon it a cover of new skin and have called it: “Spring up, O well, sing ye unto it!” And I have presented it to you as a memorial and as a reminder of love from your father, who loves you with everlasting love. (trans. and cited by Yerushalmi 1993, 71)

This attempt at effecting a rapprochement, which gently sought to remind Freud of his father’s love for him and of their shared religious and cultural heritage—implying, as one commentator puts it, “that their Bible embodies both the Jewish tradition and this love” (Gresser 1994, 31)—appeared initially not to have been successful. Freud never mentioned his father’s birthday dedication in his writings, though it was found after his death perfectly preserved in the Philippson Bible with which he had been presented, and his reductive critique of institutional religion became instead ever more sustained and pointed. Yet, at the deepest level, an ambivalence remained; as Freud acknowledged in his Autobiographical Study, “My deep engrossment in the Bible story (almost as soon as I had learnt the art of reading) had, as I recognised much later, an enduring effect upon the direction of my interest” (Freud 1959, XX 8).

The death of Jacob on 23rd October 1896 was one of the most important events in Sigmund Freud’s life and precipitated a lengthy period of reflective contemplation on their relationship. As he confessed later that year in a letter to his friend Wilhelm Fliess, “… the old man’s death has affected me deeply. I valued him highly, understood him very well, and with his peculiar mixture of deep wisdom and fantastic light-heartedness he had a significant effect on my life… in my inner self the whole past has been awakened by this event. I now feel quite uprooted” (Freud 1986, 202). The importance of the event cannot be overestimated; Jacob’s death triggered a period of sustained self-analysis in which Freud had what he considered an epiphany: the hostility which he had often felt towards his father, which had at one point made him suspect that Jacob had been guilty of sexually abusing him, was due to the fact that as a child he saw Jacob as a rival for his mother’s love. Thus was born the ideas of the Oedipus complex to which we have referred above, which, universalized by Freud, became one of the cornerstones of psychoanalytic theory. In his 1908 preface to the second edition of The Interpretation of Dreams, the work which made his reputation globally and brought him the financial security which he had craved, Freud made clear the extent to which his articulation of the new science owed to his analytical resolution of the crisis generated by Jacob’s death: “It was a portion of my own self-analysis, my reaction to my father’s death—that is to say, to the most important event, the most poignant loss of a man’s life” (Freud 2010, xxvi). Still awaiting resolution at that point, however, was the conflict generated in Freud’s life by the demand to find a means of affirming the richness and particularity of his Jewish cultural heritage, as his father had urged in his dedication, without acceding to the Biblical and theological orthodoxies associated with it. A number of scholars (Rice, 1990; Gresser, 1994) have suggested that this problem is one of the keys to an understanding of his final work, Moses and Monotheism.

3. Philosophical Connections

Two of the major formative influences upon Freud were those of the philosophers/psychologists Franz Brentano (1838—1917) and Theodor Lipps (1851—1914). Brentano was author of the seminal Psychology From an Empirical Standpoint (1973, orig. 1874); Freud took two philosophy courses under his direction when he first enrolled at the University of Vienna, as part of which he encountered Feuerbach’s writings on religion. Freud was captivated by the scope and clarity of Brentano’s lectures and found the latter’s emphasis on the need for empirical methods in psychology and for philosophy to be informed by logical rigour and scientific findings highly congenial. Less congenial to him, perhaps, were Brentano’s rational theism and his dismissal of the notion of unconscious mental states; these were two key issues on which Freud was subsequently to diverge sharply from him.

Freud—like other gifted students of Brentano such as Edmund Husserl (1859—1938) and Alexius Meinong (1853—1920)—was enthralled by him as a teacher and scholar, describing him in correspondence as “a darned clever fellow, a genius” (in Boehlich (ed.) 1992, 95). Such was the impact of Brentano’s influence that, at one stage, Freud resolved to take his doctorate in philosophy and zoology, a proposal towards which Brentano was favourably disposed but which faculty regulations at the University prevented from being realised.

In seeking to modernise psychology, Brentano had returned to the Aristotelian definition of the subject, understanding it as “the science which studies the properties and laws of the soul, which we discover within ourselves directly by means of inner perception, and which we infer, by analogy, to exist in others” (Brentano 1973, 5). In that connection, he revitalised the famous principle of intentionality from scholasticism as the defining criterion of mental phenomena and processes: unlike the physical counterparts from which they must be distinguished, mental or psychical phenomena, he argued, are necessarily directed towards intentional objects. Further, since such phenomena are accessible to us directly by means of “inner perception,” their existence and nature comes, he argued, guaranteed with an epistemic certainty and transparency that is markedly lacking in relation to our perception of physical phenomena, where, for example, we sometimes misapprehend such subjective characteristics as colour and taste as objective properties of things.

Given this distinction between the physical and the mental, Brentano considered that one of the key problems for an empirical psychology was that of constructing an adequate picture of the internal dynamics of the mind from an analysis of the complex interplay between diverse mental phenomena, on the one hand, and the interactions between the mind and the external world, on the other. This conception was to have a profound influence upon the development of Freudian psychoanalysis, into which it was to become prominently incorporated. However, Brentano set his face implacably against admitting the notion of unconscious mental states and processes into a fully scientific psychology. In this he was in part motivated by his conviction that all mental states are known directly in introspection or “inner perception” and are thus, by definition, conscious; mental acts, he considered, are pellucid in the sense that they take themselves as secondary objects and so are consciously apprehended as they occur. Further, the positing of the existence of unconscious mental states also seemed to him to introduce uncertainty and vagueness into the field of psychology and to carry with it an implication of the impossibility of the very rigorous, empirically-based science of mind which he sought to establish.

While Freud adopted Brentano’s characterisation of the intentional nature of mental phenomena throughout his work, he did not, of course, accept that all such phenomena are conscious, and indeed extended the very notion of intentionality, in the guise of symbolic meaning, to the level of the unconscious. For the primary focus of Freud’s interest was medical and his therapeutic practice was, from the outset, predicated upon the assumption of a level of scientific understanding of aberrant behaviour and abnormal mental states. And it seemed evident to him from an early stage that the restriction of psychology to the level of conscious processes and events had made, and would continue to make, such a goal unattainable, and that it was precisely because traditional psychology had operated with that restriction that it found such occurrences problematic and inexplicable. Thus, while both Brentano and Freud were motivated by the desire to create a fully scientific science of mind, they reached diametrically opposed positions on the question of the inclusion of the unconscious in its terms of reference. In contrast with Brentano’s belief that the very notion of the unconscious lacks intellectual validity, Freud was convinced that a scientific approach to the area of the mental requires the concept of the unconscious as a critical presupposition.

Freud found strong support for this conviction in Theodor Lipps, a thinker who was as committed as Brentano to the ideal of an empirically grounded psychology governed by an experimental methodology, but who, unlike Brentano, considered that this necessitated, at a fundamental level, reference to the unconscious. Lipps’ account of the nature of the unconscious was of particular importance to the development of Freud’s thought for two reasons: In the first instance, when Freud encountered Lipps’ view that consciousness is an “organ” which mediates the inner reality of unconscious mental processes, he found in it a theory which was almost identical to one at which he had independently arrived. Secondly, in his account of humor—which also anticipated much of Freud’s later work on that subject—Lipps had extended the notion of aesthetic empathy (Einfühlung; “in-feeling” or “feeling-into”) from Robert Vischer (1847—1933) into the psychological realm to designate the process that allows us to comprehend and respond to the mental lives of others by putting ourselves in their place, which involved the key notion that meaningful interaction between humans necessitates the projection of mental states and occurrences from the self to others.

Freud adopted and integrated Lipps’ account of projection centrally in his psychoanalytic theory, regarding it as a precondition for establishing the relationship between patient and analyst which alone makes the interpretation of unconscious processes possible. But perhaps of even greater consequence in connection with the analysis of religion is the fact that concomitant to the idea of psychological projection is the notion that the human need to ascribe psychological states to others can and does readily lead to situations in which such ascriptions are extended beyond their legitimate boundaries in the human realm. As David Hume had observed, “There is an universal tendency among mankind to conceive all beings like themselves, and to transfer to every object those qualities with which they are familiarly acquainted, and of which they are intimately conscious” (Hume 1956, Section 111). It is in that way that personifications or anthropomorphisms arise: human beings, particularly at the early stage of their development, have an innate tendency to go beyond the legitimate boundaries of application of the psychological concept-range and thus to misapply human-being concepts. A child relates to its environment at large most readily through such a process: in the narratives provided by story­books, school text-books and film and televisual animation, the child’s interest, attention, and above all, its understanding, are engaged through the attribution of anthropomorphic qualities to non-human objects and organisms: bees worry, trees are sad, ants are curious, and so on.

In his Essence of Christianity (1841; English trans. 1881), Ludwig Feuerbach had offered a sustained critique of religion predicated upon the notion that the very idea of God is such an anthropomorphic construct, with no reality beyond the human mind, and that specific characteristics attributed to God in religion (Love, Benevolence, Power, Knowledge, and so forth) embody an idealized conception of human nature and of the values esteemed by human beings. This projectionist view, which he first encountered under Brentano’s—no doubt, critical—tutelage, was one which Freud came to accept implicitly and indeed to extend, holding that the insights offered by psychoanalysis into the workings of the human mind can explain just why and how religious anthropomorphisms arise. Freud accordingly integrated his account of religion into the broader project of psychoanalysis, suggesting that “a large portion of the mythological conception of the world which reaches far into the most modern religions is nothing but psychology projected into the outer world… We venture to explain in this way the myths of paradise and the fall of man, of God, of good and evil, of immortality and the like—that is, to transform metaphysics into meta-psychology” (Freud 1914, 309. Italics in original).

4. The Orientation of Freud’s Approach to Religion

In articulating this project, Freud drew deeply upon a wide variety of anthropological sources, particularly the work of such contemporary luminaries as John Ferguson McLennan (1827—1881), Edward Burnett Tylor (1832—1917), John Lubbock (1834—1913), Andrew Lang (1844—1912), James George Frazer (1854—1941) and Robert Ranulph Marett (1866—1943) on the connection between social structures and primitive religions. Freud’s claim to originality in this context resides in his attempt to situate projectionism within the framework of psychoanalysis, ultimately interpreting the social origins and cultural significance of the religious impulse in terms paralleling his account of the father-son relationship in individual psychology.

The evolutionist paradigm, which projected a universal linear cultural development from the primitive to the civilized, with the differences found in human societies reflecting stages in that development, gradually came to function as a background assumption in Freud’s thought from an early stage. Tylor, whose Primitive Culture (1871) and Anthropology (1881) are generally regarded as foundational to the then emergent science of cultural anthropology, held that, in terms of human interaction with the world at large, civilization progresses through three developmental “stages,” from magic through religion to science, with contemporary Western culture representative of the final stage. This view was rearticulated by Frazer in his famous Golden Bough and referenced approvingly by Freud (2001, 90), though he emphasized that elements of the first two stages continue to operate in contemporary life. Accordingly, Freud gradually adopted the position of one who seeks to explicate the significance of religion in the context of a cultural milieu in which, having supplanted attempts to control the world through sympathetic magic, it has itself been superseded by science. Furthermore, Freud found in Tylor’s and Frazer’s evolutionist account of cultural progress an implication which had been affirmed explicitly by Feuerbach: “Religion is the childlike condition of humanity” (Feuerbach 1881, 13); it belongs to a social developmental stage paralleling that of the individual, through which each civilization must pass en route to the maturity of scientific understanding. It was perhaps this latter, more than any other factor, which was to suggest to Freud that the psychoanalytical techniques which he pioneered in his account of individual psychology could be applied socially, to explain the nature of the religious impulse in human life generally.

5. Totemism and the Father Complex

Some of Freud’s earliest comments on religion give immediate evidence of the psychologically reductionist direction which his thought was to take, which represented the dynamic underpinning religion as deriving from the powerfully ambivalent relationship between the child and his apparently omnipotent father. For example, in his 1907 paper “Obsessive Actions and Religious Practices” he drew attention to similarities between neurotic behavior and religious rituals, suggesting that the formation of a religion has, as its “pathological counterpart,” obsessional neurosis, such that it might be appropriate to describe neurosis “as an individual religiosity and religion as a universal obsessional neurosis” (Freud 1976 S.E. IX, 125-6), a view which he was to retain for the remainder of his life.

Freud’s first sustained treatment of religion in these terms occurs in his 1913 Totem and Taboo, in the context of his account, heavily influenced in particular by the work of James George Frazer, Andrew Lang and J.J. Atkinson, of the relationship between totemism and the incest prohibition in primitive social groupings. The prominence and strength of the incest taboo was of considerable interest to him as a psychologist, not least because he saw it as one of the keys to an understanding of human culture and as deeply linked to the concepts of infantile sexuality, Oedipal desire, repression and sublimation which play such a key role in psychoanalytic theory. In tribal groups the incest taboo was usually associated with the totem animal with which the group identified and after which it was named. This identification led to a ban on the killing or the consumption of the flesh of the totem animal and on other restrictions on the range of permissible behaviors and, in particular, it led to the practice of exogamy, the prohibition of sexual relations between members of the totem group.

Such prohibitions, Freud believed, are extremely important as they constitute the origins of human morality, and he offered a reconstruction of the genesis of totem religions in human culture in terms which are at once forensically psychoanalytical and rather egregiously speculative. The primal social state of our pre-human ancestors, he argued, closely following J.J. Atkinson’s account in his Primal Law, was that of a patriarchal “horde” in which a single male jealously maintained sexual hegemony over all of the females in the group, prohibiting his sons and other male rivals from engaging in sexual congress with them. In this account, the psycho-sexual dynamic operating within the group led to the violent rebellion of the sons, their murder of the father and their consumption of his flesh (Atkinson 1903, chapters I-III; Freud 2001, 164). However, the sons’ subsequent recognition that no one of them had the power to take the place of the father led them to create a sacred totem with which to identify him and to reinstate the practice of the exogamy which the parricide was designed to abolish: the creation of the totem yielded a totem clan within which sexual congress between members was forbidden. The identification of the totem animal with the father arose out of a displacement of the deep sense of guilt generated by the murder, while simultaneously being an attempt at reconciliation and a retrospective renunciation of the crime by creating a taboo around the killing of the totem. “They revoked their deed by forbidding the killing of the totem, the substitute for their father; and they renounced its fruits by resigning their claim to the women who had now been set free” (Freud 2001, 166). This identification, Freud asserted, confirmed the link between neurosis and religion suggested by him in 1907: given that the totem animal represents the father, then the two main taboo prohibitions of totemism, the ban on killing the totem animal and the incest prohibition, “coincide in their content with … the two primal wishes of children [to kill the father and have sexual intercourse with the mother], the insufficient repression or re-awakening of which forms the nucleus of perhaps all psychoneuroses” (Freud 2001, 153).

The parricidal deed, Freud asserted, is the single “great event with which culture began and which, since it occurred, has not let mankind a moment’s rest” (Freud 2001, 168), the acquired memory traces of which underpins the whole of human culture, including, and in particular, both totem and developed religions. Such a view, of course, presupposes the validity of the essentially Lamarckian idea that traits acquired by individuals, including psychological traits such a memory, can be inherited and thus passed through the generations. This was a controversial notion to which Freud, who never fully accepted the Darwinian account of evolution through natural selection, steadfastly adhered throughout his life, in the face of scientific criticism. He also took it as being consistent with Ernst Haeckel’s (1834—1919) view that ontogeny recapitulates phylogeny, that is, that the stages of individual human development repeat that of the evolution of humanity—which he took as scientific justification of his belief that psychoanalytical techniques could be applied with equal validity to the social as to the individual.

The counterpart to the primary taboo against killing or eating the totem animal, Freud pointed out, is the annual totem feast, in which that very prohibition is solemnly and ritualistically violated by the tribal community, and he followed the Orientalist William Robertson Smith (1846—1894) in linking such totem feasts with the rituals of sacrifice in developed religions. Such feasts involved the entire community and were, Freud argued, a mechanism for the affirmation of tribal identity through the sharing of the totem’s body, which was simultaneously an affirmation of kinship with the father. Freud saw no contradiction in such a ritual, holding that the ambivalence contained in the father-complex pervades both totemic and developed religions: “Totemic religion not only comprises expressions of remorse and attempts at atonement, it also serves as a remembrance of the triumph over the father” (Freud 2001, 169). The father is thus represented twice in primitive sacrifice, as god and as totem animal, the totem being the first form taken by the father substitute and the god a later one in which the father reassumes his human identity. The dynamic which operates in totem religions, Freud argued, is sustained by and underpins the evolution of religion into its modern forms, where the need for communal sacrifice to expiate an original sin should also be understood in terms of parricide guilt.

6. Religion and Civilization

In time Freud came to consider that the account which he had given in Totem and Taboo did not fully address the issue of the origins of developed religion, the human needs which religion is designed to meet and, consequently, the psychological motivations underpinning religious belief. He turned to these questions in his The Future of an Illusion (1927; reprinted 1961) and Civilization and its Discontents (1930; reprinted 1962). In the two works he represented the structures of civilization, which permit men to live in mutually beneficial communal relationships, as emerging only as a consequence of the imposition of restrictive processes on individual human instinct. In order for civilization to emerge, limiting regulations must be created to frustrate the satisfaction of destructive libidinal drives, examples of which are those directed towards incest, cannibalism and murder. Even the religious injunction to love one’s neighbor as oneself, Freud argued, springs from the need to protect civilization from disintegration. Given that history demonstrates that man is “a savage beast to whom consideration towards his own kind is something alien” (Freud 1962, 59), the fashioning of a value system based upon the requirement to develop loving relationships with one’s fellow man is a social and cultural necessity, without which we would be reduced to living in a state of nature. For Freud, the principal task of civilization is thus to defend us against nature, for without it we would be entirely exposed to natural forces which have almost unlimited power to destroy us.

Extending his account of repression from individual to group psychology, Freud contended that, with the refinement of culture, the external coercive measures inhibiting the instincts become largely internalized. Humans become social and moral beings through the functioning of the superego in effecting a renunciation of the more antisocial drives: “external coercion gradually becomes internalized; for a special mental agency, man’s super-ego, takes it over and includes it among its commandments… Those in whom it has taken place are turned from being opponents of civilization into being its vehicles” (Freud 1961, 11). However, the effect of such renunciations is to create a state of cultural privation “resembling repression” (Freud 1961, 43), which in order to foster social harmony must in turn be dissipated by sublimation, the creation of substitute satisfactions for the drives.

Professional work, Freud argued, is one area in which such substitutions take place, while the aesthetic appreciation of art is another significant one; for art, though it is inaccessible to all but a privileged few, serves to reconcile human beings to the individual sacrifices that have been made for the sake of civilization. However, the effects of art, even on those who appreciate it, are transient, with experience demonstrating that they are insufficiently strong to reconcile us to misery and loss. For that effect, in particular for the achievement of consolation for the suffering and tribulations of life, religious ideas become invoked; these ideas, he held, consequentially become of the greatest importance to a culture in terms of the range of substitute satisfactions which they provide.

The role which religion has played in human culture was thus described by Freud in his 1932 lecture “On the Question of a Weltanschauung” as nothing less than grandiose; because it purports to offer information about the origins of the universe and assures human beings of divine protection and of the achievement of ultimate personal happiness, religion “is an immense power, which has the strongest emotions of human beings at its service” (Freud 1990, 199). Since religious ideas thus address the most fundamental problems of existence, they are regarded as the most precious assets civilization has to offer, and the religious worldview, which Freud acknowledged as possessing incomparable consistency and coherence, makes the claim that it alone can answer the question of the meaning of life.

For Freud, then, the cultural and social importance of religion resides both in reconciling men to the limitations which membership of the community places upon them and in mitigating their sense of powerlessness in the face of a recalcitrant and ever-threatening nature. In this respect again, Freud held, group psychology is an extension of individual psychology, with the powerful father figure in patriarchal monotheistic religions providing the required protection against the threat of destruction: “Now that God was a single person, man’s relations to him could recover the intimacy and intensity of the child’s relation to his father” (Freud 1961, 19). It is in this sense, he argued, that the father-son relationship so crucial to psychoanalysis demands the projection of a deity configured as an all-powerful, benevolent father figure.

Genetically, Freud argued, religious ideas thus owe their origin neither to reason nor experience but to an atavistic need to overcome the fear of an ever-threatening nature: “[they] are not precipitates of experience or end results of thinking: they are illusions, fulfilments of the oldest, strongest and most urgent wishes of mankind. The secret of their strength lies in the strength of those wishes” (Freud 1961, 30). In declaring such ideas illusory Freud did not initially seek to suggest or imply that they are thereby necessarily false; an illusory belief he defined simply as one which is motivated in part by wish-fulfillment, which in itself implied nothing about its relation to reality. He gives the example of a middle-class girl who believes that a prince will marry her; such a belief is clearly inspired by a wish-fantasy and is unlikely to prove justified, but such marriages do occasionally happen. Religious beliefs, he suggested in The Future of an Illusion, are illusions in that sense; unlike delusions, they are not, or are not necessarily, “in contradiction with reality” (Freud 1961, 31). However, by the time he wrote Civilization and its Discontents he was prepared to take his religious skepticism a stage further, explicitly declaring religious beliefs to be delusional, not only on an individual but on a mass scale: “A special importance attaches to the case in which [the] attempt to procure a certainty of happiness and a protection against suffering through a delusional remolding of reality is made by a considerable number of people in common. The religions of mankind must be classed among the mass-delusions of this kind” (Freud 1962, 28).

Given that religion has, as Freud acknowledged, made very significant contributions to the development of civilization, and that religious beliefs are not strictly refutable, the question arises as to why he came to consider that religious beliefs are delusional and that a turning away from religion is both desirable and inevitable in advanced social groupings. The answer given in Civilization and its Discontents is that, in the final analysis, religion has failed to deliver on its promise of human happiness and fulfillment; it seeks to impose a belief structure on humans which has no rational evidential base but requires unquestioning acceptance in the face of countervailing empirical evidence: “Its technique consists in depressing the value of life and distorting the picture of the real world in a delusional manner—which presupposes an intimidation of the intelligence” (Freud 1962, 31). He took this as confirming his belief that religion is akin to a universal obsessional neurosis generated by an unresolved father complex and is situated on an evolutionary trajectory which can only lead to its general abandonment in favor of science. “If this view is right,” he concluded, “it is to be supposed that a turning-away from religion is bound to occur with the fatal inevitability of a process of growth, and that we find ourselves at this very juncture in the middle of that phase of development” (Freud 1961, 43). That Freud saw the movement from religious to scientific modes of understanding as a positive cultural development cannot be doubted; indeed, it is one which he saw himself facilitating in a process analogous to the therapeutic resolution of individual neuroses: “Men cannot remain children for ever; they must in the end go out into ‘hostile life’. We may call this education to reality. Need I confess to you that the sole purpose of my book is to point out the necessity for this forward step?” (Freud 1961, 49).

In Civilization Freud mentions that he had sent a copy of The Future of an Illusion to an admired friend, subsequently identified as the French novelist and social critic Romain Rolland. In his response, Rolland indicted broad agreement with Freud’s critique of organised religion, but suggested that Freud had failed in his attempt to identify the true experiential source of religious sentiments: a mystical, numinous feeling of oneness with the universe, “a sensation of ‘eternity’, a feeling as of something limitless, unbounded—as it were, ‘oceanic’” (In Freud 1962, 11). The occurrence of this feeling, Rolland argued, is a subjective fact about the human mind rather than an article of faith; it is common to millions of people and is undoubtedly “the source of the religious energy which is seized upon by the various Churches and religious systems” (In Freud 1962, 11). Thus, he suggested, it would be entirely appropriate to count oneself as religious “on the ground of this oceanic feeling alone, even if one rejects every belief and every illusion” (In Freud 1962, 11). In that sense, he concluded, there is an important sense in which Freud’s account of the origins of religion missed its mark to a significant degree.

Freud was clearly troubled by Rolland’s challenge, confessing that it caused him no small difficulty. On the one hand his respect for Rolland’s intellectual honesty made him take seriously the possibility that his analysis of religion might be deficient in failing to take cognizance of mystical feelings of the kind described. On the other hand, he was confronted with the obvious problem that feelings are notoriously difficult to deal with in a scientific manner. Additionally—and perhaps more importantly—Freud admitted to being unable to discover the oceanic feeling in himself, though he was not disposed on that ground to deny the occurrence of it in others. Given that such a feeling exists, even on the scale suggested by Rolland, the only question to be faced, Freud declared, is “whether it ought to be regarded as the fons et origo of the whole need for religion” (Freud 1962, 12).

Dismissing the possibility of accounting for the oceanic feeling in terms of an underlying physiology, Freud’s response was to focus on its “ideational content,” that is, the conscious ideas most readily associated with its feeling-tone. In that connection, he offered an account of the oceanic feeling as being a revival of an infantile experience associated with the narcissistic union between mother and child, in which the awareness of an ego or self as differentiated from the mother and world at large has yet to emerge in the child. In that sense, he contended, it would be implausible to take it as the foundational source of religion, since only a feeling which is an expression of a strong need could function as a motivational drive. The oceanic feeling, he conceded, may have become connected with religion later on, but he insisted that it is the experience of infantile helplessness and the longing for the father occasioned by it which is the original source from which religion derives (Freud 1962, 19).

However, while this analysis of the relation between religion and mystical experience is acknowledged as important and influential, few commentators have deemed it entirely adequate, the self-confessed absence of any direct experience of the oceanic feeling in Freud’s own case seeming to many to have led to an underestimation on his part of the significance of such feelings in the genesis of religion.

A very significant body of literature has since grown up around the idea that religion might have emerged genetically, and derive its dynamic energy, as Rolland suggested, from mystical feelings of oneness with the universe in which fear and anxiety are transcended and time and space are eclipsed. The work of thinkers as diverse as Paul Tillich (1886—1965), Ludwig Wittgenstein (1889—1951) and Paul Ricoeur (1913—2005) in this connection has proven influential and has established an ongoing dialogue between psychology and philosophy/theology (compare Parsons, 1998, 501). Additionally, Freud’s dismissal of the possibility of a physiological approach to mystical experience has been questioned. Recent scientific investigation of the neurophysiological correlates of mystical or spiritual experiences, utilizing magnetic resonance imaging (MRI) and related technologies, while extremely controversial, appears to demonstrate that some deep meditative practices trigger alterations in brain metabolism, occasioning the kind of numinous feelings specified by Rolland (compare d’Aquili, & Newberg 1999, ch. 6; Saarinen 2015, 19).

7. The Moses Narrative: The Origins of Judaic Monotheism

In 1939, while exiled in Britain and suffering from the throat cancer which was to lead to his death, Freud published his final and most controversial work, Moses and Monotheism. Written over a period of many years and sub-divided into discrete segments, two of which were published independently in the periodical Imago in 1937, the book has an inelegant structure. The many repetitions that it contains, coupled with the initial strangeness of the arguments advanced, persuaded some that it was the product of a man whose intellectual powers had fallen into serious decline. The analysis of Judaism offered in the text also evoked a vitriolic response from some quarters and even led to allegations of Jewish self-hatred on Freud’s part. However, in more recent times the book has become recognized as one of the most important in the Freudian canon, offering an innovative contribution to the understanding of the nature of religious truth and of the role played by tradition in religious thought.

The focal point of the work is the figure of Moses and his connection with Egypt, which had exerted a fascination on Freud since his childhood study of the Philippson bible, as evidenced also in his publication of the essay “The Moses of Michelangelo” in 1914. Accordingly, at this late juncture in his life and with the threat of fascist antisemitism looming over Europe, he turned his attention once more to the religion of his forefathers, constructing an alternative narrative to the orthodox Biblical one on the origins of Judaism and the emergence from it of Christianity. Developing a thesis partly suggested by work of the protestant theologian Ernst Sellin (1867—1946) in 1922, Freud argued that the historical Moses was not born Jewish but was rather an aristocratic Egyptian who functioned as a senior official or priest to the Pharaoh Amenhotep IV. The latter had introduced revolutionary changes to almost all aspects of Egyptian culture in the 14th century B.C.E., changing his name to Akhenaten, centralizing governmental administration and moving the capital from Thebes to the new city of Akhetaten. More significantly, he had also introduced a strict new universal monotheistic religion to Egypt, the religion of the god Aton or Aten, in the process outlawing as idolatrous the veneration of the traditional Egyptian polytheistic deities, including the then dominant religion of Amun-Ra, removing all references to the possibility of an afterlife and prohibiting the creation of graven images. He had also proscribed all forms of magic and sorcery, closed all the temples and suppressed established religious practice, thereby undermining the social status and political power of the Amun priests. In Freud’s words, “This king undertook to force upon his subjects a new religion, one contrary to their ancient traditions and to all their familiar habits. It was a strict monotheism, the first attempt of its kind in the history of the world as far as we know and religious intolerance, which was foreign to antiquity before this and for long after, was inevitably born with the belief in one God” (Freud 1939, 34-5). This religion was represented as a universal rather than a local one, reflective of the fact that imperial conquest had extended the Pharaoh’s rule beyond the borders of Egypt into Nubia, Syria and parts of Mesopotamia, which brought with it the novel idea of exclusivity: that the God Aton was not merely the supreme god, but the only god.

These radical innovations were not well received either by the disempowered Amun priestly caste or by the Egyptian general populace; predictably, they produced a fanatical desire for retribution and the return of the traditional religious practices on the part of the priests and the discontented people, “a reaction which was able to find a free outlet after the king’s death” (Freud 1939, 39). Thus, when the Pharaoh died in 1358 B.C.E. the religion of Aton was ruthlessly suppressed in Egypt and Akhenaten became known to his successors as the “heretic king” whose memory they sought to expunge from the historical record. In his narrative, Freud depicts a despairing Moses, a devotee of the Aton religion, seeing “his hopes and prospects destroyed” (Freud 1939, 46), responding to these events by placing himself at the head of an enslaved Semitic tribe which had long been in bondage in Egypt and leading them to freedom across the Sinai. In the process he converted them to an even more spiritualized, rigorous and demanding form of monotheism, which involved the Egyptian custom of circumcision, a symbolic act of submission to the Divine Will.

In the Freudian narrative the onerous demands of the new religion ultimately led his followers to rebel and to kill Moses, an effective repetition of the original father murder outlined in Totem and Taboo, after which they turned to the cult of the volcano god Yahweh. But the memory of the Egyptian Moses remained a powerful latent force until, several generations later, a second Moses, the son-in-law of the Midianite priest Jethro, shaped the development of Judaism by integrating the monotheism of his predecessor with the worship of Yahweh. By this means the guilt deriving from the murder of the original Moses survived in the collective unconscious of the Jewish people and led to the hope of a messiah who would redeem them for their forefathers’ murderous act.

While Freud evidently retained his view of religion as the analogue of an obsessional neurosis, this account now contained the recognition that, as such, its effects are not necessarily pathological, but, on the contrary, can also be socially and culturally beneficial in a marked way. Thus he points out in his narrative that, through the example and guidance of the great prophets, there arose an ethical tradition within Judaism, ultimately traceable back to Moses the Egyptian, which proscribed iconic representation and ceremonial performance, demanding in their place belief and “a life of truth and justice” (Freud 1939, 82), a tradition with which Freud evidently had deep affinity. In his view, the Judaic ethic was one which demanded restrictions on the gratification of certain instincts as being incompatible with its spiritualised view of human nature and dignity, in a manner paralleling that in which the totem laws had imposed the rule of exogamy within the totem clan. Such restrictions, he argued, enabled Jewish culture to flourish and to take on its unique character. The prophets “did not tire of maintaining that God demands nothing else from his people but a just and virtuous life: that is to say, abstention from the gratification of all impulses that according to our present-day moral standards are to be condemned as vicious” (Freud 1939, 187). In this account, the murder of Moses was thus the initial event which provoked a sense of guilt that in turn shaped the ethical content of Judaic monotheism. This guilt, Freud argued, marked what he termed “the return of the repressed” (Freud 1939, 197), the emergence of compulsive patterns of behavior in the life of a social group generated by a dynamic originating in a traumatic event lying in the distant past but mediated and transmitted to the present in covert form by a tradition inspired, and partly shaped, by unconscious memory-traces. “All phenomena of symptom-formation can be fairly described as ‘the return of the repressed’,” he argued; “The distinctive character of them, however, lies in the extensive distortion the returning elements have undergone, compared with their original form” (Freud 1939, 201). This is something, he held, which constitutes an “archaic heritage” that does not need to be reacquired by each generation, but merely to be reawakened, and he charted the development of that heritage by means of an enumeration of the stages by means of which the repressed returns, from the primeval father through to the totem, to the hero, then to the polytheistic gods and finally to the monotheistic concept of a single Highest Being.

On this account, the obsessional sense of guilt governing and shaping the ascetic, highly spiritualized ethic implicit in Judaism has been passed on through the generations, such that it has become the very essence of the Jewish character: “The origin … of this ethics in feelings of guilt, due to the repressed hostility to God, cannot be gainsaid. It bears the characteristic of being never concluded and never able to be concluded with which we are familiar in the reaction-formations of the obsessional neurosis” (Freud 1939, 212). To recognize, through this form of (psycho)analysis, the genesis of the ethical system in the guilt arising from a nefarious historical deed is, he suggested, to free oneself from its obsessive features while simultaneously accepting its entirely human origins. But such a recognition does not entail an abandonment of the core value system, as there is a sense, as Freud acknowledged to be true in his own case, in which that ethical heritage cannot be repudiated once it is acquired.

This narrative account of the rootedness of the Jewish monotheistic tradition in the life and murder of the man Moses captures what Freud believed to be its most essential feature, something “majestic,” an eternal truth, “historic” rather than “material,” that “in primaeval times there was one person who must needs appear gigantic and who, raised to the status of a deity, returned to the memory of men” (1939, 204). For this reason, a number of commentators, in particular, Gresser and Friedman, argue persuasively that the Moses text should be seen as a response to the question posed by many of Freud’s critics after the publication of the Hebrew edition of Totem and Taboo as to the sense in which he remained, as he claimed, “in his essential nature a Jew,” given his psychologically reductive analysis of religion and his perceived hostility to religious orthodoxy. The answer, they suggest, could be offered by him in Moses and Monotheism only in terms of what he saw as essential to Judaism itself, a rigorous, spiritually intellectualized life ethic, centering on the virtues of truth and justice, derived from the man Moses, its human creator, through the work and influence of the prophets (compare Whitebook 2017, 68-9).

In early Christianity, Freud argued, the guilt of Moses’ murder became reconfigured in the Pauline tradition as the notion of an original sin for which atonement must be sought through a sacrificial death, the effect of which was to abolish the feeling of guilt and supplant Judaism with Christianity: “Paul, by developing the Jewish religion further, became its destroyer. His success was certainly mainly due to the fact that through the idea of salvation he laid the ghost of the feeling of guilt” (Freud 1939, 141). Once again, this historical transition was interpreted by Freud in clear Oedipal terms: “Originally a Father religion, Christianity became a Son religion. The fate of having to displace the Father it could not escape” (Freud 1939, 215). However, he held that the advent of Christianity was in some respects a step back from monotheism and a reversion to a covert form of polytheism, with the panoply of saints standing as a surrogate for the lesser gods of pagan antiquity. He accordingly saw the process whereby Christianity supplanted Judaism as comparable to the historical expunging of the monotheistic religion of Aton in ancient Egypt after the death of the Pharaoh Akhenaten: “The triumph of Christianity was a renewed victory of the Amon priests over the God of Ikhnaton” (Freud 1939, 142).

What is arguably of most importance in the Moses narrative is that it constitutes a final effort by Freud to reconcile himself with his own Jewish heritage; as one critic suggests, “Freud uses Moses to re-affirm his loyalty to a people whose religion he does not share but whose claim on him he steadfastly refuses to disavow” (Friedman, 1998, 148). The Jewish people, Freud pointed out, have a self-confidence which springs from the idea of being chosen by God from amongst the peoples of the world, an idea which derives strength from the related notion of participation in the reality of a supreme Deity. But the tenet of the Judaic religion which historically has had perhaps the most significant effect of all, he contended, has been the prohibition, derived from the religion of Aton, of graven images as idolatrous. That forces the believer into worship of a dematerialized God, an abstraction apprehensible only to the intellect, a movement described by Freud as “a triumph of spirituality over the senses” (Freud 1939, 178). This shift from the sensible to the conceptual was, he believed, “unquestionably one of the most important stages on the way to becoming human” (Freud 1939, 180), and it gave a preeminence to abstractions in Jewish intellectual life that made possible some of its key contributions to Western mathematics, science and literature, including, of course, the discipline of psychoanalysis. In that sense, he ultimately recognized that the very science of mind which he had pioneered and with which he sought to expose the Oedipal nature of religion was itself a cultural product of the Judaic religious impulse.

8. Critical Responses

Freud’s utilization of the conceptual apparatus of psychoanalysis in his treatment of religion yields a naturalistic account rooted in psychoanalytic theory which, while being arguably one of the more self-consistent to be found in the modern age, is also one of the most controversial. In its main features it strongly anticipated, and almost certainly influenced, contemporary critiques of religion associated with the “New Atheism” movement of the late 20th and early 21st centuries, such as those of Daniel Dennett, Richard Dawkins, Sam Harris and Christopher Hitchens (1949—2011). The impact of Freud’s psychoanalytical projectionism can also be traced in the development of contemporary radical theology, particularly in the work of Don Cupitt and Lloyd Geering. The responses to it, in turn, occupy a very wide spectrum, from enthusiastic affirmation to condemnatory repudiation. A representative sample of these would include the following.

a. The Anthropological Critique

 The idea of the “primal horde” was derived by Atkinson and Freud from what was no more than a cautious suggestion by Darwin in his Descent of Man that, amongst several possibilities regarding the social organization of “primeval” humans, one was that it might have consisted of small patriarchal groups led by a single dominant male, “each with as many wives as he could support and obtain, whom he would have jealously guarded against all other men” (Darwin 1981, II 362). This suggestion, which became one of the linchpins of Freud’s account of totem religion, has not received scientific corroboration, and it remains questionable whether the idea has any basis in reality (compare Smith, R.J. 2016). Further, the progressivist evolutionary paradigm championed by Freud, with its projection of a universal linear cultural development from the primitive to the civilized, is largely rejected by contemporary ethnologists and social anthropologists, in particular those influenced by the work of Franz Boas (1858—1942). The assimilation of prehistoric humans with contemporary “primitive” humans on which it is based, and the narrative constructed out of that assimilation, is generally regarded as Eurocentric in its presuppositions and as deriving from the mindset of 19th century imperialism (Kenny, R. 2015). Thus, in his influential review of Freud’s Totem and Taboo in 1919, the eminent American anthropologist Alfred L. Kroeber, who was a disciple of Boas, subjected Freud’s account of totemism to an extended and trenchant critique, suggesting that the method employed in it amounted to “multiplying into one another, as it were, fractional certainties … without recognition that the multiplicity of factors must successively decrease the probability of their product” (Kroeber 1920, 51). Kroeber attributed this almost entirely to the reliance by Freud on the speculative approach taken by such nineteenth century ethnologists as Tylor and Frazer; their anthropological work, he stated bluntly, “is not so much ethnology as an attempt to psychologize with ethnological data” (Kroeber 1920, 55). In a less trenchantly-worded retrospective review written 20 years later, Kroeber—who had in the interim spent some time as a practicing lay psychoanalyst—sought to make conceptual space for a reconciliation of Freud’s theory with scientific ethnology by making a distinction between “historical” and “psychological” thinking, suggesting that Freud’s account should be understood as involving the latter rather than the former (Kroeber 1939, 447). However, notwithstanding that, Kroeber’s strongly negative assessment in his original review of Freud’s incursion into the field of scientific anthropology is now generally accepted within the discipline. Accordingly, Freud’s account of totemism, considered as a direct contribution to an understanding of the development of human culture, would now be viewed with considerable suspicion by professional anthropologists.

b. Myth or Science?

For these reasons, Freud’s projectionist theory of religion as evolving from a primal parricide has been called into serious question as a scientific or historical hypothesis, and with it, the status of psychoanalysis itself. Karl Popper (1902—1994) and Ludwig Wittgenstein have both argued against Freud’s repeated claim for the scientific status of psychoanalysis and—by implication—the account of religion which he developed from it. Popper did so on the grounds that the terms in which psychoanalytic theory is couched make it unfalsifiable in principle and thus unscientific. The theories of Freud and Adler, he argued, describe some facts, but “in the manner of myths. They contain most interesting psychological suggestions, but not in a testable form” (Popper 1963, 37), unlike, for example, the propositions of the natural sciences which almost certainly served as a model for Freud. Wittgenstein, who considered Freud to be one of the few contemporary thinkers with “something to say” (Wittgenstein 1966, 41), albeit one whose whole way of thinking “wants combatting” (ibid., 50), was intrigued by Freud’s focus on mythology in his narratives, and saw that much of the persuasive force of his work derived from the claim that it has constructed a scientific explanation of ancient myths. However, he considered that what Freud had effected was of a different order: “What he has done is propound a new myth” (Wittgenstein 1966, 51).

In a similar vein, Paul Ricoeur, in conceding that the primal parricide depicted by Freud is constructed out of ethnological scraps “on the pattern of the fantasy deciphered by analysis” (Ricoeur 1970, 208), proposed that it, and indeed the entire edifice of Freud’s psychoanalytic theory, should itself be read as being essentially mythical rather than scientific. He thus argued that “one does psychoanalysis a service, not by defending its scientific myth as science, but by interpreting it as myth” (Ricoeur 1970, 20). This latter stratagem, with some variations, has subsequently been adopted by a number of other commentators who seek a mechanism to validate the Freudian cultural narrative in the face of its undeniable ethnological shortcomings (compare, for example, Paul, 1996). It is worth noting that Ricoeur’s conception of the mythic is complex, and occurs within the context of his construction of a religious hermeneutics that engages and intersects with the Freudian psychoanalytic one while seeking to go beyond it, a hermeneutics that regards myths not as fables, “but rather as the symbolic exploration of our relationship to beings and to Being” (Ricoeur 1970, 551). On such a view, the deficiencies presented by the Freudian narrative are read as being hermeneutic rather than scientific, open to further articulation and refinement through a more nuanced and balanced interpretation of the symbolic structure of religious discourse.

However, the hermeneutic construal of the Freudian enterprise is itself open to the charge that it fails utterly to acknowledge the over-arching importance attributed by Freud to his claim that psychoanalysis is to be properly regarded as a rigorous science of the mind and has been vigorously critiqued on those and related grounds by Adolf Grünbaum (1923—2018). For Grünbaum, the hermeneutic approach to Freud constitutes a serious distortion of its subject matter and is reflective of an objectionable scientophobia; rather immoderately, he accused it of having “all of the earmarks of an investigative cul-de-sac, a blind alley rather than a citadel for psychoanalytic apologetics” (Grünbaum 1984, 93). By contrast, he insisted on seeing psychoanalysis precisely as a testable theory, but one which is based upon clinical reports from therapeutic practice rather than rigorous experimentally-derived evidence. He pointed out that Freud, whom he considered “a sophisticated scientific methodologist” (ibid., 128), was fully aware of and highly sensitive to the question of the logic of the confirmation and disconfirmation of psychoanalytic interpretations, but contended that his utilization of the notion of consilience in that connection could not meet the demands of full scientific probity. Grünbaum accordingly came to view psychoanalysis as being based upon an inadequate conception of scientific confirmation; the clinical data ostensibly adduced in its favor from therapeutic sessions—which Ernest Jones had described as “the real basis” of psychoanalysis (Jones 1959, 1:3) —are, he argued, the products of a shared influence and are irremediably contaminated by suggestion on the part of the analyst. They cannot therefore properly be regarded as providing confirmatory evidence for the theory, while contemporary psychoanalysis has not met the objection that successful therapy operates as a placebo.

c. Lamarckian vs. Darwinian Evolutionary Principles

As we have seen, Freud’s transposition of the father complex from individual infantile development to the social order relied heavily on Haeckel’s thesis that ontogeny recapitulates phylogeny. The latter is now largely rejected by contemporary science, in particular the manner in which Freudians have adopted it to model the social evolution of human beings analogically with the psychological development of children. Further, it seems evident that Freud’s transposition is deeply problematic and leaves psychoanalysis unable to explain the wide variety of culturally determined personality structures which are demonstrated by contemporary empirical research. Freud’s commitment to Lamarckian evolutionary principles has, of course, also received significant critical comment from the scientific community (Slavet 2009, Ch. 2; Yerushalmi 1993, Ch. 2), though it must be noted that his account of acquired memory traces as being partly constitutive of Jewish identity in Moses and Monotheism owes as much to August Weissmann’s germ-plasma theory of inheritance as it does to Lamarckism (Slavet 2009, 28).

d. The Primordial Religion: Polytheism or Monotheism?

The entire enterprise of accounting for the origins of religion as an evolutionary trajectory from polytheism to monotheism has been challenged by the work of the ethnologist Father Wilhelm Schmidt (1868—1954), whose multi-volume Der Ursprung der Gottesidee (The Origin of the Idea of God; 1912—1955) is a wide-ranging study of primitive religion. In it Schmidt argued that the “original” tribal religion was almost invariably a form of primitive monotheism, focused on belief in a single benevolent creator god, with polytheistic religions featuring at a later stage of cultural development. Schmidt, who was influenced by Boas and his followers, was accordingly critical of evolutionist accounts of religious development, contending that they frequently lack solid grounding in the historical and anthropological evidence, and was dismissive on those grounds of the totemic theory propagated by Freud. It must be added that Freud was aware of Schmidt’s work and was less than impressed by its quality or its scientific impartiality. He saw Schmidt, whom he held partially responsible for the abolition of the journal Rivista italiana di Psicoanalisi in Italy, as an implacable enemy of psychoanalysis, who was motivated by a desire to undermine Freud’s account of the genesis of religion. Freud feared for a possible suppression of psychoanalysis in Vienna in the mid-1930s by the ruling Catholic authorities, with whom Schmidt had considerable influence. That fear, combined with hope—which proved unfortunately ill-grounded—that those authorities might function as a bulwark against the threat of Nazism, persuaded Freud to defer publication of the full text of Moses and Monotheism until after he had taken up residence in England (see Freud 1939, Prefatory Notes to Part 111), a fact which itself had a considerably negative effect on the literary coherence of the work. The substantive issue between Freud and Schmidt on the temporal primacy of polytheism or monotheism remains unresolved and is almost certainly irresolvable; as the theologian Hans Küng puts it, the scientific search for the primordial religion should be called off, as “neither the theory of degeneration from a lofty monotheistic beginning nor the evolutionary theory of a lower animistic or preanimistic beginning can be historically substantiated” (Küng 1990, 70).

e. Religion as a Social Phenomenon

It is instructive to compare Freud’s attempts to deal with the social dimension of religion with that of his near contemporary, the sociologist Émile Durkheim (1858—1917), whose study The Elementary Forms of Religious Life (1995; orig. 1912) has been highly influential, though it should not in any way be seen as a response to Freud. In The Elementary Forms Durkheim set himself the task of analyzing religion empirically as a social phenomenon, holding that such a treatment alone can reveal its true nature. For Durkheim, the social dimension of human life is primary; human individuality itself is largely determined by, and is a function of, social interaction and organization. This was a point missed by Freud, who, we have seen, sought to deal with the social dimension of religion by an extension of psychoanalytical principles from individual to group psychology. What Durkheim termed “social facts” play an important role in his analysis; they are the collective forces external to individuals which compel or influence them to act in particular ways. Such facts exist at the level of society as a whole and arise from social relationships and human associations, and include law, morality, contractual relationships and, perhaps most importantly, religion.

Durkheim defined religion as “a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden—beliefs and practices which unite in one single moral community called a Church, all those who adhere to them” (Durkheim 1995, 44). He saw the connection between religious beliefs and practices as a necessary one; for him, religious experience is rooted more in the actions associated with rites than it is in reflective thought. Traditional accounts of religion have tended to treat religious beliefs as essentially hypothetical or quasi-scientific in nature—an approach clearly evident in Freud—which almost inevitably raises skeptical doubts about their validity, whereas Durkheim saw that what is important to the believer is the normative dimension of faith. The true function of religion is to deliver salvation by showing us how to live; as such, it originates in and receives legitimation from, moments of “general effervescence” (Durkheim 1995, 213), in which members of a group gather together to perform religious rituals. This often leads the participants into a state of psychological excitement resembling delirium, in which they come to feel transported into a higher level of existence where they make direct contact with the sacred object. Participation in such rituals has the effect of affirming and strengthening the collective identity of the group and must be renewed periodically in order to consolidate that identity.

Durkheim took pains to ensure that his use of terms like “delirium” in such contexts should not be misunderstood: the “delirium” associated with religious rituals is, he stressed, “well-founded”  (Durkheim 1995, 228) in that it is produced by the operation of social factors that are both irreducibly real and crucially important. Given that it is a foundational postulate of sociology that no human institution rests upon an error or a lie, he declared it unscientific to suggest that systems of ideas of such complexity as religions could be delusory or be the product of illusion, as Freud was to do. In that clear functionalist sense, he concluded, all religions are true; “Fundamentally then, there are no religions that are false. All are true after their own fashion: All fulfil given conditions of human existence, though in different ways” (Durkheim 1995, 2).

This vindication of religion in general, however, has as its counterpart a commitment on Durkheim’s part to an account of the nature of sacred objects or gods which was no less egregiously projectionist than Freud’s. If it is impossible for religious belief, considered as a set of representations relating to the sacred, to be erroneous in its own social right, error can and does emerge, he argued, in the interpretation of what those representations mean, even within the framework of a particular culture. At that level, Durkheim conceded, false beliefs are the norm, because all collective representations are delusional and religion is merely a case in point in that regard: “The whole social world seems populated with forces that in reality exist only in our minds” (Durkheim 1995, 228), non-religious examples of which are the meanings attributed by people to flags, to blood and to humans themselves as a class of being. This point regarding the socially-imposed nature of the meanings associated with collective representations can perhaps be most clearly illustrated by reference to now-defunct cultures and religions. For example, while we readily recognize that the Moai, the deeply impressive monolithic statues of Easter Island, unquestionably had a particular political, aesthetic and religious significance for the Rapa Nui people who created them, the meaning of that symbolism largely escapes us—archeological and anthropological reconstruction aside—as we view them from a perspective external to that culture.

Durkheim contended that in a religious context, the sacred object, which is indeed greater than the individual, is nothing more or less than the power of society itself which, in order to be represented symbolically at all, has be objectified through a process of projection. Gods or sacred objects then, are “a figurative expression of … society” (Durkheim 1995, 227); they are society refined, idealized and apotheosized. As such, they represent a power beyond all individual humans, but are ultimately existentially interdependent with them: “while it is true that man is a dependent of his gods, this dependence is mutual. The gods also need man; without offerings and sacrifices, they would die” (Durkheim 1995, 36).

Durkheim’s treatment of religion, then, utilizes a methodology which offers a sharp contrast with Freud’s highly-individualistic, psychological approach to the subject, a contrast which highlights some of the sociological shortcomings of the latter. Unlike Freud, Durkheim also sought to provide an account of religion which achieves full scientific probity while simultaneously doing justice to the richness of the actual lived experiences of believers. Notwithstanding that, however, it seems clear that in the final analysis his anti-skeptical stratagem works satisfactorily only on its own, scientific terms; a believer could scarcely derive comfort from a view which legitimates his belief-system qua sociological fact while implying that the personal God of worship which is its intentional object is, in reality, nothing other than society personified.

f. The Projection Theory of Religion

This raises the whole question of the intellectual plausibility of the projection theory of religion. The question is a complex one, a fact which Freud scarcely acknowledges in his works. As we have seen, the theory, which has a number of related but distinct forms, arose in modernity as a response to the anthropomorphic nature of the attributes which the conceptualization of a personal God in many of the great world religions seems to necessitate. Freud, like Feuerbach, took this as entailing strict anthropotheistic consequences: Feuerbach’s argument reduced God to the essence of man, and Freud sought to go beyond him in offering a psychoanalytical explanation, in terms of the father complex, of why it is human beings have a need to hypostasize their own subjective nature. Belief in God, and the complex patterns of behavior and of rituals associated with that belief, he argued, arise essentially out of the deep psychological need for a Cosmic father.

However, it has been pointed out that such a view underestimates the logical gulf that exists between wishes and beliefs; the former may on occasion be a necessary condition for the latter, but are rarely a sufficient one: an athlete may wish to triumph in an event with every fibre of his being, but that will not necessarily generate a belief that he can do so, much less the delusion that he has done so. Thus, even if it is true that there is a universal wish for a Cosmic father, it is implausible to suggest that such a wish is a sufficient condition for religious belief and the complex practices and value systems associated with it (Kai-man Kwan 2006). Further, as Alvin Plantinga (1932—) argues, in the absence of compelling empirical evidence to support the view that such a universal wish exists, Freud was left with no option but to contend that such wishes are equally universally repressed into the unconscious, a move which opens his theory to the accusation of being empirically untestable (Plantinga 2000, 163).

It is to be noted too that concerns about anthropomorphisms in religious language are in no way restricted to religious skeptics: apophatic or negative theology, for example, grew out of recognition of the logical difficulties implicit in attempts to express the nature of the divine in language. As a result, theologians such as Maximus the Confessor (580—662),  Johannes Scotus Eriugena (815—877) and—in Judaism—Maimonides (1138—1204) repudiated the positive attribution of characteristics to God in favour of “referencing” God exclusively in terms of what He is not, through the via negativa. It is also important to note that some proponents of the projection theory, such as Spinoza and possibly Xenophanes, saw the projection theory as invalidating only those forms of religious belief which are anthropotheistic in nature. Thus projectionism, so far from being hostile to all forms of religious belief and practice, is in fact consistent with themes relating to the avoidance of idolatry long central to the Abrahamic religions in particular, as evidenced in the proscription on naming God in Judaism and in aniconism, the prohibition of figurative representations of the Divine in the early Orthodox Church, in Calvinism and also in Islam (Thornton, 2015: 139-140).

It is thus perfectly consistent to accept projectionism as an account of religious concept formation without thereby repudiating religious belief. Indeed, the logical compatibility of projectionism with religious belief has led some contemporary religious thinkers to go so far as to embrace projectionism as a condition of a reflective religious commitment. The view that religious representations are products of the human imagination, it has been argued, can be accepted implicitly by believers, as the “mark of the Christian in the twilight of modernity is … trust in the faithfulness of the God who alone guarantees the conformity of our images to reality and who has given himself to us in forms that may only be grasped by imagination” (Green, 2000, 15). This argument is closely paralleled by a suggestion from Plantinga that wish-fulfillment as a mechanism could have arisen out of a divinely created human constitution. For while it may not, in general, be the function of wish-fulfillment to produce true belief, that in itself does not rule out the possibility, Plantinga contends—at least for those who believe in God—that humans have been so constituted by the creator to have a deeply-felt need and wish to believe in him. On this view, the very existence of the wish for a transcendent Father may be taken as evidence for the truth rather than the falsity of the beliefs which it inspires: “Perhaps God has designed us to know that he is present and loves us by way of creating us with a strong desire for him, a desire that leads to the belief that in fact he is there” (Plantinga 2000, 165).

Whatever level of plausibility may be assigned to these views, it is in any case clear that the projection theory is also reflective of the difficulties which certain forms of religious discourse generate: the characterization of God as possessing attributes such as Love and Wisdom, however qualified such attributions may be, seems invariably to invite the kind of challenge that is found in Feuerbach, Freud and even in Durkheim. In that sense, the projection theory highlights deep theological and philosophical issues relating to the nature and meaning of religious language. One of the more promising approaches to this issue is that suggested by the work of of Wittgenstein, who, in his Philosophical Investigations (1974), propounded his language-game theory of meaning, which argued that the meaning of any term is determined by its actual use in a living language-system. In that connection, he brought out the complex interplay of linguistic and non-linguistic activities and practices in human life, in a manner analogous to Durkheim’s functionalism. An application of this to religious discourse implies that the latter cannot be understood in isolation from the broad web of cultural practices, beliefs and concerns in which it is imbedded and from which it derives its meaning. This suggests that concerns that skeptical conclusions necessarily follow from our use of human-being predicates in speaking about the Divine are misguided; such concerns gain credence only when accompanied by the deeply pervasive, but uncritical, philosophical assumption—clearly evident in Freud—that the attributions of anthropomorphic predicates to God are to be understood exclusively as factual descriptions of a particular kind, an assumption which is at the very least gratuitous.

This point is made cryptically by Wittgenstein in an indirect allusion to the projection theory: “‘God’s Eye Sees Everything’—I want to say of this that it uses a picture…. [in saying this] I meant: what conclusions are you going to draw? etc. Are eyebrows going to be talked of, in connection with the Eye of God?” (Wittgenstein, 1966, 71). In other words, while in factual discourse references to human eyes have an internal relationship to references to human eyebrows, such that the occurrence of one may and frequently does give rise to the other, no such correlation is possible or necessary in religious discourse about God’s Eye (or Mercy, Anger, Love, and so forth). Thus while “God’s Eye Sees Everything” conjures up the image of a stern, judgmental all-seeing parental figure which, at one level, is amenable to the Freudian father-complex analysis, at another, arguably deeper, level it is clear that the web of relations that holds between the anthropomorphic terms used cannot meaningfully be compared with that which holds in factual discourse about earthly fathers; even the most literal-minded do not seek to speak of God’s eyebrows. The occurrence of anthropomorphisms in religious discourse, then, does not in itself necessitate the acceptance of anthropotheistic conclusions.

g. Moses and Monotheism: Interpretive Approaches

Moses and Monotheism is the most controversial of Freud’s works, seeking as it does to both utilize psychoanalytic theory to reinterpret key historical events and to embed psychoanalysis within a historiographical narrative. Not alone did it contest the orthodox Biblical narrative of the role of Moses in the history of Judaism, it did so at a time when the Jews of Europe were threatened with complete annihilation. It is unsurprising, then, that it should have become the subject of very strong criticism, on the grounds both of methodology and content; indeed, because its central account of the Egyptian origins of Judaic monotheism has seemed so egregiously at odds with both tradition and the historical evidence, much of the critical interest has focused on the question of Freud’s motives in propagating it. The Freudian narrative is, of course, problematic in the extreme when considered as a putative exegesis of the Exodus story; as one commentator puts it, “There is hardly any need to state that Moses and Monotheism does not operate at the level of an exegesis of the Old Testament and in no way satisfies the most elementary requirement of a hermeneutics adapted to a text” (Ricoeur 1970, 545). Though Moses is almost certainly an Egyptian name, the evidence that Moses was an Egyptian is not conclusive and it has also been suggested that his life was not in fact contemporaneous with that of Amenhotep IV (Banks 1973, 411). Freud’s willingness, towards the very end of his life, to construct such an apparently speculative narrative on the very origins of Judaism has long puzzled scholars, but it is possible to distinguish three broad exegetical approaches relating to the Moses text in the secondary literature:

  1. For much of his life Freud presented an image of himself to the world as an urbane, cosmopolitan intellectual, committed to the ideals of secular humanism and modern science, and at times that seemed to necessitate downplaying his Jewish background and education. Some scholars, such as Jones (1957) and, more recently Gay (1987), have accordingly represented the Moses text primarily as a critique of Judaism, a comprehensive application of the reductive analysis of religion offered in Freud’s earlier works to the religion of his forefathers. In a similar vein, Jan Assmann (1998) sees Freud as continuing the more general task, initiated by Baruch Spinoza (1632—1677), of combating monotheism and undoing the negative values, such as intolerance, religious hatred and the configuration of alternative religions as idolatrous, generated by the absolute conception of truth which monotheistic religions seem to require.
  2. The second approach, associated in particular with Yerushalmi (1993), Bernstein (1998) and Slavet (2009; 2010) repudiates what it sees as a confusion of meaning with motivation in the secondary literature regarding Freud’s text, stressing that what is of importance is what Freud sought to convey, not what motivated him to do so. While acknowledging the resonances within the text of personal factors operating in Freud’s life at the time of publication, such as his relationship with the memory of his father, the resurgence of antisemitism and the personal and professional threat presented by Nazism from which he so narrowly escaped, this approach rejects any autobiographical interpretation of the text, focusing instead on Freud’s account of the nature of the Jewish religion and the factors which constitute and determine Jewish identity. Thus Bernstein sees in Freud’s Moses text a powerful new account of religion in general and of Judaism in particular, centering on the idea that a religious tradition derives its dynamic from a complex interplay of conscious and unconscious forces. Slavet attributes to Freud a racial theory of memory and sees Moses and Monotheism as “the culmination of a lifetime spent investigating the relationships between memory and its rivals: heredity, history, and fiction” (Slavet 2009, 7) in the context of the question of “Jewishness.” On this view, Freud sought to show that the advancement of intellectualized spirituality (Geistigkeit) has been the most important part of the legacy of Judaic monotheism, but that this owed as much to the working out of collective trauma, the return of the repressed, as it did to the conscious influence of the patriarchs and prophets.
  3. Finally, there is the semi-autobiographical approach, largely taken in this article, which sees the text as primarily concerned with the long-standing problem for Freud of resolving his personal father complex. That, in psychoanalytical terms, amounted to the implementation of an instance of “deferred obedience” by defining in a positive way his relationship with the religion into which he was born, albeit with an emphasis on the human origins of the Judaic ethic (Rice 1990; Gresser 1994; Friedman 1998).

In a thinker as complex as Freud, these approaches can neither be taken as exhaustive nor as entirely mutually exclusive, as significant textual evidence can be invoked for all three. What seems evident, at any rate, is that Freud was seeking, at that critical point in Jewish history, to affirm his cultural and intellectual indebtedness to the ethical basis of the religion of his forefathers while simultaneously seeking to demonstrate that the validity of that ethic is not contingent upon the Biblical and theological accretions traditionally associated with it. On such a reading, the question of the accuracy of the historical detail in the Freudian narrative becomes as peripheral as it is—on a non-literal interpretation—to that of the Biblical one. The import of the book, as Friedman puts it, may reside ultimately in a purpose which can certainly be discerned in it: to preserve Judaism and articulate Freud’s own Jewish identity at a stage in a historical process in which his people come to progress from worship of a transcendent God “to the rational and self-conscious appreciation of themselves as a people of great accomplishment descended from a great but human leader” (Friedman 1998, 139).

9. References and Further Reading

a. References

  • Alter, R. 1988. The Invention of Hebrew Prose, Modem Fiction and the Language of Realism (Samuel and Athea Stroum Lectures in Jewish Studies). University of Washington Press.
  • Assmann, J. 1998. Moses the Egyptian: The Memory in Western Monotheism. Cambridge, MA: Harvard University Press.
  • Banks, R. 1973. ‘Religion as Projection: A Re-Appraisal of Freud’s Theory’. Religious Studies, vol. 9 (4), 401-426.
  • Berke, J. 2015. The Hidden Freud: His Hassidic Roots. London: Karnac Books.
  • Bernstein, R.J. 1998. Freud and the Legacy of Moses. Cambridge: University Press.
  • Boehlich, W. (ed.) 1992. The Letters of Sigmund Freud to Eduard Silberstein, 1871-1881 (trans. A. Pomerans). Harvard University Press.
  • Brentano, F. 1973 (orig. 1874). Psychology From an Empirical Standpoint (trans. A.C. Rancurello, D.B. Terrell and L.L. McAlister). London: Routledge.
  • d’Aquili, E.G. & Newberg, A.B. 1999. The Mystical Mind: Probing the Biology of Religious Experience. Minneapolis: Fortress Press.
  • Darwin, C. 1981. Descent of Man and Selection in Relation to Sex. Princeton University Press.
  • Durkheim, É. 1995 (orig. 1912). The Elementary Forms of the Religious Life (trans. Karen Fields). New York: Free Press.
  • Feuerbach, L. 1881. The Essence of Christianity, 2nd edition (trans. George Eliot). London: Trübner & Co., Ludgate Hill.
  • Frazer, J. G. 2002 (orig. 1890). The Golden Bough. New York: Dover Publications.
  • Freud, S. 1914 (orig. 1901). The Psychopathology of Everyday Life (trans. A.A. Brill). London: T. Fisher Unwin.
  • Freud, S. 1939. Moses and Monotheism (trans. Katherine Jones). London: The Hogarth Press and Institute of Psycho-Analysis.
  • Freud, S. 1957 (orig. 1910) ‘The Future Prospects of Psychoanalytic Therapy’, in The Standard Edition of the Complete Psychological Works of Sigmund Freud ( & and ed. J. Strachey) Volume X1 (1911-1913). W. W. Norton & Company, 139-151.
  • Freud, S. 1959. ‘An Autobiographical Study’, in The Standard Edition of the Complete Psychological Works of Sigmund Freud (trans. & ed. J. Strachey). Volume XX (1925-1926). London: The Hogarth Press and the Institute of Psychoanalysis, 7-70.
  • Freud, S. 1961 (orig. 1927). The Future of an Illusion (trans. James Strachey). New York; W.W. Norton.
  • Freud, S. 1962 (orig. 1930). Civilization and its Discontents (trans. James Strachey). New York; W.W. Norton.
  • Freud, S. 1976. ‘An Obituary for Professor S. Hammerschlag’, in The Standard Edition of the Complete Psychological Works of Sigmund Freud (trans. & and ed. J. Strachey) Volume IX (1906-1908). W. W. Norton & Company, 255-6.
  • Freud, S. 1976 (orig. 1907). ‘Obsessive Actions and Religious Practices’, in The Standard Edition of the Complete Psychological Works of Sigmund Freud (trans. & ed. James Strachey) Volume IX (1906-1908). W. W. Norton & Company, 115-128.
  • Freud, S. 1986. The Complete Letters of Sigmund Freud to Wilhelm Fliess, 1887-1904 (trans. & and ed. J. Moussaieff Masson). The Belknap Press of Harvard University Press.
  • Freud, S. 1990 (orig. 1933). New Introductory Lectures on Psycho-analysis (trans. James Strachey). New York: W.W. Norton.
  • Freud, S. 2001 (orig. 1913). Totem and Taboo: Some Points of Agreement between the Mental Lives of Savages and Neurotics (trans. James Strachey). Oxford: Routledge Classics.
  • Freud, S. 2010 (orig. 1900, 1908) The Interpretation of Dreams (trans. James Strachey). New York: Basic Books.
  • Friedman, R. 1998. ‘Freud’s Religion: Oedipus and Moses’. Religious Studies, 34 (2), 135-149.
  • Gay, Peter. 1987. A Godless Jew? Freud, Atheism and the Making of Psychoanalysis. New Haven: Yale University Press
  • Goodnick, B. 1992. ‘Jacob Freud’s Dedication to His Son: A Reevaluation’. The Jewish Quarterly Review, Vol. 82 (3-4), 329-360.
  • Green, G. 2000. Theology, Hermeneutics and Imagination: The Crisis of Interpretation at the End of Modernity. Cambridge: Cambridge University Press.
  • Gresser, M. 1994. Dual Allegiance: Freud as a Modern Jew. Albany, NY: State University of New York Press.
  • Grünbaum, A. The Foundations of Psychoanalysis. Berkeley: University of California Press.
  • Hume, D. 1956 (orig. 1757). The Natural History of Religion (ed. H.E. Root). London: A.C. Black.
  • Jones, E. 1957. Sigmund Freud. Life And Work: Volume Three – The Last Phase 1919-1939. London: Hogarth Press.
  • Jones, E. 1959 (ed). Freud: Collected Papers in 5 Volumes (trans. Joan Riviere). New York: Basic Books.
  • Kai-man Kwan. 2006 “Are Religious Beliefs Human Projections?” in Raymond Pelly and Peter Stuart, eds., A Religious Atheist? Critical Essays on the Work of Lloyd Geering. Dunedin, New Zealand: Otago University Press, 41-66.
  • Kenny, R. 2015. ‘Freud, Jung and Boas: the psychoanalytic engagement with anthropology revisited’. Notes and records of the Royal Society of London. Jun 20; 69(2): 173–190. Online: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4424604/
  • Kroeber, A.L. 1920. ‘Totem and Taboo: An Ethnologic Psychoanalysis’, American Anthropologist, New Series, Vol. 22 (1), 48-55.
  • Kroeber, A. L. 1939. ‘Totem and Taboo in Retrospect’. American Journal of Sociology, Vol. 45 (3), 446-451
  • Lang, A. & Atkinson, J.J. 1903. Social Origins and Primal Law. London: Longmans Green.
  • Parsons, W.B. 1998. “The Oceanic Feeling Revisited.” The Journal of Religion, vol. 78 (4), 501–523.
  • Paul, R. A. 1996. Moses and Civilization: The Meaning Behind Freud’s Myth. New Haven; London: Yale University Press.
  • Plantinga, A. 2000. Warranted Christian Belief. Oxford University Press.
  • Popper, K. 1963. Conjectures and Refutations: The Growth of Scientific Knowledge. London: Routledge.
  • Rice, E. 1990. Freud and Moses: The Long Journey Home. Albany, New York: SUNY Press.
  • Ricoeur, P. 1970. Freud and Philosophy: An Essay on Interpretation (trans. D. Savage). New Haven & London: Yale University Press.
  • Saarinen, J.A. 2015. A Conceptual Analysis of the Oceanic Feeling – With a Special Note on Painterly Aesthetics. Jyväskylä: Jyväskylä University Printing House. Online at: https://jyx.jyu.fi/dspace/bitstream/handle/123456789/45384/978-951-39-6078-0_vaitos07032015.pdf?sequence=1
  • Schmidt, W. 1912-1955. Der Ursprung der Gottesidee: Eine historisch-kritische und positive Studie. (12 vols.) Münster in Westfalen: Aschendorff.
  • Slavet, E. 2009. Racial Fever: Freud and the Jewish Question. Fordham University Press.
  • Slavet, E. 2010. ‘Freud’s Theory of Jewishness For Better and for Worse’. In A.D. Richards (ed.) The Jewish World of Sigmund Freud: Essays on Cultural Roots and the Problem of Religious Identity, 96-111. North Carolina: McFarland & Co.
  • Smith, R.J. 2016. ‘Darwin, Freud, and the Continuing Misrepresentation of the Primal Horde’, Current Anthropology 57 (6), 838-843.
  • Thornton, S. ‘Projection’, In R.A. Segal and K. von Stuckrad (eds.) Vocabulary for the Study of Religion (vol. 3). Leiden/Boston, 2015, 138-144.
  • Tylor, E.B. 1871. Primitive culture: researches into the development of mythology, philosophy, religion, language, art, and custom (2 vols). London: John Murray.
  • Tylor, E.B. 1881. Anthropology: an introduction to the study of man and civilization. London: Macmillan & Co.
  • Whitebook, J. 2017. Freud: An Intellectual Autobiography. Cambridge University Press.
  • Wittgenstein, L. 1966. Lectures & Conversations on Aesthetics, Psychology and Religious Belief (ed. C. Barrett). Oxford: Basil Blackwell.
  • Wittgenstein, L. 1974. Philosophical Investigations (trans. G.E.M. Anscombe). Oxford: Basil Blackwell.
  • Yerushalmi, Y.H. 1993. Freud’s “Moses”: Judaism Terminable and Interminable. Yale University Press.

b. Further Reading

  • Alston, W.P. 2003. ‘Psychoanalytic theory and theistic belief’. In C. Taliafero, & P. Griffiths (eds.). Philosophy of Religion: An anthology (123-140). Oxford: Blackwell Press.
  • Bingaman, K. 2012. Freud and Faith: Living in the Tension. Albany, NY: State University of New York Press.
  • Blass, R.B. 2004. ‘Beyond illusion: Psychoanalysis and Religious Truth’. The International Journal of Psychoanalysis, 85, 615-634.
  • Derrida, J. 1998. Archive Fever: A Freudian Impression (trans. E. Prenowitz). University of Chicago Press.
  • Gay, P. 2006. Freud: A Life for our Time. London: W.W. Norton & Company.
  • Ginsburg, R. et.al. (eds). 2006. New Perspectives on Freud’s Moses and Monotheism (Conditio Judaica) 1st Edition. Tübingen: Max Niemeyer Verlag.
  • Hewitt, M.A. 2014. Freud on Religion. London & New York: Routledge.
  • R.A. 1986. Emile Durkheim: An Introduction to Four Major Works. Beverly Hills, CA: Sage Publications.
  • Kolbrener, W. (2010). ‘Death of Moses Revisited: Repetition and Creative Memory in Freud and the Rabbis’. American Imago, 67 (2), 243-262.
  • Milfull, J. 2002. ‘Freud, Moses and the Jewish Identity’. The European Legacy, vol. 7, 25-31.
  • Nobus, D. 2006. ‘Sigmund Freud and the Case of Moses Man: On the Knowledge of Trauma and the Trauma of Knowledge’. JEP: European Journal of
  • Psychoanalysis: Humanities, Philosophy, Psychotherapies. Number 22 (1). Online at http://www.psychomedia.it/jep/number22/nobus.htm
  • Ofengenden, A. 2015. ‘Monotheism, the Incomplete Revolution: Narrating the Event in Freud’s and Assmann’s Moses’. Symploke, Volume 23 (1-2), 291-307.
  • Palmer, M. 1997. Freud and Jung on Religion. London & New York: Routledge.
  • Said, E. 2004. Freud and the Non-European. London: Verso.
  • Smith, D.L. 1999. Freud’s Philosophy of the Unconscious. Studies in Cognitive Systems, vol. 23. Dordrecht: Springer.
  • Tauber, A.I. 2010. Freud, The Reluctant Philosopher. New Jersey: Princeton University Press.

Author Information

Stephen Thornton
Mary Immaculate College, University of Limerick
Ireland

Frege’s Problem: Referential Opacity

The problem of referential opacity is to explain why a certain inference rule of classical logic sometimes produces invalid-seeming inferences when applied to ascriptions of mental states. The rule concerns substitution of terms for the same object, and here is one of the controversial examples. It involves the mental states of Lois Lane, who believes that Superman can fly. However, she does not know Superman is her coworker Clark Kent, and it is very natural to say that she doesn’t believe that Clark can fly. Yet the inference rule in question apparently allows the following dubious inference:

Superman is identical to Clark Kent.

Lois Lane believes that Superman can fly.

 So, Lois Lane believes that Clark Kent can fly.

This inference rule is commonly called Leibnizʼs Law, or Substitutivity of Identicals, or Identity Elimination. The problem it creates is often designated the problem of referential opacity, but because the word “opacity” promotes a particular theory, this article typically employs the more neutral nomenclature “(apparent) substitution-failure.” The term “Leibnizʼs Law” is used instead for

(1) If x and y are the same object, then x and y have the same properties.

And the terms “Identity Elimination” (“=E”) and “Substitutivity of Identicals” are reserved for the specific rule substitution rule illustrated above.

To formulate this rule precisely, we specify it as a rule of natural deduction. It applies to a major premise, which is an identity sentence (for example, “Superman is identical to Clark Kent”), and a minor premise, which contains at least one occurrence of the term on the left of the major premise. The rule permits replacing at least one such occurrence with the term on the right of the major premise. For example, =E is used to make the following inference:

Istanbul is identical to Constantinople.

 Istanbul straddles Europe and Asia.

So, Constantinople straddles Europe and Asia.

This particular use produces a valid argument. However, applications of the rule in other sentences sometime produces very counter-intuitive results, as illustrated by the case of Lois Lane, and so we get the problem of apparent substitution-failure. Philosophers of language disagree about how to explain, or explain away, such seeming failures.

The problem was introduced into modern discussion by Quine (1956, 1961). Important early contributions include Marcus (1961, 1962, 1975) and Smullyan (1948). The papers (Kaplan 1986) and (Fine 1989) are influential engagements with Quine. However, the essential problem was raised in the seminal (Frege 1892), and so it is also known as Fregeʼs Puzzle.

Table of Contents

  1. Identity Elimination and Its Misuses
    1. Quotation
    2. “So-Called”
    3. Modality
  2. The De Re/De Dicto Distinction
    1. Defining the Distinction
    2. Skepticism about the Distinction
    3. The de re and Leibniz’s Law
  3. Frege’s Theory of Substitution-Resistance
    1. The Sense/Reference Distinction Applied to Attitude Ascriptions
    2. The Hierarchy Problem
    3. The Semantic Innocence Objection
    4. Do Name-Senses Exist Anyway?
    5. Alternative Accounts of the Sense of a Name
  4. Hidden-Indexical Semantics
    1. Two Kinds of Hidden-Indexical Theories
    2. Kripke’s Puzzle
  5. Russellianism
    1. Salmon’s Theory
    2. Commonsense Psychology
    3. Saul on Simple Sentences
    4. Richard’s Phone Booth
  6. References and Further Reading

1. Identity Elimination and Its Misuses

A little more formally, the rule of inference =E can be stated as:

Identity Elimination Schema

Major: t1 = t2

Minor: ϕ(t1)

Conclusion: ϕ(t2)

Here t1 and t2 are expressions which refer to entities (for example, proper names of people or cities). ϕ(t1) is a sentence containing at least one occurrence of t1, and ϕ(t2) is a sentence that results from replacing at least one occurrence of t1 in ϕ(t1) with an occurrence of t2, eliminating the “=” of t1 = t2. Recurring ti presumes that ti is univocal throughout, and recurring ϕ presumes that the sentential context ϕ is not altered, syntactically or semantically, by the replacement. If these uniformity conditions are not met, then the inference scheme is being misapplied, and it is no wonder that false conclusions are derivable. For example, in the inference “The man behind Fred = the man in front of Bill; the man behind Fred saw him leave; therefore, the man in front of Bill saw him leave,” the context “saw him leave” is not uniform, since substitution of “the man behind Fred” by “the man in front of Bill” changes the reference of “him” (Fine 1989:222–3; Linsky 1967:104).

In discussing the problem with apparent substitution-failure by using =E, many examples will be drawn from the fictional story of Superman, treated as if it were true. In the story, a child from the planet Krypton, Kal-El, is sent to Earth, where physical conditions cause him to acquire superpowers. Wearing specific clothing (red cape, blue jumpsuit), Kal-El prevents disasters, rescues endangered innocents, and foils would-be perpetrators of crimes, such as Lex Luthor. People call Kal-El “Superman” when talking about Kal-El’s actions of this kind.

But Kal-El also takes a day job as a reporter, using the name “Clark Kent.” A coworker, Lois Lane, treats him with indifference in the office, but has a pronounced crush on, as she would put it, Superman, unaware they are the same individual.

The problematic examples discussed below involve ascriptions of mental states to Lois (or occasionally Lex), arrived at by applying the rule =E to the major premise “Superman is Clark” and a carefully chosen minor premise. Lois has a crush on Superman (minor premise), so, by =E, Lois has a crush on Clark. But this latter seems false, and would certainly be rejected by Lois herself. Also, Lois believes that Superman can fly, but does not seem to believe that Clark can; she hopes to see Superman again soon, but seems not much to care when she next sees Clark; she would like a date with Superman, but apparently has no interest in one with Clark; and so on. For a problematic use of =E, consider this paradigm example:

(2)
a. Superman is Clark Kent.                                      Major
b. Lois believes that Superman can fly.             Minor
c. ∴ Lois believes that Clark Kent can fly.         a, b =E

It is not a solution to the problem of referential opacity to say that when we apply the rule in an instance like (2), the flaw is that the major premise is one that Lois does not realize is true. No doubt her ignorance explains psychologically why she does not draw the conclusion that Clark can fly, in those very words, but it does not explain semantically how the inference rule can carry us from two truths to a seeming falsehood: “Lois realizes (2a) is true” is not itself a premise for the application of the rule in (2), so its falsehood is irrelevant to what is dubious about the application. Indeed, the rule enables the inference that Lois does realize (2a) is true: simply change the minor premise of (2) to “Lois realizes Superman is Superman,” surely unobjectionable once she has acquired the name “Superman” from watching Kal-El perform heroic deeds.

Some terminology is commonly encountered in discussions of cases like (2). Mental-state ascriptions like (2b) and (2c) are called attitude ascriptions, since the subject is being ascribed a mental attitude. When the thing the attitude is toward is specified by a “that”-clause (or by a clause complementized by “if” or “whether”), the ascription is called a propositional attitude ascription. This is because the “that”-clause is standardly taken to specify a proposition, the one expressed by the sentence which “that” prefixes (but see, for example, Davidson 1969, Bach 1997, and Moltmann 2003, 2008, 2017 for criticism of this). So (2b) says that Lois has the attitude of belief toward the proposition that Superman can fly. The sentence following the “that” in (2b) and (2c) is called the content-sentence, though in English, “that” can often be dropped (it is not obligatory in (2b) and (2c)).

a. Quotation

There is mileage to be gained from the idea that the reason we get counterintuitive instances such as (2) is that the rule of =E is being misapplied in some way, or, relatedly, that the rule as formulated is not a faithful reflection of the motivation provided by Leibniz’s Law, as stated in (1)—a better formulation would have to be misapplied to get (2). There are some well-known cases of misapplication of the rule which motivate critiques of (2) as a relevantly similar misapplication. One sort of case, emphasized by Quine (1961), is

(3)
a. Istanbul is Constantinople.
b. “Istanbul” has eight letters.
c. ∴ “Constantinople” has eight letters.

This is a misapplication of =E because the name “Istanbul” does not occur univocally in (3). In the major premise, it is used in the normal way to refer to a certain city. But in the minor premise, it is not used to refer to that city (perhaps it is not used to refer at all). Rather, it occurs as part of the complex quotation-name “‘Istanbul,’” referring to the name “Istanbul,” not the city Istanbul (this is a Tarskian rather than Fregean account of quotation—see further Richard 1986, Washington 1992, Saka 2006—but the nonuniformity objection to (3) holds on either). (3b) correctly predicates “has eight letters” of the word “Istanbul,” as opposed to unintelligibly predicating “has eight letters” of the city Istanbul. So (3) has no more force than a variant in which the minor premise reads “the first name used in (3a) has eight letters” and the conclusion reads “the second name used in (3a) has eight letters,” and which at best seems to presume the absurd principle that if two names refer to the same thing then they have the same number of letters.

Quine thought examples like (3) instructive. The position of “Istanbul” in (3b) is not open to substitution, like the position of “Superman” in (2b), and “Istanbul” does not seem to be referring normally in (3b), so perhaps the same should be said of “Superman” in (2b): the position “Superman” occupies in (2b) is referentially opaque, hence the terminology. But it is unclear how instructive (3) really is. Quine suggests (1956:186) that we should give “serious consideration” to construing mental state ascriptions such as (2b) as involving quotation. (2b) so-construed would say that Lois believes-true “Superman can fly” as a sentence of English.

But he immediately hedges by adding that this “is not to suggest that the subject speaks the language of the quotation, or any language…We may treat a mouse’s fear of the cat as his fearing-true a certain English sentence.” Unfortunately, we are left in the dark about what it is to believe-true or fear-true a sentence as a sentence of L when one does not know L. Quine then admits that the quotational construal of mental state ascriptions will only yield a “systematic agreement in truth-value…and no more.” But even that is doubtful. If “believes-true … as a sentence of L” is simply jargon for “believes that … is true-in-L,” a monolingual Czech who believes that Superman can fly would not do so according to this analysis (she may not even have heard of English); conversely, she may believe that “Superman can fly” is an example of a sentence that is true in English, because she has been told so by a reliable informant; clearly, this does not mean she believes Superman can fly, since she does not know what “fly” means. (See Church 1950 for a famous discussion of quotational accounts, and Schweizer 1993 for a technical investigation of quotational accounts of modal logic.)

A quotational account that does rather better, Quine notes, is that (2b) says that Lois believes the meaning of “Superman can fly,” which avoids the problem of the monolingual Czech. But then it is not really the presence of quotation that is blocking substitution. For if this new quotational account is correct, (2) is valid reasoning if (2a) guarantees that “Superman can fly” and “Clark can fly” mean the same. So (2)’s being a fallacy will require that (2a) not be sufficient for these two sentences to mean the same. This in turn seems to require an account of names on which names can be coreferential yet, one way or another, differ in meaning; and indeed, some accounts to be considered below pursue this. And then substitution-resistance need not be pinned on the presence of quotation.

b. “So-Called”

Quine has another example of misapplication of =E, but one which tends to undermine the thought that there is something referentially peculiar about the position occupied by the substitution-resistant name (though he appears to regard the example as supporting this idea). His well-known “Giorgione” case (Quine 1961:17) is as follows:

(4)
a. Giorgione is Barbarelli.
b. Giorgione is so-called because of his size.
c. ∴ Barbarelli is so-called because of his size.

In (4), there is nothing unusual about the way in which any of the names is used: in each use, there is simply reference to a certain artist. The reason the inference fails to be a legal application of =E is that the sentential context “is so-called because of his size” does not recur uniformly, since the reference of “so” changes in moving from (4b) to (4c): in (4b), “so” refers to the name “Giorgione,” but in (4c), it refers to the name “Barbarelli.” The supposed application of =E is therefore a simple fallacy of equivocation, brought about by the substitution having a hidden truth-condition-altering side-effect (altering the reference of “so”). But it may be an instructive fallacy, if anything like a covert “so” is present in attitude ascriptions. (For other examples of nonuniformity, see Fine 1989:222–36; for more on “so-called,” Forbes 2006:154–7, Corazza 2010, and Predelli 2010.)

c. Modality

Our last example of misuse of =E involves intensional operators, which are operators which do not allow interchange within their scope of accidentally coextensive expressions (two predicates are coextensive if and only if (iff ) they actually apply to exactly the same things, and accidentally coextensive iff they are coextensive, but there could have been something to which one applies and the other does not; two sentences are accidentally coextensive iff they have the same actual truth-value but could have differed in truth-value). The standard cases of intensional operators are modal operators such as “it is necessary that,” “it is possible that,” and “it is contingent that.”

To illustrate how intensional operators can induce failure of substitution of accidentally coextensive predicates, suppose I have in my garage three cars, all

Bentley racing cars from the 1920s, and that these are the only three in existence (the only three that Bentley ever built). Then for any x, x is a car in my garage iff x is a Bentley racing car. But it surely could have been that a car in my garage is not a Bentley, in the sense that there is a way things could have gone as a result of which a car from a different manufacturer ends up in my garage. By contrast, it is not possible that a Bentley racing car is not a Bentley. The problem is that the two predicates “x is a car in my garage” and “x is a Bentley racing car” are only accidentally coextensive, while modal operators are sensitive to what might be called the “modal profile” of expressions within their scope: the array of semantic values they have, sets in the case of predicates, across ways things could have gone, or “possible worlds.” “x is a car in my garage” and “x is a Bentley racing car” would have the same modal profile iff at each world, the set of things the first applies to is the same set as the set of things the second applies to. But as we have said, there is a possible world w where the set of things one predicate applies to is different from the set of things the other applies to, since there is, say, a Bugatti in my garage in w. As the example shows, attempts to substitute predicates which are not necessarily coextensive within the scope of a modal operator easily go awry, resulting in absurdities such as a Bentley that is not a Bentley: within the scope of “possibly” or “it could have been that,” “car in my garage” cannot be replaced by the accidentally coextensive “Bentley racing car” in the sentence “a car in my garage isn’t a Bentley.”

The same can happen with expressions which are accidentally coreferential. Suppose there are nine planets in our solar system, and that this is a contingent fact: there could have been more or fewer planets (on that definition of “planet”).

Then the following use of =E derives a false conclusion from true premises:

(5)
a. The number of planets = 32
b. It is contingent that the number of planets = 9
c. ∴ It is contingent that 32 = 9.

The conclusion is false because true mathematical identities such as “32 = 9” are the paradigm cases of necessary truths: in every way things could have gone, the number 9 is the outcome when the number 3 is multiplied by itself.

(5) differs from previous examples in that one of the terms in the major premise, “the number of planets,” is not a proper name, but rather what is called a singular definite description: “definite” because “the” coupled with a singular nominal implies exactly one, and “description” because the expression, if it picks out anything, picks out the individual that is the unique satisfier of the descriptive condition “F” in “the F,” in this case “number of planets.”

However, definite descriptions can be classified in at least two ways. One option is that they are treated as belonging to a unitary semantic category of singular terms, together with other grammatical categories such as proper names, demonstratives, and indexicals: expressions of all these types “designate” objects. The classification of definite descriptions with names goes back to Frege (1892). The other approach classifies a definite description “the F” as a first-order quantifier, like “some F,” “each F,” “no F,” and so on (the apparent structural similarity between “the F is G” and “{some/each/no} F is G” is seen as genuine). A quantifier like “some F” is a combination of a det(erminer) “some” with a predicate F, that then combines with a second predicate. In “(det F is G),” “F” is the restriction, or restrictor, in the quantifier “det F,” and “is G” is the quantifier’s scope. In symbols, to take a simple example, “no dog barked” would be represented as “(no x: x is a dog)[x barked],” and so by parallelism, “the dog barked” would be “(the x: x is a dog)[x barked]”: as in English, only det changes as we formalize “the dog barked,” “each dog barked,” “some dog barked,” and so on (for further discussion, see Davies 1981:149–52). (Russell’s Theory of Descriptions (1905) is a quantificational account in the looser sense that Russell took “the F” to be an apparent singular term in need of analysis by the standard determiners some and every. There is also a “predicate” account of some descriptions, as in Fara 2001.)

Only the singular-term account of descriptions raises the problem of referential opacity, for if the descriptions in (5a) are quantifiers rather than singular terms, they are not referential and =E could not be applied in the first place: the major premise is not of the form t1 = t2, but is rather “(the x: Fx)[(the y: Gy)[x = y]].”

However, even if descriptions are singular terms, they may be a special case semantically, which could make (5) not very illuminating about (2). Assuming the singular-term analysis, definite descriptions other than mathematical ones are, apart from certain unusual cases, nonrigid designators: they do not pick out the same object at all possible worlds (Kripke 1972, 1980:48ff). For example, the number nine is the unique satisfier of “number of planets” at the actual world, but in some other possible world, a different (natural) number is the unique satisfier, or, perhaps, there is no satisfier because there are no planets. “32” is the less common case, a rigid definite description: “32” abbreviates “the product of the number three with itself,” and nine uniquely satisfies “product of the number three with itself” at every possible world, since numbers exist in every possible world, “the number three” is another rigid description, and the product operation is the same at every possible world. (As hinted above, there are other ways of cooking up rigid descriptions; see Davies and Humberstone 1980. For more on nonrigidity, see Tichy 2004.)

According to Kripke (1972), proper names, unlike typical descriptions, are rigid designators: they denote the same object with respect to every possible world. To see the case for rigidity, suppose we say that the planet Jupiter could have failed to exist. Here we are talking about a specific heavenly body which in the actual world orbits the Sun between Mars and Saturn, but which, we might say, in certain other possible worlds, is simply never formed, because of different behavior on the part of the original protoplanetary disk, or because a physical universe never comes into existence, or for whatever possible reason. When we say that Jupiter does not exist in such circumstances, we mean to be talking about our relatively familiar planet (it is the third brightest object in the night sky) and saying that it does not exist. So “Jupiter” denotes Jupiter at each possible world w, no matter what happens in w, even failure of Jupiter to exist (see further Salmon 1981:32–40).

It is crucial to problematic uses of =E in the style of (5) that at least one of the singular terms in the major premise be nonrigid. For if they are both rigid and also codesignate, then the minor premise and the conclusion will agree in truth-value. So we might propose a restriction on =E that makes the application in (5) illegal. The weakest restriction motivated by the failure of (5) is that t1 and t2 must have the same modal profile: for each w, either t1 designates the same thing as t2 at w, or neither designates anything at w. A slightly stronger restriction is that t1 and t2 have the same modal profile and at each w, each designates something. Here we are proposing a sui generis addition to the constraints that correct application of =E in modal languages must meet, a constraint that is required because we are treating definite descriptions as singular terms. But allowing application of =E in formal modal languages only if the terms in the major premise have the same modal profile is not workable, since two terms which have the same profile in one interpretation of the language (at each world, they denote the same thing) may have different profiles in another interpretation. So the standard approach is (i) to decree that =E is only applicable when t1 and t2 are proper names, and (ii) in the semantics stipulate that names are always rigid designators. (Some might object that it is illegitimate to sneak semantics into the statement of an inference rule, as the combination of (i) and (ii) does.)

Using “□” for “necessarily,” we can then prove

(6)
c
= d  ⊢ □(c = d),

simply using =E once, with the minor premise “□(c = c),” which is a theorem and therefore does not need to be mentioned on the left in (6). But (using “∃!” for “there exists exactly one”) we will not be able to prove even

(7)
the F
= the G ⊢ □([(∃!x)Fx & (∃!x)Gx] → (the F = the G)),

much less with the unconditional version of the conclusion, “□(the F = the G).” The restriction in =E to names blocks anything like a proof of (7) analogous to that of (6) just mentioned, and there is no way of formulating sound rules for “the” to get round this. So we can classify (5) as a misuse of =E, since in (5a) at least one term is not a proper name.

The relevant question for us is whether there is anything in our discussion to justify the claim that the definite description “the number of planets” occurs opaquely in (5b). As already noted, the idea that “the F” is really a quantifier would have to be rejected before the question whether descriptions are referentially opaque in modal contexts could even arise, since quantifiers are not referential. So for “referentially opaque” to be an accurate characterization of the occurrence of “the number of planets” in (5b), we must take a side, not necessarily the most plausible side, on the singular-term/quantifier issue.

Yet even granting that definite descriptions are singular terms, it is implausible that

“the number of planets” is functioning deviantly in (5b), or in some other way that merits the term “opaque.” In an extensional language, the designation of a definite description in given circumstances is calculated following the semantic structure of the description. For example, “the man who first set foot on the Moon” will designate the unique entity, if there is one, that satisfies both “is a man” and “first set foot on the Moon.” To satisfy “first set foot on the Moon,” such an entity must be the first satisfier of “set foot on the moon,” which in turn has further semantic structure. This evaluation procedure, of following the structure to arrive at a unique object (if there is one), does not change when we move to an intensional language; it is simply that in interpreting an intensional language there are varying circumstances with respect to which an expression can be evaluated. A conjunction A & B may have different truth-values in different circumstances, but no one would accuse “&” of being problematic on account of this. Similarly, the fact that “the F” can have different designations in different circumstances is hardly a cause for concern.

Of course, (5) may seem to indicate a problem; but then, so may the sequent

(8)
A B, ◇(A & C) ⊬ ◇(B & C)

(here “◇” means “possibly”; consider the case where C = ¬B). From (8), we learn that substitution on the basis of accidental equivalence does not work in modal languages, and we must constrain any substitution rule to require necessary equivalence. In the same way, from (5) we learn that substitution on the basis of accidental codesignation is invalid in modal languages, and we must constrain =E to allow its application only if the codesignation is necessary. This is exactly what we have done, by restricting the singular terms of the major premise to individual constants, whose semantics requires them to be rigid designators.

Is there an analogous restriction on =E that we could employ to make the rule acceptable for languages with attitude verbs like “believe”? That t1 = t2 be rigid designators is insufficient, as (2) shows. And we want a condition that does not make it a matter of mere mental compulsion that any thinker in the minor premise’s propositional attitude comes to be in the conclusion’s propositional attitude: it has to be logically guaranteed. Plausibly, nothing weaker than identity of proposition determined by the two “that”-clauses satisfies this demand. So if we agree that a difference in the semantics of the two names would result in the two content-sentences in (2) expressing different propositions, we will have to say that the two names in a use of =E in the likes of (2) must be synonymous.

But it is not clear what it means to apply “synonymous” to a pair of names. Names are not usually found in dictionaries, so the normal notion of synonymy, on which, say, “attorney” and “lawyer” are synonyms in virtue of having the same dictionary definition, will not help. There is also a more serious objection, due to Mates (1952), to the effect that even substitution of dictionary synonyms in attitude ascriptions can produce results not much more comfortable than (5). For example, (9a) below may well be false, yet it seems (9b) could still be true:

(9)
a. I suspect that many people doubt that everyone believes all lawyers are lawyers.
b. I suspect that many people doubt that everyone believes all lawyers are attorneys.

One moral we might draw from “Mates cases” like this is that searching for a criterion which allows substitution of t2 for t1 in attitude reports is likely to be futile. (For further discussion of attitude reports differing by a synonym, see Burge 1978 and Kripke 1979:160–1.)

To summarize, we have considered three incorrect uses of =E, (3), (4), and (5), in the hope that understanding why they go wrong will help us gain clarity about (2). But (3) turned out not to be so useful, given the drawbacks to quotational accounts of attitude ascriptions. (5) suggests trying to modify =E by limiting its use to some favored class of singular terms, but Mates cases cast doubt on whether this line will be productive (see also Kaplan 1969, Section xi). This leaves (4), which shows how a substitution can have a hidden truth-condition-altering side-effect, a paradigm to which we will return.

For the moment, we note a distinction which emerges from the unhelpfulness of (5). (5) illustrates difficulties for =E which arise from the intensionality of certain vocabulary, primarily modal operators, difficulties resolved by a more careful statement of the rule. On the other hand, the difficulties for =E illustrated by (2) do not seem to be resolvable in a similar way. So the problem manifest in (2) is said to arise from the hyperintensionality, or fine-grained intensionality, of psychological vocabulary such as attitude verbs (a context is hyperintensional iff interchange of necessarily coextensive expressions in it can fail). However, even hyperintensional semantics does not necessarily legitimize a qualified version of =E. (For a version of hyperintensional semantics that takes propositions as primitive, see Thomason 1980, Muskens 2005; for a study of some alternatives, see Fox and Lappin 2005; for the use of “impossible worlds” to analyze hyperintensionality, see the exposition and references in Berto 2013; for a derivational account of hyperintensionality, see Bjerring and Rasmussen 2018; and for an argument that “probably” is hyperintensional, see Moss 2018:§7.5).

2. The De Re/De Dicto Distinction

It is possible to get oneself into a frame of mind according to which there is no such thing as hyperintensionality, and the reasoning of (2) is not flawed at all. For if Lois believes that Superman can fly, then, since Superman is Clark, she just does believe that Clark can fly, even though she would not put it that way. What you believe is one thing, which words you are inclined to use when stating your beliefs is another, and if you are ignorant of an identity, you may disprefer or even reject particular wording that nevertheless captures what you believe. So even though Lois would laugh if someone suggested to her that Clark has superpowers (in those very words), she may still believe it.

One view about this argument in favor of (2) is that it is essentially correct. We shall return to this Russellian position later. But a second view is that it exploits an ambiguity that is present in (2b), “Lois believes that Superman can fly,” and in (2c), “Lois believes that Clark can fly.” According to this view, an attitude ascription such as (2b) can be read in a way that permits substitution and in a way that does not. Normally, we understand such ascriptions in the way that does not, which is why we reject (2), but if cajoled enough (“look, she does believe Clark can fly, she just wouldn’t say it like that”), we may switch to a reading that allows substitution. In the usual terminology, this is called the de re reading, contrasting with the more common de dicto reading, which disallows substitution. Other terminology for this reading is relational, contrasting with notional; transparent, contrasting with opaque; and wide scope, contrasting with narrow scope. We turn now to explaining what distinction these labels attempt to mark.

a. Defining the Distinction

None of the above terminology is entirely happy. It is unclear in what sense the substitution-resistant reading of (2b) is any less “about the thing” (“de re”) than a putative substitution-permitting reading, nor is it clear why the truth of (2b) understood in a substitution-resistant way makes the subject of the ascription any less related to the object the attitude is about (Lois believes Superman can fly because she has seen him do it). And “transparent/opaque” employs the notion of opacity, which, if it is not just a synonym for “substitution resisting,” suggests failure to refer in the normal way, an idea we have yet to find a justification for.

But “wide scope/narrow scope” is more useful. The rationale for “wide scope” is the thought that a substitution-permitting reading of (2) can be brought out by a formulation in which the crucial name is moved to a position in front of the attitude verb (it has wide scope with respect to the verb), as illustrated in

(10)
a. Superman is such that Lois believes that he can fly.
b. Superman is someone who Lois believes can fly.

The step from (2b) to (10a) or (10b) is called exportation, and it is intuitively plausible that the exported forms permit substitution: if Superman is someone Lois believes can fly and if Superman is Clark, then indeed Clark is someone Lois believes can fly. So if we read the minor premise and conclusion of (2) in the exported way, we have an explanation of why someone might, under pressure, accept (2) after all. For (2a) and either (10a) or (10b) entail the exported variant of (2c). Note that we are not saying that exportation is valid, for example, that (2b) entails (10a) (though it seems to—for worries about existential commitment of the kind raised in Donnellan 1974, see Forbes 1996:357–62, and more generally Kvart 1984). The point here is just that (2b) and (2c) could be understood straight off in the style of (10), which would explain why (2) might be swallowed.

One advantage of the wide-scope/narrow-scope terminology is that it reflects a difference whose existence is not in doubt, insofar as it is simply syntactic, manifested in the contrast between, say, (2a) and (10a). But of course, there is a question whether the syntactic difference marks any interesting semantic one.

To argue for a semantic difference, we may observe that the same syntactic distinction arises with definite descriptions and (other) quantifiers, where a semantic difference is undeniable. For example, we have

(11)
a. Lois believes the extraterrestrial who works at The Daily Planet likes her.
b. Lois thinks that no extraterrestrial is in this conference room.
c. Lois hopes that someone born on Krypton will come to her aid.

If the quantifiers are given narrow scope, that is, if the examples in (11) are interpreted following word-order, (11a) is false, (11b) is (say) true, and (11c) is false. (11a) is false because Lois does not think that there are any extraterrestrials who work at The Daily Planet, so would not use “The extraterrestrial who works at The Daily Planet likes me” to express any belief of hers. (11b) is true even though

Clark is in the conference room along with Lois and she sees and recognizes him. But since Lois presumes none of her colleagues is an extraterrestrial, she will happily use “No extraterrestrial is in this conference room” to say what she believes about the planetary origins of those in the room. And (11c) is false because (let us suppose) Lois has never heard of the planet Krypton; therefore, she will not think or say “Would that someone born on Krypton comes to my aid!” At least, these are the commonsense verdicts about the examples in (11), based, as is evident, on maintaining a close connection between the content of mental states and their verbal expression by the subject (on which, see Burge 1978:132).

However, these judgments of truth-value reverse themselves when we consider the exported forms:

(12)
a. The extraterrestrial who works at The Daily Planet is someone who Lois believes likes her.
b. No extraterrestrial is someone Lois thinks is in the conference room.
c. Someone born on Krypton is such that Lois hopes that person will come to her aid.

(12a) is true because Clark is the extraterrestrial who works at The Daily Planet and Lois believes Clark likes her; (12b) is false because Clark is an extraterrestrial and Lois thinks Clark is in the conference room; and (12c) is true because Superman was born on Krypton and Lois hopes Superman will come to her assistance. (The intuition that (12a) and (12c) are true and (12b) false suggests that what is required for the truth of, say, (12a), is that Lois have at least one name t of Kal-El such that she expresses a belief of hers with an assertion of “t likes me” literally construed. So the falsehood of (12a) would require her to have no such name; that she will not use “Superman likes me” to express a belief of hers is insufficient for the falsity of (12a).)

Not only does this contrast between (11) and (12) indicate that exportation makes a semantic difference, it also indicates what that difference is. The false cases in (11) are false because they make attitude attributions to Lois using concepts that either she lacks (“born on Krypton”), or thinks empty (“extraterrestrial who works at the Daily Planet”) and so would not employ positively in any belief she has; while the true case, (11b), is true precisely because “no extraterrestrial” is used to specify the content of her belief. In (12), on the other hand, problematic material is kept out of the specification of Lois’s mental states, which allows (12a) and (12c) to be true, while in (12b), we get a falsehood precisely because “no extraterrestrial” functions simply as an objectual quantifier, without characterizing the content of her belief. So in propositional attitude attributions with wide-scope material binding into the content-sentence, the content-sentence only partially characterizes the attitude, while if there is a “closed” content-sentence within the scope of the attitude verb, that is, if there is no exported material, the content-sentence fully characterizes the attitude. And we can then, if we like, resurrect the “de re/de dicto” terminology and use it in the same way as “wide scope/narrow scope.” The hallmark of a de re attribution is not that it says that the subject of the attribution stands in a special relation to the thing the attitude is about, but that the attribution designates or characterizes that thing in a way the ascriber chooses irrespective of whether the subject would accept the characterization, and the subject’s resisting the characterization is not even prima facie reason to think the attribution false; while a contested de dicto attribution is prima facie false. (See further Brogaard 2008:105–7 and Yalcin 2015:210–13; also see Marcus 1962 and Kazmi 1987 on the interpretation of exported quantifiers.)

This gives us a nontendentious way of using “de re/de dicto,” aligned with “wide scope/narrow scope,” that justifies our proposed diagnosis of any inclination to say that (2) passes muster: the diagnosis is that such judgment relies on construing the minor premise and conclusion as if they were in exported form, that is, construing them as de re attributions in the just explained sense. Still, it is worth observing that on this account we are equating the permits-substitution/resists-substitution distinction in the examples in question with a scope ambiguity. This may be too strong: there may be a substitution-permitting reading of, say, (2b), “Lois believes that Clark can fly,” which is not to be explained as involving a wide-scope reading for “Clark.” We will return to this point later, in connection with hidden-indexical semantics.

b. Skepticism about the Distinction

We have arrived at an apparently defensible way of understanding the de re/de dicto distinction, however the distinction is to be employed. We must therefore note that there are expressions of skepticism about it in the literature, for example Dennett (1982), Richard (1990:128–31), Sosa (1970), and Taylor (2002), whose points have not been addressed here. So, let us briefly consider a selection.

Taylor points out that even if using a definite description provides an accurate characterization of what a subject J believes or doubts, in the sense that the content-sentence containing the description echoes the sentence J would produce to express J ’s attitude, an ascriber will in certain cases resist using the description. These are cases where the ascriber thinks that the definite description is improper (a singular definite description the F is improper iff it is not the case that there is exactly one F). Thus, on seeing Smith’s dismembered corpse, Jones may leap to the conclusion that he was murdered and say “Smith’s murderer must be insane”; this is a “whoever that is” use of a description (Donnellan 1966; I am assuming “Smith’s murderer” is a form of “the murderer of Smith”). But if Black knows or believes that Smith was in fact savaged to death by an escaped tiger, she will not make ascriptions like “Jones thinks Smith’s murderer is insane” or “Jones expects the police to capture Smith’s murderer quickly.” This is puzzling if we have the practice of making de dicto ascriptions to reflect the content of the subject’s attitudes, and there is no reason to doubt that Jones’s statement “Smith’s murderer must be insane” expresses in his mouth what he believes (see further Maier 2015).

This reluctance to ascribe may be a result of pragmatic considerations. One reason to think so is that even in the circumstances of the case, it seems that Jones can properly self-ascribe notionally with “I believe Smith’s murderer is insane.” If Black asserts “Jones believes Smith’s murderer is insane” just before realizing she should not, and if “believe Smith’s murderer is insane” is univocal between Black’s ascription and Jones’s self-ascription, the difference in assertibility most probably has to do with the shift in context of utterance, specifically the shift in speaker. One might flesh this out in terms of “the” being a presupposition-trigger, entailing, even when in the scope of normally entailment-canceling operators such as negation, that its restriction is uniquely satisfied, which in our case means that exactly one person murdered Smith. Then since Black knows that Smith was not murdered, she will not say anything that entails that he was. Nonfactive attitude verbs are often said to suppress the triggering (“projection”) of presuppositions (see Kadmon 2001:116), but in view of Taylor’s examples, this may be wrong, or at least too simple.

A weaker pragmatic approach proposes that using a definite description in a belief-ascription conveys (merely) that the ascriber grants or takes the description to be proper. And cooperative speakers who know this do not use descriptions they think improper. So the difference between Black’s ascription and Jones’s self-ascription is explained. The question would then be how this implicature arises.

So far as undermining the idea that there are de dicto or notional ascriptions goes, one might say that the use of presupposition-triggers in the content-sentence creates a principled exception. One would then expect the phenomenon noted above to recur with other triggers. Jones may say “I think I will manage to save enough money,” but Black should not report “Jones thinks that he will manage to save enough money” unless Black grants Jones’s presupposition that saving enough money will be difficult. For if Black knows that the sum is small and that Jones can easily afford it, on this account she would not want to use “manage,” unless ironically.

There is also a question about how manifest the phenomenon that Taylor isolates is with other quantifiers. If Jones says “everyone who attacked Smith will be brought to justice” (he now thinks there were multiple killers), would Black, who knows about the tiger, happily report “Jones thinks everyone who attacked Smith will be brought to justice,” even though Jones says so? If the report seems infelicitous, that may be a point in favor of a pragmatic account if it is combined with a presuppositional account of “every F” in “every F is G.” According to such an account, the restriction F, in this case “person who attacked Smith,” is presupposed to be nonempty (see Heim and Kratzer 1998:159–72).

Sosa (1970) has an interesting example which tries to undercut the de re/de dicto distinction by suggesting that there are no hard-and-fast limits on exportability and so no substantial cognitive relation invoked by the exported form. In an extreme case (Sleigh 1968), if S believes there are spies but only finitely many, and that all have heights but no two have the same height, S may infer and come to believe “the shortest spy is a spy,” and Sosa would allow the exported ascription “the shortest spy is someone S believes is a spy.” So if Phil Kimbly is the shortest spy, Phil Kimbly is someone S believes is a spy (strangely, S, though the most upright of citizens, never thinks of contacting the FBI).

The argument for this laissez-faire stance about exportation is that there are examples where it is perfectly natural. For instance (Sosa 1970:890), the Commanding Officer (CO) may say to the captain, “Tomorrow I want the shortest platoon member to go first” or “I think the shortest platoon member should go first tomorrow.” The CO has no idea who the shortest platoon member is, but in fact it is the unfortunate Smith again (this is before he meets the tiger). The captain knows Smith is the shortest, and says to the sergeant, “The CO wants Smith to go first tomorrow”/“The CO thinks Smith should go first tomorrow,” or to Smith, “The CO wants you to go first tomorrow.” It is perfectly natural for the captain to say such things, yet the ascriptions seem to be arrived at by first exporting a description used by the CO in a whoever-that-is way, and then substituting a name or pronoun. But should not we object to the exporting, on the grounds that the CO does not have a desire or belief or doubt about Smith, that such-and-such? His desire that the shortest platoon-member go first seems to be no more about Smith than S’s belief that the shortest spy is a spy, arrived at as described, is about Phil Kimbly. But why then is “The CO wants Smith to go first tomorrow” so natural?

According to Kripke (2008:348), examples like these are “toy duck” cases: a child in a toy store points at a stuffed animal, asking his mother if it is a goose, and she replies “No, it’s a duck.” Kripke implies that what the mother says, no matter how natural, cannot really be true: “no dictionary should include an entry under ‘duck’ in which ducks…may not be living creatures at all” (346). Another example might be that you and I go to an exhibition of the work of a famous forger who specialized in analytic cubism. Pointing at one of his forgeries on the wall, I ask “Is that a Picasso?”, to which you reply, “No, it’s a Braque.” This is a natural conversation, but the painting is not really a Braque, and we should not explain the use of artists’ names as predicates of their works in a way that permits an NN not to be by NN. Of course, the simplest explanation of the naturalness of these dialogues is that the remarks “It’s a {duck/Braque}” are true, even though the duck is made of artificial fibers and Braque had nothing to do with the Braque (see Partee 2003 for how this could be). So if we follow Kripke in rejecting that explanation, we need to find another. Fortunately, at least in Sosa’s case of “The CO wants Smith to go first tomorrow,” it is not hard to see what the naturalness consists in: Smith is the person whose going first tomorrow will satisfy the CO’s desire that the smallest platoon-member, whoever he is, go first tomorrow; and Smith is the person whose going first tomorrow would realize the quantified eventuality the CO believes should obtain. Rather than leave it up to the sergeant to find out who the relevant individual is, the captain just tells him, and rather than do so by some laborious step-by-step reasoning about how to satisfy the CO’s desire, the captain makes an attitude ascription that is strictly false, but serves both his and the sergeant’s interests in seeing that the CO’s order is obeyed; for to obey the order, an individual has to be identified. By contrast, the Phil Kimbly ascription seems unnatural because there is no surrounding context to give it a rationale. Perhaps we could invent one, but doing so would not turn an incorrect exportation into a correct one, and nor does it in Sosa’s example. An ascription can be well motivated and promote efficiency in communication, but still be literally false.

c. The de re and Leibniz’s Law

Assuming that the de re/de dicto distinction survives skeptical attack, there is one more issue we can address with its aid. At the start of this essay, we distinguished Leibniz’s Law, “if x and y are the same object, then x and y have the same properties,” from the inference rule of =E. Problem cases for the rule might suggest that the Law itself is dubious. Why have we not considered this possibility?

The reason is that the Law is formulated in terms of objects and properties, and to regard examples like (2)–(5) as threats to it, we would have to construe these inferences as specifying properties of objects in their minor premises; but when we do this, we see that the apparent threat to the Law fades, as follows.

(3) is a “wrong object” case, for (3b) ascribes a property to a word, but in (3a) the objects x and y are cities. (4) is a case of failure to specify a property of an object: (4b) seems to involve the property being so-called because of its size, but the italicized phrase fails to specify a property, because of the uninterpretability of its “so”: “so” needs a context, linguistic or otherwise. There is certainly at least one property of objects in the offing, that of having a name which was endowed on the basis of size. But in conformity with the Law, that property is shared with Barbarelli, and the sentence attributing it, “Giorgione has a name endowed on the basis of his size,” falls short of what (4b) says. There is also the property being called “Giorgione” on account of size, but this is shared with Barbarelli too.

As for (5), there is certainly a reading of (5b) in terms of properties of objects: the property of contingently being 9 is ascribed to the number that numbers the planets. But then (5b) is false, since this number is 9, and 9 is not contingently 9. In other words, this property-of-objects construal requires a de re reading of (5b), with the description “the number of planets” exported, resulting in a falsehood.

Another property-of-objects construal of (5b) is one where the property is contingency and the object is the proposition that the number of planets is 9. On this reading, (5b) is true. But this turns (5) into another wrong object case, since in the major premise the objects are numbers, not propositions. And if we change (5a) to make it about propositions, it would have to say that the proposition that the number that numbers the planets is 9 is the same proposition as the proposition that 32 is 9. If (5) is reformulated this way, it is clearly a correct use of =E, but the falsity of the conclusion, that the proposition that 32 is 9 is contingent, means the rewriting of the major premise to state an identity between propositions produced a falsehood: they are not the same proposition at all.

So what of the original (2)? Here the property-of-objects construals of the minor premise are parallel to those in (5), but we do not want to say quite the same things about them. One property-of-objects reading of (2b) is that Superman has the property of being believed by Lois to be able to fly. (2a) is an identity involving Superman, so certainly we can use =E, in this case to infer that Clark has the property of being believed by Lois to be able to fly. This is just a slightly different formulation of the way of understanding the argument that we identified above as underlying an inclination to say that (2) is valid: the crucial point is that the names that are syntactically in the scope of “believes” are interpreted semantically to be exported from its scope. But we do not arrive at (2c), understood as false: that would require importation of “Clark” back into the scope of “believes,” and the fact that (2c) is by default understood as false shows that importation is invalid.

As with (5), we can reconstrue the minor premise and conclusion of (2) to be specifically about propositions. (2b) would then say that the proposition that Superman can fly is believed by Lois, and (2c) would say that the proposition that Clark can fly is believed by Lois. To prevent this just being another wrong-object case, (2a) would then have to be changed to an identity between propositions. Specifically, it would assert that the proposition that Superman can fly is the same proposition as the proposition that Clark can fly. The =E inference is then entirely in accord with Leibniz’s Law. The problem, of course, is that one is inclined to infer that the asserted identity between the propositions is false.

Perhaps we should say, then, that (5) is partially instructive as regards (2), in that there are parallel property-of-objects readings. What (5) does not help with is the formulation of a restriction on the terms used in =E that allows syntactically unstructured individual constants to be substituted in formulations like those actually used in (2); moreover, there seems to be no way to do this.

3. Frege’s Theory of Substitution-Resistance

a. The Sense/Reference Distinction Applied to Attitude Ascriptions

According to the framework for semantics of natural language sketched in Frege (1892), every meaningful phrase of natural language has potentially two sorts of meaning, a reference (Bedeutung) and a sense (Sinn, a cause of many puns in the titles of worthwhile pieces—for example, Dummett 1973 Ch. 17, Burge 1979, Forbes 1990 (if I may), Salmon 1990; for issues about the translations of these German words, see the discussion and references in Kripke 2001:254, n.1). A meaningful expression e, or a use of e, expresses a sense. Its sense determines its reference (if it has a reference) by virtue of being a way of thinking (or “mode of presentation”) of that reference, but whether there is a reference can depend on how things are in the world. In the case of a singular term, the reference is the thing it designates. For example, the sense of the name “Aristotle” might be articulated by “the pupil of Plato who tutored Alexander and wrote the Nicomachean Ethics.” Whether or not the name “Aristotle” has a reference then turns on whether or not there was such a person.

The same is true of sentences. A sentence expresses a thought, or, in current jargon, a proposition, and a proposition with a reference refers to a truth-value, true or false (the idea that propositions refer is a little odd, but see Dummett 1973:180–6). For example, the proposition that Aristotle was a philosopher is a way of thinking of a truth-value: this proposition is the proposition that the pupil of Plato who tutored Alexander and wrote the Nicomachean Ethics was a […] (here readers should substitute their favorite explanation of “philosopher” for the ellipsis, but please, not “one who philosophizes”). Assuming that there was such a person, then this proposition is a way of thinking of true. However, if “Aristotle” lacks a reference because there was no such person, the proposition “Aristotle was a philosopher” will lack a reference because it has a part that lacks a reference.

It is an important point about this apparatus that the calculation of the reference of the whole proposition or sentence expressing it proceeds via the references of the parts. In the case of “Aristotle was a philosopher,” the reference of the whole sentence is obtained by composing the references of “Aristotle” and “was a philosopher,” as determined by their senses, in a way which results in a truth-value. So, it is easiest to think of the reference of “was a philosopher” as a function, one which, applied to an object, produces a truth-value (functions are input-output operations, so in this case the object is the input, the truth-value the output). Then if “Aristotle” provides an object, we will get a truth-value from “was a philosopher.” But if there was no such person, this procedure will hang, waiting for an object when none is going to be provided. This motivates the verdict that in case the name is empty, the sentence is neither true nor false.

a. The Sense/Reference Distinction Applied to Attitude Ascriptions

The sense-reference distinction suggests that we may be able to explain how (13a) below can be true while (13b) is false:

(13)
a. Lois hopes Superman is nearby.
b. Lois hopes Clark is nearby.

Assuming that the names have different senses (perhaps “the red-caped superhero who flies” versus “the mild-mannered Daily Planet reporter with a crush on Lois Lane”), (13a) and (13b) will express different propositions because their embedded content-sentences do, and so (13a) and (13b) at least potentially may refer to (that is, have) different truth-values. But truth-value is at the level of reference, and the corresponding constituents of (13a) and (13b) are all coreferential (given a fixed context to determine what counts as “nearby”). Specifically, the references (truth-values) of (13a) and (13b) are calculated from the references of their three main constituents: (i) “Lois,” referring to Lois; (ii) “hopes,” referring to the hoping relation; and (iii) “Superman is nearby” and “Clark is nearby,” respectively, which refer to the same truth-value. Since (i) and (ii) are common to (13a) and (13b), (13a) and (13b) must also have the same reference, that is, same truth-value, even if they express different propositions by virtue of having content subsentences that express different propositions. So it looks as if Frege’s apparatus does not get us any closer to an account of how (13a) and (13b) might differ in truth-value.

Explanation of references as functions may be extended to expressions other than singular terms and sentences. For example, “hopes” at this point is assumed to refer to a function f that takes a truth-value as input, say the truth-value of “Superman is nearby,” and produces as output another function, g, the reference of the verb-phrase “hopes Superman is nearby.” g takes the referent of the name “Lois” as input and produces the truth-value of (13a) as output. The problem is then that “Superman is nearby” and “Clark is nearby” present the same truth-value to f, which must therefore output the same function g as the referent of the two verb-phrases “hopes Superman is nearby” and “hopes Clark is nearby” (same input requires same output). Thus, Lois is mapped to true by both verb-phrase functions, or to false by both, since they are both the function g; and so (13a) and (13b) are equivalent.

The source of the difficulty is clear: we have taken the reference of “hope” to be a function of the truth-values of content-sentences that follow it. This is not arbitrary, for the calculation of the reference of any complex phrase uses the references of its constituent phrases along the way, and the content-sentence of the ascription does indeed refer to a truth-value, at least when asserted in isolation, or more broadly, when it occurs extensionally, not in an intensional or hyperintensional context. But this is a very unintuitive account of the reference of “hope.” The thing the attitude of hoping is taken toward is surely a proposition, not a truth-value: the proposition that Superman is nearby is what Lois hopes to be true, not the proposition’s truth-value.

So, on the one hand, we want “hope” to take the reference of its complement sentence as its input, because reference is computed from referents. On the other hand, we want “hope” to take the proposition expressed by its complement sentence as its input, because it is propositions whose truth we hope for. But the proposition is the sense of the content-sentence, not the reference.

To solve this conundrum, Frege made a move of what Kaplan called “brilliant simplicity” (Kaplan 1969:117): we attribute to attitude verbs the property of switching the reference of the material that follows in the ascription from the “customary” reference of that material to a different reference, namely, the customary sense (also known as the “indirect” reference). So in (13a), the (customary) reference of “hopes Superman is nearby” is obtained by applying the (customary) reference of “hope” to the reference “Superman is nearby” has in (13a), its indirect reference, that is, its customary sense. Thus, the reference of “hope” gets the proposition that Superman is nearby as input, as we wanted. This means reference is relativized to linguistic context of occurrence. If “Superman is nearby” occurs extensionally, it refers to its truth-value. But if “Superman is nearby” is the S-part of a complex phrase V+(that)S, where V is an attitude verb, “Superman is nearby” refers to its sense, the proposition that Superman is nearby.

On this account, “hope” refers not to a function that takes a truth-value and produces, as the meaning of the verb-phrase “hopes Superman is nearby,” a function that takes individuals (such as Lois) to truth-values. Rather, “hope” refers to a function which takes a proposition as input, for example the proposition that Superman is nearby, though it still produces, as the meaning of the verb-phrase “hopes Superman is nearby,” a function which maps some individuals, like Lois, to true, and others, like Lex Luthor, to false. However, since we have already agreed that “Superman is nearby” and “Clark is nearby” express different propositions (when occurring extensionally, as we would now add) because of the different senses of “Superman” and “Clark,” this means that the input to the reference of “hope” in (13a) is different from its input in (13b): two different propositions, rather than the single truth-value which is all that is available in the absence of the switch in reference of the content-sentences. Consequently, the verb-phrases “hope Superman is nearby” and “hope Clark is nearby” can refer to different functions; “hope Superman is nearby” can refer to a function which maps Lois to true, while “hope Clark is nearby” can refer to a function which maps Lois to false. This is Frege’s account of how (13a) and (13b) can differ in truth-value, and is the first example of what is nowadays called “switcher semantics”(Gluer and Pagin 2006, 2012; Pagin and Westerståhl 2010).

The reference-switch thesis has immediate application to the question of what is wrong with (2). The Fregean answer is that (2) is a fallacy of equivocation. In (2a), “Superman” and “Clark Kent” have their customary referents, namely, Kal-El. But in (2b), “Superman” refers to its customary sense, the concept of being the red-caped superhero who flies; “Clark” also refers to its customary sense. As the example shows, identity of customary reference does not justify substituting one singular term for another in the content-sentence of an attitude attribution, since identity of customary reference falls far short of the identity of indirect reference (identity of sense) that would be needed for (2) to be valid.

Indeed, Frege’s theory predicts that it will be hard to find any nontrivial sound arguments in the style of (2), even if we change the major premise to be of the form “the sense of t1 = the sense of t2.” For then the major premise is true only if two different names have the same sense, and it is not clear under what circumstances that would happen. Perhaps it might be self-evident in the acquisition process that the names refer to the same person: the speaker introduces herself to x with “Hi! My name is Roberta, but people call me Bobbie.” But even if x correctly recalls this, Mates cases can be constructed: x may coherently think that everyone knows Roberta is Roberta but wonder if everyone knows Roberta is Bobbie. Perhaps we should say that for x, for a while, the two names have the same sense, but x envisages that others may use the names with different senses, and the semantics of “everyone knows that Roberta is Bobbie” allows, one way or another, for this possibility. (See also Schiffer’s discussion of the individuation of senses (1992:502–3). For a theory on which senses are never needed to deal with the likes of (2), see Millikan 2000, and for a pro-Fregean critique, Lawlor 2006.)

b. The Hierarchy Problem

There are problems of detail with Frege’s theory. One such is how to accommodate intersubjective variation in sense (see Zalta 2001). But perhaps the best known is the “infinite hierarchies” problem. As we have already seen with Mates sentences, one attitude ascription can be embedded within another. A simple case is:

(14)
a. Kal-El wonders if Lois has begun to notice that Clark is never around when Superman is.
b. Lois has begun to notice that Clark is never around when Superman is.
c. Clark is never around when Superman is.

According to Frege, “Lois has begun to notice that Clark is never around when Superman is” refers in (14a) to the sense it expresses in (14b), since it is within the scope of “wonders” in (14a). And “Clark is never around when Superman is” refers in (14b) to its customary sense, the sense it expresses in (14c) (curiously, the names in (14c) also seem to resist substitution, despite the lack of attitude verbs; we will return to this in our discussion of “simple sentences”). These sentence-senses are obtained systematically from the senses of their constituent words. So in (14b), “Clark” refers to the way of thinking of Kal-El it expresses in (14c), which we label m1. But whenever a word refers, it does so by expressing a way of thinking of that reference. So “Clark” in (14b), referring as it does to m1, must express a way of thinking of m1, which we label m2. Plausibly, m2 cannot be m1 over again, for (i) m2 = m1 would require the same way of thinking to be of both a person, Clark, and of a way of thinking of that person, m1; and, (ii), m2 = m1 means that m1 is a way of thinking of itself, an idea not breathtaking in its intelligibility (see further Peacocke 2009:162–3; but see also Dummett 1973:264–9 for an attempt to get by with just m1). So these considerations motivate the idea that in (14b), “Clark” expresses a way of thinking m2 which is of m1 and not identical to m1.

Now, (14b) occurs in (14a) within the scope of the hyperintensional “wonders,” so its reference in (14a) and the referents of its constituent words in (14a) must switch; they switch from the referents they have in (14b) to the senses they express in (14b). This means that in (14a), “Clark” refers to m2. But then, “Clark” in (14a) must express a sense which is a way of thinking of m2, since this is the only way “Clark” could refer to m2. Call this sense m2. As before, it is implausible that m2 is the same as m2, since, first, it would have to be a way of thinking of itself, and second, it would have to be both a way of thinking of m2, but also, since ex hypothesi it is m2, would have to be a way of thinking of m1. m2, then, appears to be something new.

And so we are off. We can make (14a) the content-sentence of a new attitude ascription, say

(15)
Lex suspects that Kal-El wonders if Lois has begun to notice that Clark is never around when Superman is.

Now the sense (14a) expresses becomes the reference of (14a) in its appearance as the content-sentence of (15), and the words of (14a) will express new senses in (15), ways of thinking of the senses they express in (14a); for example, in (15), “Clark” will express m, a way of thinking of m2, so that “Clark” in (15) can refer to m2. Since there is no principled restriction on how deeply attitude verbs may be embedded within other attitude verbs, we have, apparently, an unending sequence of senses. In particular, “Clark” can express infinitely many ways of thinking, none of which are intelligible beyond the first or second. Some Frege scholars have developed formal models of sense and reference which embody such hierarchies; see, for example, Church (1951) and Anderson (1980). However, others have tried, in effect, to stop at m2; see especially Parsons (1981, 2009).

c. The Semantic Innocence Objection

Problems of detail aside, there are two main objections to Frege’s account which have emerged in the last few decades, the semantic innocence objection and the no-such-thing-as-senses objection. We take the former first.

The semantic innocence objection is so-called because of its famous statement by Davidson (1969:172):

If we could recover our pre-Fregean semantic innocence… it would seem to us plainly incredible that…words [in the content-sentences of attitude attributions] mean anything different, or refer to anything else, than is their wont when they come in other environments.

This is, admittedly, simply an appeal to intuition, but it is a powerful one (see also Loar 1972:43). It is indeed very difficult to detect a switch in the reference of “Superman” if Lois remarks “Superman is nearby, if I’m in luck” versus if she remarks “I hope that Superman is nearby.” The reference-switch thesis also causes problems for the treatment of anaphoric pronouns. In “Galileo thought that the Earth moves, and he knew what he was talking about, so it moves,” it is undeniable that the “it” refers to the Earth. But then the pronoun does not directly inherit its reference from its antecedent (see further Segal 1989). No doubt there are epicycles which get round this, but it is questionable whether that road is worth going down, given the lack of intuitive support at its starting point.

d. Do Name-Senses Exist Anyway?

An even more damaging objection to Frege’s account of substitution-failure for names is that the entities which play the crucial role, senses or ways of thinking of individuals, are chimerical. That Fregean name-senses do not exist is the core argument of Kripke (1972). Briefly, suppose that “Aristotle” does express a reference-determining sense, captured by, say, the singular definite description “the pupil of Plato who tutored Alexander and wrote the Nicomachean Ethics.” One possibility is that this description articulates the meaning of the name in much the way that a dictionary might articulate the meaning of “philosopher.” Then it should be both necessary and a priori that Aristotle tutored Alexander. But it is neither. Aristotle could have been killed in an Athenian traffic accident in his youth, so it is not necessary that he tutored Alexander; and that he did so is clearly an empirical claim, which only historical evidence can confirm or disconfirm. Similarly, not even “if Aristotle and Alexander existed, the former tutored the latter” is necessary or a priori.

A somewhat weaker thesis is that the reference of “Aristotle” is fixed by the description, without being synonymous with it. But even merely this would predict, of some perfectly intelligible statements, that they are semantically problematic. For example (based on Kripke’s “Gödel case,” 1972, 1980:83–5), suppose that someone claims on a fake-news website to have found documents showing that Aristotle was not a pupil of Plato, did not tutor Alexander and did not write the Nicomachean Ethics. The first two items Aristotle deliberately falsified on his CV in order to attract students, and though he published the Nicomachean Ethics under his own name, that was after stealing the manuscript from the true author (not a pupil of Plato), whom he murdered to ensure his silence. And as time passed, the false claims became firmly lodged in popular lore about Aristotle.

If it went viral, this story about Aristotle would outrage historians of philosophy. But the very fact that they would be outraged shows that they understand the story well enough. Yet, if the reference of the name is fixed by the description, the story is self-refuting (if it is true, then it is not true): Aristotle did not lie about tutoring Alexander, for according to the story, “Aristotle” is an empty name, so “Aristotle lied” should be either false or neither true nor false. But no historian would contest the story on the grounds that it is self-refuting: the debate would be over the existence or trustworthiness of the documents that the story is based on. The ability to debate the truth of the story, with both sides treating “Aristotle lied about Plato” as at least debatable, is hard to explain if the reference of “Aristotle” is fixed by the proposed description. And if some other description of the same “famous deeds” sort is substituted, a similar example would surely be constructible.

If the weaker, reference-fixing thesis, does not support attribution of senses to names, perhaps we should go back to the stronger, meaning-giving thesis, and try a different kind of description. Kripke considers modifications like (whoever it is who is) “the person commonly thought to have been a pupil of Plato who tutored Alexander and wrote the Nicomachean Ethics.” He argues that this is vulnerable to counterexamples involving subjects who have not kept up with what is commonly thought about whom (1980:88), and he raises a circularity objection (loc. cit.).

The new description identifies Aristotle as the person commonly thought to be thus-and-so. So there is a certain range of thoughts s1,…,sn had by members of the linguistic community, thoughts of various people to the effect that Aristotle tutored Alexander, Aristotle was taught by Plato, and so on, and these determine the reference of “Aristotle.” But ex hypothesi, “Aristotle” as it occurs in these thoughts means “the person commonly thought to be…,” referring us back once again to s1,…,sn. There is an unending loop here, and we never escape from the thoughts s1,…,sn to a specific object as the reference of “Aristotle.”

Kripke also points out that we manage to refer easily enough even when there are no identifying descriptions we could cite. He gives the example of “Richard Feynman,” a name many people use without having an associated definite description (1980:81—this was before Feynman’s incisive testimony at the Challenger disaster inquiry). An associated indefinite description might be “a famous physicist at Caltech who won the Nobel Prize.” But “a” cannot be strengthened to “the,” since Murray Gell-Mann is also a famous physicist at Caltech who won the Nobel Prize. And if we insert “not identical to Gell-Mann” into the description, we make it impossible to refer to Feynman without having a way of thinking of Gell-Mann (not to get into the looming indeterminacy problem).

e. Alternative Accounts of the Sense of a Name

If Kripke’s arguments show that Fregean senses of names do not exist, then the Fregean solution to the problem of opacity collapses, rather like a well-worked-out theory of human behavior in which demonic possession plays a large and crucial role. However, it would be fair to say that Kripke’s counterexamples tell mainly against “famous deeds” descriptivism and some modifications of it involving qualifiers like “commonly thought.” It is reasonable to focus on famous-deeds descriptions, since Frege says that everyone who uses the name expresses a reference-determining sense with it, and so to guarantee that each individual is in possession of such a sense, one naturally looks to information that is easily come by. But perhaps there are other options for the content of name-senses besides famous deeds.

One alternative, due to Chalmers and developed in the two-dimensional framework of Stalnaker (1987), is two-dimensional sense. A two-dimensional sense is an ordered pair consisting in an epistemic sense and a subjunctive sense. For a name, the epistemic sense is a function from “scenarios” to individuals, and the subjunctive sense is a function from possible worlds to individuals (Chalmers 2011:596–9). A scenario is something like a coherent total description of how things might have turned out to be, and the epistemic sense of a name may be a nonrigid function on such items: in one scenario, a name may refer to x, while in another it may refer to a distinct y. But subjunctive senses are rigid: they denote the same object in any two worlds. The idea is then that epistemic operators are sensitive to the epistemic sense, and modal operators to the subjunctive sense, which, since it is a rigid function, may be identified with the object to which it stably refers (2011:597, T4, T5).

If epistemic senses are just famous-deeds descriptions or their like, Kripke’s objections arise over again. And it would certainly be unfortunate if epistemic and subjunctive senses came apart over actual reference, since then statements like “it’s a posteriori that Aristotle was a philosopher” and “it’s contingent that Aristotle was a philosopher” would be about different people. However, Chalmers has a proposal on which this difficulty and certain others will not arise. Asking what might replace a famous-deeds descriptivist account of how names refer, Kripke suggested a “historical chain” account (1972; 1980:91–4):

[S]omeone, let’s say a baby, is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain… it’s in virtue of our connection with other speakers in the community, going back to the referent himself, that we refer to a certain man.

The same idea was advanced by Geach (1969:288–9):

[F]or the use of…a proper name there must in the first instance be someone acquainted with the object named…But …the…name…can be handed on from one generation to another… Plato knew Socrates, and Aristotle knew Plato, and Theophrastus knew Aristotle, and so on in apostolic succession down to our own times. That is why we can… use “Socrates” as a name the way we do.

One thing required for x to refer to Socrates with “Socrates” nowadays, then, is that x belong to a linguistic community in which there is an apostolic succession from Socrates to x along which the name “Socrates” is passed. (Following Kripke, x also has to intend to defer in x’s use of the name to those from whom x acquired it—if x decides that “Socrates” would be a fine name for x’s pet turtle, that does not count.)

Kripke mentions that Nozick once remarked to him that if any theory of reference is correct, some descriptivist theory is immune to counterexamples in the style of Naming and Necessity. This would be a descriptivist theory on which the descriptions are theory-laden: they incorporate the reference-determining conditions the correct theory formulates (Kripke 1980:88, n.38). Chalmers exploits this option: taking the historical chain theory as a plausible account of reference-determination, he suggests that the epistemic sense of a name NN might just be “the object NN refers to in the mouths of those from whom I acquired it” or its like (Chalmers 2002:641). This will be a nonrigid function, since in some scenarios, the apostolic succession for “Socrates” will lead to contemporary users but start from an individual x who is not Socrates.

Since the description suggested above involves the term “refer,” there is an obvious circularity worry if the sense is to be reference-determining. Chalmers argues (2002:641–3) that there is no reason to worry, since the evaluation of one person’s epistemic sense takes us back to other people, and their epistemic senses will carry us back to even earlier people, until we arrive at the “initial baptism” introducing the name. The question would then be whether the concept of reference is ineliminably invoked at this point, as in “we hereby name this child NN,” and how significant a problem that would be.

A second question is whether epistemic senses are otiose as far as determining reference is concerned. Is the reason why I can use “Socrates” to refer to Socrates not simply that I belong to a community in which there is a chain of uses of “Socrates” linking me to Socrates in the way the historical chain theory describes, and I have added the name to my repertoire with the intention to use it in a way that preserves the reference of those from whom I acquired it? Perhaps adding the name to my repertoire with such a deferential intention is the very same thing as attaching a theory-laden sense to it. But if not, the postulation of an epistemic sense seems redundant: the reference of the name in my mouth is already determined by my social situation, and if I express a certain epistemic sense with it, that is just a private epiphenomenon.

A second alternative to famous-deeds senses is what we might call “cognitive descriptivism,” since it is based on a (somewhat metaphorical) hypothesis about cognitive architecture. The idea is that we organize our information about what we take to be separate objects that we have encountered into separate mental files, or dossiers. This seems to have first been proposed by Grice (1969:141–4), and was used in an account of the senses of names in Forbes (1990). The neo-Fregean idea is that the sense of a name NN for x is “the subject of this dossier,” where the mental demonstrative “this dossier” refers to the dossier labeled NN by x in x’s mental filing system.

Clearly, questions about circularity and redundancy arise much as they do for two-dimensional sense (see Fine 2007:67–8). If what makes x the subject of the dossier labeled NN is that x is the referent of the name NN, then we have circularity. But if being the subject of the dossier labeled NN consists in—to use the causal theory of Evans (1973)—being the dominant causal source of the information in the dossier, why not cut out the detour through dossiers and just say that the reference of a name NN is the dominant causal source of information that would be expressed in statements of the form “NN is…”? Such issues are pursued in Recanati (2012) and Saka (2018), and are far from settled in the literature. But it is clear from these examples that famous-deeds descriptivism is not in sole possession of the field as an elaboration of Frege’s notion of the sense of a name.

However, whatever viable theory of sense may ultimately be produced, the semantic innocence objection will have to be dealt with. Thomason (1980) is unmoved by it, but we shall next consider accounts of senses that may be invoked by attitude ascriptions in a way that explains failure of =E, yet allows those senses to have their customary references, thereby meeting Davidson’s complaint.

4. Hidden-Indexical Semantics

The reference-switch hypothesis is one version of the more general notion that the words used in the content-sentence of an attitude ascription have a special role that they do not play in other contexts. If the special role does not displace their normal role, we arrive at Loar’s idea of a dual contribution (1972:52–3). On the one hand, as Davidson insists, the words of the content-sentence play their normal role. But there is another semantic mechanism at work in which they are also complicit. There is a wide range of such dual contribution accounts in the modern discussion of opacity, perhaps starting with Loar (1972). Field (1978) has the content-sentence invoking a sentence of the “language of thought.” Bealer (1993) proposes an ambiguity theory, on which the content-sentence of an ascription introduces both an entity composed of the referents of the words, thereby explaining the innocence intuition, and an entity like a Fregean proposition, thereby accounting for the intuition of substitution-resistance in the likes of (2). And Larson and Ludlow (1993) develop a semantics on which a propositional attitude is an attitude to an “interpreted logical form” (ILF) which is a tree structure in which a node is occupied by both the reference of the expression at that node and the expression itself. Consequently, “Superman can fly” and “Clark can fly” are different ILFs simply in virtue of “Superman” and “Clark” being different names.

a. Two Kinds of Hidden-Indexical Theories

Some versions of the dual contribution approach are known as “hidden-indexical” accounts (Schiffer 1979), because of the role context-dependence plays in determining the second contribution of the content-sentence, or because there actually is an indexical expression postulated to occur covertly in the ascription. For example, in Crimmins and Perry (1989) and Crimmins (1992), belief-ascriptions are said to be made true by items supplied by the context in which the ascription is made, items called “unarticulated constituents” because there is no expression in the ascription responsible for their intrusion into the truth-condition. Different but coreferential names may be associated with different normal notions of the same object, and an inference like (2) fails because the substitution changes which normal notion of Kal-El is, in their technical sense, “involved” (there is no reference-switch on the part of the names). Similarly, in Richard (1990), the content-sentence of a belief-ascription invokes a “Russellian annotated matrix” (RAM), which, like an ILF, is an item that contains both Fregean referents and the expressions referring to them, and the truth-condition requires that the RAM in the ascription correlate with a RAM believed by the subject of the ascription. What correlates with what is context-dependent, and (2) fails because substitution need not preserve correlation, even though it preserves Fregean reference (Richard 1990:133–41). While in Forbes (1990, 1996) and Recanati (2000:137–63) there is a hidden “so” in belief-ascriptions, as if “believes” were “so-believes,” which blocks substitution much as it does in Quine’s “Giorgione” case, (4), since the “so” refers to the content-sentence of the ascription.

One respect in which the above theories differ is over what kind of thing is believed. In Schiffer’s general scheme for hidden-indexical theories (1992:503–4), what is believed is a proposition of a non-Fregean kind, but the ascription includes as part of its literal meaning that this proposition is believed under a way w of thinking of it. Here w is something like a Fregean proposition in certain respects, and is specified by the very words used in the content-sentence of the ascription. Substitution then has the side-effect of changing the relevant way of thinking, say from the “Superman can fly”-way to the “Clark can fly”-way, and this opens the door to change of truth-value.

The kind of proposition of which w is a way of thinking is known as a “Russellian” proposition, after a famous exchange between Russell and Frege (Frege and Russell 1904). Frege had claimed that Mont Blanc “with its snowfields” is not itself a component of the thought that Mont Blanc is more than 4,000 meters high, to which Russell replied that “in spite of all its snowfields Mont Blanc itself is a component part of what is actually asserted…a certain complex.” Accounts of Russellian propositions have been given in some detail (for example, Cresswell 1985, Crimmins 1992:117–24; see Jespersen 2003 for critical discussion), and in Schiffer’s scheme, attitude ascriptions invoke quasi-Fregean ways of thinking of such complexes, while the attitude itself is to a Russellian proposition.

In the approach of Forbes (1990, 1996), however, it is a Fregean proposition to which an attitude is held, but one that is specified as the way of thinking of the referent of the content-sentence, where this way is determined by that very sentence. The referent is not a truth-value, as Frege would have had it, but rather an abstract state of affairs, which is a structured entity not unlike a Russellian proposition, though one that fits better into a Fregean scheme. So (2a) becomes

(16)
That Superman can fly is so-believed by Lois or more long-windedly,

(17)
Lois believes her so-labeled way of thinking of the state of affairs that Superman can fly

in which “so” refers to “Superman can fly,” sealing it off from substitution in the same way as it does for “Giorgione” in (4). (17) requires for its truth that the ascriber’s content-sentence be a “linguistic counterpart” of some sentence of Lois’s that she would use to express the belief that (17) is attempting to ascribe to her (compare Richard’s notion of correlation), a belief which is a way of thinking of the state of affairs that Superman can fly (which is equally the state of affairs that Clark can fly and equally the state of affairs that Kal-El can fly).

One problem for (17) is that it requires reference-determining senses, whereas Schiffer-style approaches need not. Additionally, (17) departs from (16) in a rather substantial, if not frequently noticed, way: the “that”-clause disappears, and the clausal form of “believes” is replaced by the transitive one (the direct object in (17) is everything following “believes”). But though there seems to be an equivalence between believing that… and believing the proposition (thought, so-labeled way of thinking) that…, it does not generalize to other attitude verbs. For example, suspecting that Lex Luthor is involved is not the same thing as suspecting the proposition that Lex Luthor is involved (is anyone so paranoid as to suspect propositions?—Moltmann (2003:82) credits Arthur Prior with first noticing this issue). The same thing occurs, though for different reasons in different cases, with such verbs as “announce,” “anticipate,” “ask,” “boast,” “calculate,” “caution,” “complain,” “conclude,” “crow,” “decide,” “detect,” “discover,” “dream,” “estimate,” “forget,” “guess,” “hope,” “insinuate,” “insist,” “interrogate” (literary theory), “judge,” “know,” “notice,” “observe,” “plan,” “prefer,” “pretend,” “rejoice,” “require,” “see,” “suggest,” “surmise,” “suspect,” “understand,” and various cognates of these. The verbs for which the equivalence holds include inference verbs like “deduce” and “infer,” plus a few other examples like “doubt,” “establish,” and “verify.” Unfortunately, it would take us far afield were we to address the issue of how to modify (17) for the verbs for which the equivalence fails (see Forbes 2018 for one account).

As the previous paragraph indicates, some hyperintensional clausal verbs that can be used to ascribe propositional attitudes have hyperintensional transitive forms that can be used to ascribe what we might call objectual attitudes. These seem to generate failures of =E much as their clausal counterparts do. For example, “Lex fears Superman” is true, but “Lex fears Clark” does not seem any more plausible than “Lex fears that Clark will crush him.” The apparatus in (17) can be employed to express a hidden-indexical theory for the transitive verb case: the substitution-resistant reading of “Lex fears Superman” is “Lex fears Superman as such,” or “Lex fears Superman so-personified,” and the references of the “such” and “so” will change if “Clark” replaces “Superman,” producing the false “Lex fears Clark {as such/so-personified}.” A fuller version of the substitution-resisting semantics for “Lex fears Superman” might be

(18)
Lex fears Superman under the way of thinking of him that is so-labeled.

Here “under” forms an adverbial phrase modifying the whole verb-phrase in (18) headed by “fears” (there is some dispute about how such an “under” is to be accommodated; see Schiffer 1996, Ludlow 1996).

Hidden-indexical theories all preserve semantic innocence in roughly the same way: there is some entity, whether Russellian proposition or abstract state of affairs, determined by the customary referents of the words of the content-sentence, so the result is compatible with a Davidsonian decrying of any theory which claims that words in attitude ascriptions abandon their customary referents for something else. The “something else” is involved in a different way, a strategy which (17) and (18) illustrate.

Hidden-indexical semantics also offers an alternative formal account of the de re/de dicto distinction. Standardly, the difference is brought out in terms of scope distinctions, as we did in (10). But another possibility is that de re readings are those in which a hidden-indexical refers only to a part of the content-sentence: if Lois believes that her coworker Mary has gone to St. Petersburg, we may point at Mary and say “Lois believes that that woman is in St. Petersburg,” meaning that she believes some way of thinking of the state of affairs, partially labeled “is in St. Petersburg.” This would explain why the awkward locutions in (10) are rarely encountered in ordinary speech and writing.

b. Kripke’s Puzzle

One application of hidden-indexical semantics is to Kripke’s “puzzle about belief” (1979). Kripke doubts that there is a specific problem of interchange of coreferential names in attitude ascriptions, to be resolved by a semantics on which such substitution is fallacious. Rather, he thinks substitutivity problems are a mere symptom of broader anomalies in psychological discourse (“It would be wrong to blame…substitutivity. The reason does not lie in any specific fallacy [for example in (2)] but rather in the nature of the realm being entered,” 1979:157). So he gives examples meant to bring out anomalies even in the absence of substitution.

His main example is that of a subject, Peter, who encounters the same individual under the same name in different contexts and does not realize it was the same person all the time. Suppose Peter goes to a recital by a pianist named Paderewski, and, picking up the name from the recital program, comes to believe on the basis of the performance that Paderewski has musical talent. Later, at a railway station, he observes an individual surrounded by reporters, and someone tells him “That’s Paderewski, the Polish Prime Minister.” Far from connecting the man he sees with the man he heard play, Peter, who believes that no politician has musical talent, remarks out loud, “Ah, a person of no musical talent, then.” But, of course, Ignacy Jan Paderewski, the Prime Minister of Poland after the First World War, was also a celebrated composer and concert pianist.

Kripke wants us to try to answer the question, “Does Peter, or does he not, believe that Paderewski has musical talent?”, and in the course of our attempting to answer it, to realize that no answer can be given, because of “the nature of the realm being entered.” However, from the Fregean perspective, the example is less troubling, as Kripke recognizes (see also Taschek 1988). Peter has two lexical entries for “Paderewski,” in the same way that the present writer has three for “Socrates”—one for the Ancient Greek philosopher, another for the late Brazilian footballer, and a third for the former Portuguese Prime Minister (the latter two individuals had different first names, but I do not know what they are, and I do not know if the first individual had any other name; on the individuation of names, see Kaplan 1990). Of course, the difference between Peter and myself is that the names in Peter’s two lexical entries are coreferential, while the names in my three are, pairwise, not, unless the footballer, on retiring from the game, moved to Portugal and went into politics.

However, an ascriber A may only have one name for Paderewski (one mental file so-labeled), which puts A at a certain expressive disadvantage relative to Peter, if the ability to make an accurate report about Peter’s beliefs requires A to use names which match Peter’s. A would then need two names for Paderewski. But there is a very natural way around this (which Kripke uses himself, in n.37): A can simply say that Peter believes that Paderewski the pianist has musical talent, while Paderewski the statesman does not (Forbes 1990:561). From the perspective of a semantics like that of (17), the appositive uses of “the pianist” and “the statesman” determine different ways of thinking of the single state of affairs that Paderewski had musical talent. And it is only the way of thinking labeled with Peter’s linguistic counterpart of A’s “Paderewski the pianist has musical talent” that he believes: the appositives help us identify which of Peter’s ways of thinking of Paderewski we wish to invoke in our ascriptions. The question remains to explain why the major premise that Paderewski the pianist is Paderewski the statesman does not license the inference to “Peter believes that Paderewski the statesman has musical talent.” This would partly recapitulate our discussion of (2), though of course the appositives may bring their own complications.

It is also conceivable that ascribers in the know about Peter’s situation, addressing an audience also in the know, can rely on context to fix which belief is ascribed to Peter using “Paderewski has musical talent”; for instance, if the discussion concerns Peter’s evaluations of various pianists, the possessive description “Peter’s so-labeled way of thinking” is proper, rather than improper, since the other way of thinking, labeled with Peter’s linguistic counterpart of “Paderewski the statesman has musical talent,” will not be in the domain of the context, even if the discussion takes place after the railway-station encounter.

One can therefore resist Kripke’s question whether Peter does or does not believe that Paderewski had musical talent, just as I would resist the question “Was Socrates, or was he not, a chain-smoker?” The footballer was, but (I suppose) the philosopher was not, so absent contextual clues I would require disambiguation of the question: “Are you asking whether Socrates the footballer was a chain-smoker, or Socrates the philosopher?” In the Paderewski case, there is no referential ambiguity, but there is still an ambiguity, or indeterminacy, over which way of thinking of the state of affairs in question is being invoked: “Are you asking whether Peter believes Paderewski the pianist has musical talent, or Paderewski the politician?” would be a perfectly proper response. The explanation why it is perfectly proper is clear enough on hidden-indexical theories, but may not be so on others (see also Soames 2002, Chs. 2, 3).

Obviously, this account only works if there is a viable notion of the sense of a name. For those skeptical about the prospects of such a thing, Fine (2007) offers an alternative treatment of the puzzle. Fine begins with an explanation of the difference between “Superman is Superman” and “Superman is Clark”: in “Superman is Superman,” the two names are coordinated, but not in “Superman is Clark.” One manifestation of this is that someone who wonders whether Superman is Superman thereby demonstrates a failure to grasp what is said, while Lex can wonder whether Superman is Clark without demonstrating any failure of understanding. Since Fine takes the coordinated/uncoordinated distinction to be of semantic import, his view could be regarded as neo-Fregean, since he thinks “Superman is Superman” and “Superman is Clark” have different semantics, though his view of how the difference arises is quite unlike Frege’s (see Pickel and Rabern 2017 on some questions that arise for Fine’s account here).

Fine then argues that the case of Peter presents us with a puzzle whose solution is to be formulated in terms of this notion of coordination (2007:100–105). The puzzle is that our normal practices of belief-reporting dictate that we report Peter as believing that Paderewski has musical talent, and that we also report him as believing that Paderewski has no musical talent. At the same time, according to Fine, we do not want to make a “composite” report, that Peter believes that Paderewski has musical talent and believes that Paderewski has no musical talent, since this represents Peter as rather unreflective, which is unjustified (more reflection will not help). Yet the composite report is a simple “and”-Introduction inference from the acceptable reports. How can it sensibly be resisted?

Fine’s suggestion (2007:102–3) is that the composite report is unacceptable precisely because the reporter (who is in the know about Peter’s situation) uses

“Paderewski” in a coordinated way across the content-sentences of the composite report, while Peter does not use coordinated “Paderewski’s” in giving voice to his two beliefs. But the individual reports are acceptable, taken in isolation: there is nothing to be coordinated in an individual report, so we can simply take at face value Peter’s assertion of “Paderewski has musical talent,” even asserted after he has both entries in his lexicon, and ascribe such a belief to him. Whereas, for the Fregean, if there is nothing in the context to point toward one of “Paderewski the pianist” and “Paderewski the statesman” rather than the other, it will be indeterminate what belief is being ascribed (unless some feature of context settles it). And for the Fregean, the composite report, if it is the conjunction of two determinate ascriptions, is acceptable. Perhaps it makes Peter sound unreflective; but so does “The present writer believes Socrates was a chain-smoker and believes Socrates was not (ever) a chain-smoker,” though as I write it, it is true.

5. Russellianism

At the beginning of section 2, we noted that there is a possible response to the appearance of substitution-failure in (2) according to which the reasoning is not flawed at all: if Superman is Clark and Lois believes Superman can fly, she simply does believe that Clark can fly, even though she would not put it that way. The main motivation for this account is the view of propositions advanced by Russell in his letter to Frege quoted above, according to which Mont Blanc itself, not a way of thinking of it, is the sole constituent the name contributes to the proposition about its height. The locus classicus of this theory is Salmon (1986); other prominent contributions include Soames (1987), Saul (1997), and Braun (1998).

a. Salmon’s Theory

According to Salmon, belief-ascriptions invoke both Russellian propositions and ways of taking or of grasping those propositions. The apparently two-place attitude relation of belief unfolds into a three-place relation, with a position for a variable over ways of grasping. So for A believes p, Salmon offers (1986:111)

(19)
for some way of grasping propositions w, A grasps p by means of w and bel(A,p,w).

The correctness of the substitution inference (2) is immediate from this. If (2b) is true, Lois has a way of grasping the proposition that Superman can fly under which she believes this proposition. Ipso facto, she has a way of grasping the proposition that Clark can fly under which she believes this proposition, for it is the same proposition. Thus, (2c) is also true. Ways of grasping may be like Frege’s ways of thinking in some respects, but they are not what is believed, and they are not meant to determine reference.

Also note that Fine’s concern to avoid the composite ascription “Peter believes Paderewski has musical talent and believes Paderewski has no musical talent” is allayed, since the composite ascription is harmless on Salmon’s theory. For it involves two existential quantifiers over ways of grasping: there is some way of grasping the proposition that Paderewski has musical talent under which he believes it (more accurately, bels it), and some way of grasping the proposition that Paderewski has no musical talent, under which he believes it. The second way of grasping is no mere negation of the first, so there is nothing that imputes an intellectual deficiency to Peter (Salmon 1986:130–1).

The main question this account raises is why it seems so clear that there is a way of understanding (2) on which it is invalid. Salmon answers this question by distinguishing between semantically encoded and pragmatically imparted information (Salmon 1986:78). As far as what is semantically encoded is concerned, (2b) and (2c) are the same. But they differ over what they pragmatically convey, and those who think (2b) and (2c) can have opposite truth-values are mistakenly projecting the pragmatic difference onto the semantics. For example, it may be that (2c) pragmatically conveys that Lois believes that “Clark can fly” expresses a truth and that she would assent to it if asked. Loading this into the semantics would be like the mistake made by students in beginning logic classes when they reject “all Fs are G” on being informed that some Fs are G. The defeasible “not all” conveyed pragmatically by “some” obscures their view of the consistency of the two quantified statements.

A different explaining-away of the appearance of falsity in (2c) is provided by Braun (1998). Braun notes that since “Superman can fly” and “Clark can fly” express the same Russellian proposition, (2b) and (2c) express the same Russellian proposition as well. But someone judging (2b) and (2c) may take their common content in one way when judging (2b) and in another when judging (2c), which makes it at least intelligible that they resist the substitution inference.

So, there are things the Russellian can say about conversations among the screenwriters for Superman II, when they agree that at the start of the movie Lois should be shown beginning to suspect that Clark is Superman, and should then confirm that he is, by tricking him when he is personified as Clark into giving himself away. That the screenplay will thereby have Lois beginning to suspect that Clark is Clark, and then tricking him into revealing it, is overlooked by the writers: it never occurs to them (as a non-Russellian would say) that these are the same identity-proposition, taken in different ways.

Russellian propositions are “coarse-grained” compared to Fregean ones, for the latter are individuated in such a way that the propositions that Clark is Clark and that Clark is Superman are two. But once one accepts the distinction between proposition and way of taking the same, it is not clear what limits there are on the coarseness of grain that may be tolerated. There seems to be no obstacle to an unstructured conception of propositions as classes of possible worlds (Lewis 1979; Stalnaker 1984, 1987), and conceivably, it is defensible that true and false are the only propositions. (The same question about how much coarseness of grain is tolerable arises for hidden-indexical theorists who postulate indexically specified ways of thinking of Russellian propositions.)

b. Commonsense Psychology

Another question for Russellianism stems from the main purpose we have in ascribing attitudes: to arrive by abduction at explanations of behavior based on psychological generalizations (“those who believe Superman is present feel safer,” Rupert 2008:83). Someone who (i) feels safer if he believes that Superman is present, and (ii) sees that Clark is present, may still behave nervously or flee, which on the face of it is hard to understand if seeing that Clark is present is the same thing as seeing that Superman is present. Similarly, there are general normative principles of rationality such as

(20)
Anyone who believes a conditional proposition and its antecedent ought to infer its consequent.

This is not to say that such a person ought to believe its consequent: once the consequent is inferred, the thinker has various options, such as rejecting the conditional, or its antecedent, as alternatives to accepting its consequent. But a person who, at a minimum, does not make the inference, betrays a failure of rationality. However, Lex may believe the proposition that if Superman is nearby, then he, Lex, should hide. Lex may then notice and so come to believe that Clark is nearby, but take no steps to conceal himself. Yet if believing that Clark is nearby is the same thing as believing that Superman is nearby (bel-ing a certain proposition via some way of taking it), it seems that we should convict Lex of a failure of rationality, in that he remains unmoved by his two beliefs and so has apparently failed to use modus ponens. (The literature on logic, rationality, and closure under consequence is relevant here; see, for instance, Jago 2009, MacFarlane 2018, Staffel 2018.)

In response to this, Braun (2000) argues that psychological explanation employs ceteris paribus (other-things-equal) principles. For example, even in a case where it is clear to Lex that Superman is nearby, his making no attempt to hide does not mean, say, that he no longer believes he should hide if Superman is nearby, or no longer trusts modus ponens. He will only hide, or try to hide, other things equal. And if he already knows that he is in a location where there are no hiding places, his motivation to seek one is thereby overridden.

So far, this is just commonsense psychology. But according to Braun, there is a special way in which things might not be equal: although a conditional and its antecedent are believed, the antecedent as it occurs as minor premise of the modus ponens and the antecedent as it occurs as a constituent of the major premise may not be grasped in matching ways (2000:209). And if they are not, grounds for anticipating the expected behavior are removed. This means the principle stated in (20) is incorrect as it stands: the correct version would require a “matching ways” restriction. So there is no lapse of rationality on Lex’s part when he fails to use modus ponens in the case where he notices Clark is nearby, and so believes that Superman is nearby, and also believes he should hide if Superman is nearby. For the constituent corresponding to “Superman is nearby” in the way he takes the conditional is different from the way he takes the proposition that Superman is nearby when he comes to believe it once he has noticed that Clark is nearby. Braun admits (2000:234) that he cannot see any other way in which (20) is in need of qualification, so there is a whiff of the ad hoc about his response; but it does allow for a version of (20) acceptable to Russellians.

c. Saul on Simple Sentences

Another prominent defense of Russellianism, due to Saul (1997a, 1997b, 1999, 2007), focuses on “simple sentences,” sentences where we have a strong intuition of substitution-resistance, but there is no sense-invoking expression in the sentence whose semantics might underwrite the intuition. We have already noted one example, (21a) below. The other examples in (21) also manifest the phenomenon:

(21)
a. Clark is never around when Superman is.
b. Clark went into the phone booth and Superman came out.
c. Superman is more successful with women than Clark is.

There is a clear challenge to the Fregean in these examples. The inference in (2) fails, according to the Fregean, because of the semantics of “believes,” which requires its complement content-sentence to behave in a special way: to switch its reference, to make a double contribution to the truth-condition of the whole ascription, or to do whatever else one’s favored account of hyperintensionality proposes. But in the examples in (21), there is no expression which might force analogous behavior on the part of the names. Yet substitution of one name for the other in (21a) and (21c) produces something impossible, so, despite their apparent truth, (21a) and (21c) must be false. And substitution in (21b) seems to alter the meaning enough that the inference fails to be truth-preserving: (21b) appears to require a change of clothing or role, but a single substitution produces something which does not. These examples show that intuitions of substitution-failure do not depend on the presence of psychological vocabulary. And in the absence of anything else to explain them, they show that such intuitions must be mistaken.

Why, then, put any store in corresponding intuitions about (2)? However, hidden-indexical theorists can justify substitution-failure for the examples in (21) if they are willing to extend the scope of hidden-indexical introduction beyond attitude verbs. For instance, perhaps what we mean by (21b) is something along the lines of “Clark, so-attired, went into the phone booth, and Superman, so-attired, came out.” The “so” here accounts for substitution-failure as usual, since the names are associated with distinct ways of dressing: the “Superman” way (dressing as Superman) and the “Clark” way. For other examples, something more general than ways of dressing is needed, and this affords us an opportunity to make a partial unification of the cases of hyperintensional and simple sentences. A more general concept is that of personification, and using it, for (21a) we would have

(22)
Clark, so-personified, is never around when Superman, so-personified, is.

We have the same element of personification in the explanation of why fear of Superman is not the same thing as fear of Clark: to fear Superman, so-personified, is a very different thing from fearing Clark, so-personified (Forbes 2006:166–74).

A possible Fregean view, then, is that (22) is the literal meaning of (21a). According to Braun and Saul (2002) however, the intuition that (21a) can be true rests on some kind of confusion between it and the likes of (22); the latter certainly resists substitution, but differs in meaning from the former precisely because of that. Why would we suffer from such a confusion? Here Braun and Saul make use of the mental files metaphor, but they do not regard it as part of an account of difference in semantic content (see also Rupert 2008). We put information we would naturally express with one name in the file labeled with that name, and information we would naturally express with the other name goes into the file that other name labels. Then in assessing (21c), say, we compare the romantic history recounted in the entries in one file with that recounted in the other, and this task diverts our attention from the fact that the files concern the same individual. The attention-diverting element then explains why we judge (21c) to be true rather than impossible. Braun and Saul draw a parallel with the “Moses illusion” (2002:15–16), in which a large majority of subjects, when asked “How many animals of each kind did Moses take into the Ark?”, respond “Two,” partly because the “how many?” question diverts their attention from their knowledge that in the Bible it was Noah who took animals into his Ark (perhaps this happened to the reader just now).

But such an account cannot apply to speakers and writers who knowingly produce sentences like those in (21). For example, in a review of books about Shostakovich, the historian Orlando Figes wrote, “Shostakovich always signalled his connections to the classical traditions of St. Petersburg, even if he was forced to live in Leningrad” (The New York Review of Books, June 10, 2004, p.14). Far from having his attention somehow diverted from the fact that St. Petersburg is Leningrad, Figes is consciously writing for an audience aware of the identity, since only they will appreciate the rhetorical punch of his remark. And he will certainly resist an editor who proposes to replace “Leningrad” with a second “St. Petersburg,” even though there is nothing hyperintensional about being forced to live somewhere.

Another example comes from an article on the transformation of Eric Blair into George Orwell (Lingua Franca vol.9 #9). The writer of the article is hardly diverted from the fact that Blair is Orwell, since his topic is exactly how one personification came to be abandoned for another in the same individual:

Diffident in private, Blair so feared failure in the literary marketplace that he invented a pseudonym for the book he wrote based on his diaries, Down and Out in Paris and London. Criticism would be directed at George Orwell, not Eric Blair. But since the book, when published in 1933, was a literary success, Eric Blair became George Orwell.

Perhaps, “criticism would be directed at George Orwell, not Eric Blair” is hyperintensional, but “Eric Blair became George Orwell” is not; it clearly resists substitution of “George Orwell,” and it would be absurd to say that the writer only makes the claim because he has allowed himself to lose sight of the fact that Blair and Orwell are the same person.

A third example: a New Yorker cartoon in which Superman, so-personified, is talking to his therapist, and reports, “I’m doing super, but Clark can’t find a paper that’s hiring.” It is unclear who the cartoonist thought would find this funny, but knowing that it is the same person is required to get the joke.

These examples and others (including my favorite, in The New York Times’s “The Philosopher Stripper” article—see Forbes 2006:167–8) show that cases like (21)’s occur outside fiction, and that those who create them do so in full awareness of the relevant identity. That (21a) means what (22) means is certainly the most straightforward explanation of why (21a) is perfectly natural. So substitution-resistance in some simple sentences does not provide as great a threat to the claim of substitution-resistance in (2) as might at first seem, since the mechanisms producing the substitution-resistance may be seen as fundamentally the same in the two cases.

d. Richard’s Phone Booth

The final argument for Russellianism to be considered here is the well-known phone booth case in Richard (1983); I have updated it to cell phones. This example exploits the context-dependence of indexical expressions such as “I,” “here,” and “now.” The phenomenon of indexicality was one on which Frege had pronounced views: he wrote about “I” that (Frege 1967:25–6)

…everyone is presented to himself in a particular and primitive way, in which he is presented to no-one else. So when Dr. Lauben thinks he has been wounded, he will probably take as a basis this primitive way in which he is presented to himself. And only Dr. Lauben can grasp thoughts determined in this way. But now Lauben may want to communicate with others. He cannot communicate a thought which he alone can grasp. Therefore, if he now says “I have been wounded,” he must use “I” in a sense which can be grasped by others, perhaps in the sense of “he who is speaking to you at this moment”….

Whatever one thinks of the last remark, the idea that for each thinker x, “I” can be used by x to express a private first-person way of thinking of x, is one which has persisted since Frege proposed it, and is of course implicitly present in much of the history of philosophy, for example, in Descartes’ cogito. (For further discussion of first-person and more generally indexical and demonstrative thought, see Anscombe 1974, Castaneda 1968, Evans 1981, Lewis 1979, Magidor 2015, Peacocke 1983, 2008 Ch. 3, and Perry 1977, 1979.)

An example in Perry (1979) provides a dramatic illustration. Perry is pushing a grocery cart around the aisles in a store when he comes across a trail of sugar on the floor. He thinks “that person is making a mess” and sets off in pursuit to let them know that a bag of sugar in their cart has burst (“that person” is an example of “deferred ostension,” referring via the sugar trail to the person whose cart the sugar bag is in; see further Borg 2002). His pursuit brings him back to the same point in the store, and he realizes, “I am the one who is making a mess.” This appears to be a new thought, and a Fregean would say it differs from “that person is making a mess” in view of the difference between Perry’s demonstrative way of thinking expressed by “that person” and his first-person way of thinking, “I.”

Fregean first-person ways of thinking are private in the sense that if x and y are distinct thinkers, y cannot employ x’s “I”-way of thinking in y’s thoughts, certainly not as a way of thinking of y. However, this does not stop y from ascribing attitudes to x that require x to be employing x’s own first-person way of thinking (see Peacocke 1981, Percus and Sauerland 2003). y might say that Perry has just realized he himself is the one making a mess, which is to make the ascription “Perry has just so-realized that he himself is the one making a mess.” The ability to describe a Fregean proposition as one that is a special way of thinking of the state of affairs that Perry is making a mess does not imply that the constituents of that proposition are available to the ascriber to use in his or her own thoughts.

But de dicto ascriptions may not always be possible. If Perry says of some store employee, “she knows that I made the mess,” he is not ascribing knowledge to her of the proposition that is his “I made the mess”-labeled way of thinking of the state of affairs that Perry made the mess. From a Fregean point of view, the most Perry can mean is the de re “I am known by her to have made the mess,” since the store employee will probably have identified the culprit demonstratively, “that guy is making the mess,” after following the sugar trail. Perry cannot even ascribe a de dicto demonstrative belief to the employee using “she believes that guy is making a mess” pointing at his own reflection in a mirror. Ascribers using a demonstrative in the content-sentences of their ascriptions are expressing their own demonstrative ways of thinking of the relevant object, not characterizing the subject’s thought, which means that the ascriptions are de re (Forbes 1987:13–15).

Let us now return to Richard’s example. It involves switching contexts (“context-hopping”) and uses Kaplan’s (1989) apparatus to manage context-dependence. In Kaplan’s semantics for context-dependent expressions, sentences are evaluated taken in a context and with respect to a possible world, the circumstances of evaluation (1989:544). A context is a sequence of entities which provides referents for the indexicals and demonstratives in a sentence S and so determines the Russellian proposition S expresses. At a minimum, we would have an agent, a time, a place, and an addressee, to be the referents of “I,” “now,” “here,” and “you,” and an object x to be the referent of a demonstrative or demonstrative pronoun (Kaplan uses “agent” rather than “speaker” to allow for a sentence such as “I am not speaking right now” to be true with respect to silent circumstances). When contexts are systematically related, the truth-values of sentences given fixed circumstances are systematically related. For example, suppose that in circumstances w, X is listening to Y at noon Mountain Time (MT), 11/16/17, and let c be a context with X as its agent, noon 11/16/17 MT as its time, and Y as its addressee.

Then the sentence “I am now listening to you” is true taken in c with respect to w. But if we obtain a new context c* from c by switching agent and addressee, then “I am now listening to you” is false taken in c* with respect to w, since Y is speaking, not listening, to X at noon MT 11/16/17, in w. However, “you are now listening to me” is true taken in c* with respect to w, since “I am now listening to you” taken in c identifies the same state of affairs as “you are now listening to me” taken in c*, the state of affairs that X is listening to Y at noon MT, 11/16/17.

In the circumstances w of Richard’s example, a man a is in his apartment, talking to a woman o on his cell phone. a is also looking out the window onto the street below, where he sees a woman talking on her cell phone. It does not occur to a that the woman he is talking to on his phone might be the woman he is watching through his window; but in fact both are o. Then a notices a man in the street acting suspiciously, apparently trying to sneak up on o from behind. In this situation, a could use “she is in danger” to make a sincere assertion to o on his phone about what he sees. But a would not use “you are in danger” to make a sincere assertion to o speaking into his phone (a might instead open the window and shout down to the street). So in the context c with a as agent, o as phone addressee, and o as the referent of “she,” and taking at face value the facts about what a would and would not say with which referential intention as indicative of what a does and does not believe, the following appear to be true:

(23)
a. I believe she is in danger.
b. I do not believe you are in danger.

But Richard argues (1990:117–8) that (23b) is in fact false; in other words, that a does have a belief he could express by asserting into his phone “you are in danger” with the intention to address the person he is talking to. For if we now consider a context c* in which the woman o is agent (and, if we like, a is addressee), the truth of (23a) in c guarantees the truth of

(24)
The person watching me believes I am in danger

in c*. Consequently, if we switch back to the context c,

(25)
The person watching you believes you are in danger is true.

But there is a true identity in c which entails the falsity of (23b), namely,

(26)
I am the person watching you.

By =E, we have the anti-Fregean conclusion

(27)
I believe you are in danger

now seen to be true in c after all.

By Russellian lights, the reasoning is impeccable. But should it move the Fregean? For the Fregean, attitude ascriptions can be ambiguous between de re and de dicto construals, and this applies to (27) in particular. Does the derivability of (27) really show that in c the protagonist a can express a belief of his by asserting “you are in danger” into his phone, using “you” with the intention to refer to the woman he is talking to? Perhaps all that the derivation establishes is the truth of the de re reading of (27), “you are someone I believe to be in danger.” Note that to say that (27)’s de re reading is true in c is not to say that the agent of c believes that it is true, so it still does not give a grounds to say “you are in danger” into his phone.

(23a) can be understood de re as “she is someone I believe to be in danger,” and if the argument is construed de re throughout, the reasoning is correct. But of course the de re conclusion is not a problem for the Fregean. A de dicto conclusion might well be problematic, but to get one we must at least start with the reading of the premise (23a) on which it is a true de dicto self-ascription. Then, if the de re but not the de dicto reading of (27) is true, there must be some step in which there is a de dicto to de re switch. The switch appears to occur in moving from (23a) to (24).

(24) is relevantly similar to an ascription of Perry’s, “the store employee knows that I made the mess.” Here Perry is not ascribing knowledge of the proposition that is his “I made the mess”-labeled way of thinking of the state of affairs that Perry made the mess. By the same token, we should not construe (24) as o’s making an ascription to a of belief in the proposition that o expresses by “I am in danger.” For that way of thinking of the state of affairs that o is in danger is simply unavailable to a, since it involves o’s first-person way of thinking of herself. The truth of (24), then, is no more than the truth of “I am someone who the man watching me believes is in danger,” whose truth in c* is a consequence of (23a)’s truth in c. Thus, the de re conclusion follows from the de dicto starting point, but, to repeat, the de re conclusion is acceptable to the Fregean, since it is silent on what way of thinking the man watching o employs in his “she is in danger” thought.

Richard considers this kind of response (1990:128–32; see also 190–6 for his own critique of his earlier argument) and rejects it. This is partly because he thinks the response imputes opacity to subject-position in ascriptions, and partly because he is generally skeptical about the de re/de dicto distinction. But the above criticism does not seem to involve any opacity in subject-position, that is, a failure of =E when applied to ascriber, for the use of (26) is legitimate, there is no single context in which (23a)’s “I” and (24)’s “the man watching me” are coreferential, and the content-sentence is different in (23a) and (24). Certainly, the reference of “I” in c is the same as the reference of “the man watching me” in c*, but this does not threaten the use of =E if the content-sentence is fixed and interpreted uniformly, in Fine’s sense: “the man who is agent of c believes she is in danger” and “the man who is watching the agent of c* believes she is in danger” have the same truth-value if “she” is unequivocal, and in the second ascription, “she” is not anaphoric upon the embedded “the agent of c*.”

As for general skepticism about de re/de dicto, the reader may refer to the discussion in section 2. Relevant examples arise in extensions of Richard’s case, where the apparent truth of certain statements is easily explained using the distinction, but not without. Suppose that the suspiciously behaving man turns out to be a harmless drunk who staggers on by. The phone conversation then continues in such a way that a soon realizes that the woman he is talking to is the woman he was watching. a may then say such things to o over the phone as “so it was you I thought was in danger” or “I thought you were in danger but didn’t say anything because I didn’t realize it was you I was watching.” These are perfectly natural remarks and seem to be true along with (23b). Employment of the de re/de dicto distinction provides a straightforward explanation of how they can all be true together. So there is no need to take on the obligation burdening the Russellian, of always having to explain away the appearance of truth.

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Author Information

Graeme Forbes
Email: graeme.forbes@colorado.edu
University of Colorado
U. S. A.

Sayyid Qutb (1906—1966)

Sayyid Qutb was one of the leading Islamist ideological thinkers of the twentieth century. Living and working in Egypt, he turned to Islamism in his early forties after about two decades as a secular educator and literary writer. As an Islamist, he held that all aspects of society should be conducted according to the Shari’a, that is, laws of God as derived from the Qur’an and the practice (sunna) of the Prophet Muhammad. Probably his best known and most distinctive doctrine is his interpretation of jahiliyya (pre-Islamic ignorance) as characterizing all of the societies of his time, including the Muslim ones. Another doctrine was his interpretation of faith in one God only (tawhid) as entailing the absolute sovereignty of God (hakimiyyat Allah) and the liberation of humans from service to other humans instead of God. He was executed by the Egyptian government for his Islamist activities and is thus considered a martyr, something that has added immeasurably to the impact of his ideas.

Although he did not consider himself a philosopher, he had opinions on a number of topics that interest philosophers, and he commented on the ideas of philosophers. He had a grand vision of the universe as a harmonious whole under God’s rule and of humans as called upon to be God’s deputies in managing the Earth. Humans, however, were given a measure of freedom that other beings do not have. Rightly used, this freedom would allow humans to fit in harmoniously with the rest of creation and have the highest status under God. Misused, it would introduce discord into the world and misery into human life. Jahiliyya equates to misuse of this freedom, and Qutb calls for jihad, conceived along the lines of revolution, as the response. In discussing these things, he touches on a range of topics, including the nature of God and the universe, human nature, knowledge and revelation, ethics, society, human history, death, and judgment. This article presents only the latest and most radical phase of his thought.

  1. Biography
  2. Basic Conception
  3. God
  4. Human Nature and Purpose, Other Spiritual Beings
  5. Free Will and Predetermination, The Problem of Evil
  6. Knowledge: Revelation, Worldly Knowledge
  7. Ethical Values, Shari’a
  8. The Ideal Society (Utopia), Economics. Gender Relations
  9. Jahiliyya (Dystopia) and Jihad (Revolution)
  10. Human History
  11. Death, Judgment, Martyrdom
  12. Qutb’s Legacy
  13. Final Remarks: Aesthetics, Harmony, and Essentialism
  14. References and Further Reading
    1. Primary Sources
    2. Secondary Sources

1. Biography

Sayyid Qutb (1906—1966) was and is one of the most important ideologues of the Islamist movement, which seeks to re-establish truly Islamic values and practices in Muslim societies that have become more or less Westernized. He was born and raised in an Egyptian village, attended the state primary school there, and in 1920 moved to Cairo to attend secondary school and then Dar al-‘Ulum, a teacher training institute that sought to balance traditional and modern ways. From 1933 to 1952 he worked in the Ministry of Education, first as a teacher and later as an inspector and administrator. He also became one of the secular literary elite prominent at the time, publishing more than 100 poems as well as articles and books on literary and social topics. In 1948, he rather abruptly began to publish Islamist articles and the next year published a major Islamist book, Social Justice in Islam, which was to go through a total of six editions. The reasons for this shift are not totally clear, but the chaos of Egyptian politics, the efforts of imperialist powers to reassert their position, and the establishment of the state of Israel presumably played a role. His Islamism was confirmed during a two-year (1948-1950) study tour of the United States, which he found to be technologically impressive but hopelessly corrupt morally.

After his return to Egypt he joined the Muslim Brothers, the leading Islamist organization, founded in 1928 by Hasan al-Banna, and soon became one of its leading spokespersons. The Brothers supported the Free Officers’ revolution in 1952 at first but soon withdrew support. After an attempt on the life of Abdel Nasser in 1954, the leading Brothers were imprisoned, Sayyid Qutb among them. In prison, they suffered very harsh treatment, though poor health spared Qutb the worst of it. This led to a radicalization of his ideas, including the claim that the whole world, including the “Muslim” world, is in a state of jahiliyya, that is, un-Islamic ignorance and barbarism. This radicalization was assisted by the ideas of the extremely influential Indo-Pakistani Islamist Abu’l ‘Ala’ Mawdudi (1903-1979), whose writings became known to Qutb and other Arab thinkers from about 1951. Mawdudi’s ideas about divine sovereignty, the Islamic state, jahiliyya, and other things spoke very much to Qutb’s condition and helped him to crystalize and articulate his views.

In 1964, Qutb was released from prison and published his best-known book, Milestones, effectively calling for an Islamic revolution. He also became mentor to a group of young Brothers and was soon arrested for conspiring to overthrow the government. In 1966, he was convicted of this charge and executed. He thus became a martyr to his cause, considerably multiplying his influence.

Qutb wrote a number of books during his Islamist period in addition to those mentioned, especially a multi-volume commentary on the Qur’an, In the Shadow of the Qur’an, which he began in 1952 and was still revising at the time of his death.

Qutb’s radical ideas divided the Muslim Brothers after his death. The main line group rejected them and sought to work within the existing political system, briefly achieving the presidency in 2012-2013. Smaller groups, such as the so-called Takfir wa-Hijra group, Jama‘at al-Islamiyya (Islamic group), and Tanzim al-Jihad (Jihad organization), adopted and modified Qutb’s ideas and were responsible for considerable terrorism through the 1990s (see below). His influence spread far beyond Egypt, indeed throughout the whole of the Islamic world and its diaspora. This included extreme groups such al-Qaeda, whose second leader, Ayman al-Zawahiri, was very much influenced by Qutb’s main ideas and his example as a martyr, and who first joined an Islamist group the year that Qutb was executed. In fact, Qutb has come to be seen by many as the spiritual “godfather” of such groups. On the other hand, it is possible to read him selectively, and so he has influenced many who do not fully accept his extreme views. There is a considerable literature on him both in Islamic and Western languages.

Qutb was not a philosopher by most definitions of the term, and he consciously rejected philosophy as he understood it, both Western philosophy and classical Islamic philosophy. He considered the discipline to be an effort to accomplish with human reason what can only be accomplished on the basis of divine revelation and also as a foreign intrusion on pure Islamic thought. Nevertheless, his thinking was quite systematic and did have a place for reason; moreover, he used rational arguments in criticizing philosophy and made reference to Western philosophers (mostly known to him through Arabic translations) in the process. He also deals with many topics that are of interest to philosophers. He is a good example of Weber’s Wertrationalität (rationality in accordance with moral demands).

The following article is based entirely on the last phase of his writing, from about 1958, during which he rejected many of his earlier ideas. This phase was the most radical, most systematic, and most influential.

2. Basic Conception

Qutb saw his ideas as a necessary interpretation and corollary of the basic Muslim creed: “There is no god but God; Muhammad is the Messenger of God.” His views fall within the wide spectrum of Sunni Islamic thinking but particularly within the forms of it commonly labelled “Islamist” (stressing the application of Islamic norms to society) and “Salafi” (broadly, those who emphasize the authority of the Qur’an, Sunna, and the earliest generations of successors, the salaf, over against later “innovations”). Like many popular writers on religious topics in modern times, he did not have the traditional education given to the ‘ulama’ (religious scholars) and was to some extent self-taught in this area.

The article focuses primarily on the more basic and theoretical aspects of Qutb’s writing (what we might call his philosophy or theology), which he calls the Islamic tasawwur, a word usually translated “concept” or “conception,” but which here could also be translated “worldview” or “vision.” Qutb, in the manner of fundamentalists and also scientists, does not consider this his conception but the true conception. He characterizes this conception as divinely sourced, and following from that: fixed in its basics, comprehensive, balanced, dynamically positive, realistic, and unified.

The tasawwur grows out of its divine source and does not need or accept significant influence from the outside. Therefore, Qutb criticizes not only contemporary modernists, who wish to “reform” Islam in terms of modern, that is, Western ideas and ideologies, but also the earlier Muslim philosophers and theologians, who made use of Greek philosophical ideas. We may note that Qutb is firmly of the view that ideas are prior to actions, which flow from them. The ideas are not ends in themselves, however, but are meant to undergird actions and activities. In fact, all of human life and activity flows from a creedal tasawwur of some kind. Qutb often describes Islam (and religion more generally) in terms of three stages: tasawwur, manhaj (method, program), nizam (social and political order). Each stage proceeds from the former one with almost logical necessity. All three are necessary for Islam to exist. Since Qutb believed that there was no Islamic nizam in his time, he often said that Islam has no “existence.” We may note that Qutb’s Islam is a highly reified concept, not just a label applied variously to diverse human ideas and practices.

3. God

The centrepiece of the tasawwur is God (Allah), that awesome being Whose essence and some of Whose attributes are beyond the reach of human understanding, though many attributes can be understood by the human mind. (Qutb does not discuss the relation between God’s essence and attributes, an important theme in traditional Muslim theology.) These attributes belong only to God and comprise his divinity; no other being shares in them. God is one and unique. This is the first and most basic constituent of the tasawwur, and recognition of it is called tawhid (the usual Arabic term for belief in one God). God is also eternal, without beginning or end.

This God is the creator and source of everything else in existence. These things are separate from God but totally dependent on Him and harmoniously obey regular laws, some of which can be and have been discovered by human science. These laws are not separate from God, however. God acts directly in all that happens, so that these “laws” are just His customary way of acting. Since His will is completely free, He can and sometimes does vary His action and produce what we call miracles. For example, fire usually burns things, but God might make it not do so on some occasion, as in the story of the prophet Ibrahim (Abraham) in the Qur’an. Such events do not disrupt the general order and harmony of the universe, however, since they are part of God’s larger plan. While most of creation obeys God necessarily, humans in their moral aspect may or may not obey. Instead, they are subject to a moral law established by God, the Shari’a, which will put them in harmony with creation if they obey it.

God is therefore the Lord and Sustainer of all creation, while all creation stands in a relation of servanthood to Him, necessarily in the case of most things, willingly or unwillingly in the case of humans (disobedient humans are still servants). It follows necessarily from all of these attributes that God is the only source of authority and the only sovereign in the universe, not only physically but also morally, legally, and politically. No human ruler or nation may claim sovereignty, a point of major importance for Qutb’s revolutionary doctrine. These central ideas reflect those of Mawdudi, though Qutb probably stresses them more. His term for the sovereignty of God, hakimiyyat Allah, comes from the Arabic translation of Mawdudi’s term for the same thing.

4. Human Nature and Purpose, Other Spiritual Beings

Humans hold a very special place in God’s creation, as already indicated. According to the Qur’an, God created the human body and breathed His spirit into it, and He gave humans a status above the angels, whom he commanded to prostrate to the first man. Human nature as originally created, and in its proper state, is called fitra, and this fitra has a need for God and a predisposition to serve Him. The Islamic tasawwur is congruent with it. The fitra may be obscured by human whims, desires and negligence, but is not destroyed.

The basic purpose of humans is to serve God willingly in all aspects of life. They are to do so in the honorable role of God’s deputy, khalifa, over the earth. They are responsible for making it fruitful, developing it technologically, caring for it, and organizing a just society in accordance with God’s Shari’a. This idea is very important to Qutb.

The only significant distinctions among humans in God’s sight are based on their obedience or disobedience to His will. Otherwise all are of equal value regardless of race, ethnicity, nationality, class, or gender, although in the last case there are significant differences of function to be discussed below.

Angels are spiritual beings who serve God and are always obedient to Him. They carry God’s throne, deliver God’s messages to the prophets, watch over the gates of paradise and hell, record the actions of humans, support them in their struggle against evil, pray for them, and cause them to die when their time comes. Jinn (the “genies” of the Arabian Nights) are made of fire, can live on the face of the earth or inside it, can move very swiftly, and are invisible, though they may become visible to humans. They have the power of moral choice and are commanded to serve God just as humans are. Some are believers, and some are not. They will be resurrected on the last day and go to paradise or hell. The Devil is a jinn. Satans may be humans or jinn; they tempt human beings and are enemies to prophets. We know about all of these because the Qur’an tells us. Human science knows nothing of them, though it may discover something about them some day. Awareness of these creatures expands our world beyond the limited one of physical perception.

5. Free Will and Predetermination, The Problem of Evil

But are humans really free in their moral choices, given that God is directly involved in determining everything that happens? Like earlier Muslim theologians, Qutb seeks to affirm both (this is one of the ways the Islamic tasawwur is balanced). He states that the human will works within the bounds of divine determination and that this divine determination is realized through human will. The precise relationship between them is one of those things that are beyond the capacity of human reason to comprehend. Some degree of human freedom is necessary for moral responsibility and for the activist position that Qutb took, while certainty that God is in control is important for the small, struggling revolutionary movement of which he was a part.

But why does evil exist at all and why do good people suffer? From time to time Qutb suggests various partial answers to the latter question. People suffer because they violate the physical or moral laws, or God causes them to suffer to teach them or to provide challenges. This world is a place of trial and striving, and the suffering of a good person will be compensated in the future life, and possibly also in this life. As to why God did not create a world without suffering and evil, this question is not raised by sincere believers, who respect God too much and know that the issue is beyond the capacity of the human intellect to deal with, nor is it raised by serious atheists since they do not believe in God. It is raised by those who are argumentative or not serious.

6. Knowledge: Revelation, Worldly Knowledge

How do humans know of God and of the truths enshrined in the Islamic tasawwur? The human fitra can perceive something about God in the harmony of the universe that He has created and runs (that is, the Teleological Argument), but of primary importance is God’s word revealed to messengers to whom He has given a special nature that allows them to receive His messages and particularly that given to the Prophet Muhammad in the Qur’an. The text of the Qur’an contains the verbatim words of God and provides information about God, the universe, aspects of human, divine moral and legal commands, and the final judgment of human by God. It calls on humans to reflect on the signs of God in the harmony of the universe. It is from the Qur’an that the Islamic tasawwur is directly and exclusively derived.

The Qur’an speaks to all aspects of the human fitra, not only to reason but also to the emotions and the aesthetic sense. According to Qutb and most Muslims, it has the power to influence people directly through these. Qutb gives examples of this, including one in which a woman was converted to Islam by hearing the recitation of the Qur’an. In the years before he embraced Islamism, Qutb wrote two books exploring the literary nature of the Qur’an (Artistic Depiction in the Qur’an and Scenes of the Resurrection in the Qur’an) and concluded that its power comes from producing extremely evocative word pictures for the reader. He appears to have continued to hold this theory in his Islamist period though not limiting the power of the Qur’an to it.

Qutb generally insists on interpreting the text in terms of its plain meaning, but in the case of realities that are beyond human comprehension he understands it to provide allusions that inspire the human soul. These realities include the divine essence, the connection between will of creator and creation, and the nature of the spirit. For the rest, reason can receive the revelation and interpret it, along with other faculties. On the whole, Qutb avoids metaphorical or esoteric interpretations of the Qur’an.

One should seek and may derive direct inspiration from the Qur’an, especially if one has a close and ongoing relation to it. Qutb claims to have lived for years “in the shadow of the Qur’an” (this is also the title of his Qur’an commentary). Especially important is the intention to act on what one reads. One is not to read the Qur’an simply as a devotional exercise, or to get information, but to find out what God wants one to do at a particular time and to do it. Qutb is convinced that the Qur’an will guide such a person. (This is part of what is meant by saying that the tasawwur is practical). One will not truly understand the Qur’an unless one is engaged in the struggle (jihad) for an Islamic society.

For most Muslims, the Sunna (words and deeds) of the Prophet Muhammad is authoritative along with the Qur’an; and also authoritative is the tradition of scholarship related to these. Qutb likewise relies on the Sunna and, somewhat selectively, on the later tradition. He emphasizes the Qur’an, however, more than most. He also emphasizes the generation of Muslims contemporary with Muhammad, the “Unique Qur’anic Generation” as he terms them. This generation was present at the time of revelation and drew their understanding of life and their duties exclusively from it; they received it with the intention to obey as a soldier would receive marching orders for the day; also, they broke completely with their former life. No later generation has equalled them, but they should be the model for Islamic activists today.

Still, there are many areas of life in which human reason is sufficient for understanding and making discoveries, and in so doing fulfilling part of the human role as God’s khalifa. These involve what Qutb calls the “pure” sciences, mainly the physical sciences insofar as they do not involve moral or metaphysical issues.

Splitting the atom would be included but not its use in atomic bombs. Biology is included but not Darwinian evolution. The Islamic tasawwur encourages this kind of science. It does not have the certainty of revelation but, properly done, it will not conflict with revelation. Qutb speaks of the “open book of the universe” (possibly echoing the 19th century Indian modernist, Sayyid Ahmad Khan). In fact, Western science is historically rooted in the past scientific activities of Muslims. It has developed in an anti-religious direction, but Islam can purify this science and put it on the sound basis of the fitra.

7. Ethical Values, Shari’a

General ethical values are of course part of the Islamic tasawwur. They are fixed and do not “develop” over time, although their application may vary. They provide a “fixed axis” and “fixed framework” around and within which human activity takes place. These values are not scattered or ad hoc but are systematic, constituting a complete system for all of life. As they derive from the one God, they unify humans with the creation and its Creator, and integrate individual personalities. To be valid, ethical action must be accompanied by faith in this God. Because they come from God, they provide a greater sense of obligation than secular morality can. Qutb criticizes various forms of secular morality at length.

In principle, there is no grey area in Qutb’s ethics. The contrast is stark between guidance and error, faith and kufr (unbelief, wilful rejection of faith), tawhid (recognition of God’s unity) and shirk (ascribing divinity to other beings than God). Along with this, however, he recognized that although basic ethical values do not change, their application does change with changing times and situations, both of which are experienced very much by modern revolutionaries.

The specific ethical rules and values are enshrined in the Shari’a, to which Qutb makes very frequent reference. This is commonly called the law of God but is more accurately described as a moral classification by God of all human actions into five categories: obligatory, approved, neutral, reprehensible or forbidden. The human understanding of the Shari’a is called fiqh (“understanding”) and is based on the Qur’an and the Sunna of the Prophet, along with the effort (ijtihad) of later scholars to interpret and apply these. Among Sunnis, the consensus of these scholars on any ruling has been considered to guarantee its validity, with the result that the scope for ijtihad has diminished over time. One of the major issues of modern times has been the degree of freedom contemporary interpreters should have to reverse past rulings in the light of current needs. Modernists seek a high degree of freedom in order to bring fiqh in line with prevailing values derived from the West. Qutb opposes ijtihad for this purpose, which he considers defeatism in the face of the West, and insists that there should be no ijtihad where there is a clear and authoritative text. He favors it, however, where, in his view, it represents an authentic Islamic response to current conditions. He calls this fiqh haraki (that is, a fiqh that reflects changing human activities or needs of the current Islamic movement). He also indicates approval of the unfettered use of the principle of public interest (maslaha), a principle recognized in traditional fiqh but usually with restrictions. At the same time, he regularly canvasses the views of earlier scholars on specific matters and sometimes accepts them. All of this accords with his claim that the Islamic tasawwur is realistic and practical. The term Shari’a is to some extent interchangeable or correlated with the term manhaj, and he seems to see the Shari’a as part of the Islamic manhaj. Qutb also claims that the Shari’a is perfectly harmonious with the general laws of the universe, including the physical laws of human biology, and is the only means by which the voluntary life of humans can be integrated with them, as briefly mentioned above.

8. The Ideal Society (Utopia), Economics. Gender Relations

The ideal society is one that recognizes the sovereignty of God alone, not the people, the nation, or the human ruler, and is governed by the Islamic Shari’a. Since the Shari’a is part of God’s overall law for the universe, a society truly governed by it will be in accord with the whole of the universe and with the human nature and needs of its members. It will be just, progressive, and tolerant. Class, racial, and ethnic distinctions will not influence people’s status, but rather piety, virtue, and competence. It will be a society in which people generally know who the virtuous and competent are and can choose them for leadership. He backs this up with descriptions of the society governed by the prophet Muhammad and his earliest successors, especially in Social Justice in Islam. Though the historical critic would probably claim that he is selective in his examples, Qutb’s view is that the history of Islam is not identical to the whole history of those societies called Muslim, but to the history of those societies insofar as they were truly following the Shari’a and implementing Islam.

While class, racial, and ethnic differences will not matter, religious differences will matter since the society is based on a religious creed. Qutb sometimes states that people have absolute freedom of conscience in matters of belief and that the freedom of any individual to hold and propagate his religious belief, free of compulsion, is a fundamental human right. It is not clear just how far this goes, however. No one should be forcibly converted to Islam. Jews and Christians (and possibly others) will have a place in society as granted by the Qur’an and Sunna. They may follow their own creeds and rites of worship but are limited in some areas, as specified in the traditional idea of dhimma (protected status), which Qutb generally accepts and defends. For example, they will pay a special tax called jizya, for which Qutb gives three reasons: it is a symbol of their acceptance of Islamic rule, it is in return for their protection by the Islamic government, and it contributes to the social expenses of the state. While dhimmis would be granted freedom of belief and worship, and Qutb speaks of freedom to propagate religious belief, it seems unlikely that a state run on Qutb’s interpretation would allow non-Islamic religious views to be propagated freely, among Muslims or anti-religious views at all. This is especially the case given Qutb’s view that Islam alone is the true religion and his statement in at least one place that abandoning the truth is corruption. Such a state would hardly accept the kind of religious pluralism, the legal equality in principle of all religions, assumed by many Westerners and others.

An Islamic government will be governed by the principle of consultation (shura). Qutb gives many examples of it from the early days of Islam. The exact form of shura varies with circumstances and, in accordance with the realistic and practical nature of the Islamic tasawwur, will be determined only when such a government is actually formed. Nevertheless, in a least one place he does outline a structure of government involving a ruler (imam) nominated by the recognized leaders of the community (literally: “people of binding and loosing”, a recognized phrase in Arabic) and chosen by the whole community. There will also be a parliament (majlis al-shura) whose members are chosen by the people locally. The high moral tone the government is more important, however, than these details. Qutb seems to envisage the imam as a strong and righteous leader who is normally to be obeyed implicitly, but not if he commands people to disobey God. He rejects the term “democracy” because he sees it as a Western concept involving government by the people instead of by God.

For all that Qutb seems to envisage the true Islamic state and society as a kind of utopia, he recognizes that actual Islamic societies have been less than ideal, and he severely criticizes many of the historical Muslim rulers without quite calling their government and society un-Islamic. In at least one place he states a ruler may be unjust but still be considered Islamic if he basically recognizes the authority of God.

Economics in an Islamic society is based on the fact that all wealth belongs to God, who entrusts it to human societies and thence to individuals as his khalifas. On this basis, the right to private property is guaranteed as a reward for work so that individuals are encouraged to work for their own benefit and the benefit of all. This strikes a just balance between effort and reward and accords with human nature. Private property, however, is limited legally by the institution of Zakat, which requires a portion of one’s wealth to be given away and is one of the Pillars of Islam. It is also limited by the right of the political leader to tax further when this is necessary for the welfare of the community and to assist the needy, who have a recognized right to a share in the community’s wealth. Islam also opposes the concentration of wealth in a few hands, and its rules on inheritance and opposition to usury are designed to discourage this. Likewise, the community should own collectively resources needed for the general wellbeing, and these have expanded considerably in modern times. Added to all of this is the additional moral obligation on individuals to assist the needy and contribute to social causes. In discussing economics, Qutb often goes beyond what the traditional sources of authority prescribe, especially in relation to the economic power of the state. What he writes would be largely acceptable to modernists with a moderate socialist inclination.

Qutb is at pains to point out that women and men are equal in respect of their humanity as such. He even argues that Eve was not created from Adam’s rib but created in the same way as Adam (the account of Adam’s rib is not in the Qur’an but is in later sources). In temperament, however, women and men differ. Women are more emotional and men more rational. Women’s temperament fits them for raising children and other domestic tasks, whereas men are more fitted for the world of work outside the home. Hence, men have the right to leadership within the family and women the right to protection.

The family is the basic unit of society and the institution that produces human values; its place is rooted in the cosmic order. Obedience to God in matters relating to marriage, divorce, and family is service to God no less than formal prayer. Thus, women’s primary role of caring for the family is extremely important. For this reason, women should not work outside the home unless it is absolutely necessary. Moreover, those who do are likely to be exploited both sexually and economically, turned into sex objects and underpaid. He also believes that young children should be cared for within the home, not in crèches. He draws on his experiences in the United States, among other things, to support these points. All of these things characterize a jahili society, according to him. He also argued that Western women sought election to parliament because men had been making laws unfair to women, but under a system of divinely based law the laws will be fair.

Women should dress in a manner that shows only their faces and hands but not be secluded, as in some societies. They also should not mix publicly with men as this may lead to promiscuity and weaken marriages. He defends divorce and polygyny, at least under certain conditions. If these seem to make women insecure it is because the present society is jahili and not sufficiently attuned to Islamic values. Although Muslim men are permitted in traditional fiqh to marry Jewish or Christian women, Qutb is inclined to oppose this today since it may weaken Muslims’ faith and sense of identity, given that current Muslim societies are only nominally Muslim. It is worth noting that Qutb evidently had no objection to women’s involvement in the Islamic movement. Both of his sisters were involved, and one went to prison. He was also a mentor to Zaynab al-Ghazali, a well-known woman Islamic activist in Egypt who had put into her marriage contract that her husband would not interfere with her Islamist activities.

9. Jahiliyya (Dystopia) and Jihad (Revolution)

Any society that is not governed according to the Shari’a is a jahili society. The term jahiliyya literally means ignorance with a connotation of barbarism and has most often been applied to the Arabian society on the eve of Muhammad’s mission. The term and general idea come from Mawdudi, but Qutb makes it more extreme. For Mawdudi, contemporary Muslim societies are part Muslim and part jahili, while for Qutb there is no such mid-term. The contrast is stark: a society is either Islamic or jahili. A jahili society compels or at least pressures its member to serve other humans rather than God, and its leaders presume to create values and laws rather than apply the values and laws of God, effectively claiming divine attributes and making themselves gods beside God. The moral, psychological, and social results are disastrous, though it is not these results these results that define a jahili society. Many states claim to be Islamic and claim that their laws are based on the Shari’a or partly so when in reality the laws are man-made and they are jahili societies. In fact, Qutb claimed that all so-called Islamic countries in his time were jahili, with the result that, as he put it, Islam does not exist. This does not mean that there are no Muslims, but it does mean that they cannot live a complete Muslim life. While Qutb labels societies jahili he is much less inclined to label individuals as unbelievers (kafir), unlike some of his Qutbist successors.

Although the line between Islam and jahiliyya is stark in principle, Qutb does not clearly indicate exactly how and where it is drawn. It seems that societies whose leaders sincerely recognize the Shari’a even if they often fall short in practice will still be Islamic, while others that appear morally superior but whose leaders do not accept the Shari’a, or who interpret it in a Westernizing way, will be jahili, though Qutb will assume that the moral difference is temporary or more apparent than real. This is consistent with Qutb’s views, mentioned above, that ideas are primary and that faith is necessary for works to be valid.

The answer to jahiliyya for Qutb is jihad. This word, which appears frequently in the Qur’an and the later tradition, means “striving” and the full phrase is “striving in the path of God”. It may take non-violent forms, such as the “greater jihad”, the struggle against evil tendencies within one’s self (referred to by the prophet), or other forms of righteous striving. In juristic and political circles, the term has mainly referred to the violent activity of war, with rules for proper behavior in warfare elaborated. Thus, the term is often translated “holy war”. This is the usage that Qutb draws on. In modern times, many Muslims have preferred to emphasize the non-violent forms of jihad and to limit violent jihad to defensive warfare. Qutb considers this defeatist and argues the need for both violence and the initiating of violence at times. Jahiliyya is not merely a condition of society but an aggressive and unrelenting force that can only finally be defeated by violence. Moreover, Muslims have an obligation not only to defend themselves but to fight tyranny wherever it appears and to remove obstacles to the preaching of Islam.  Jihad is part of the Islamic mission to liberate humans from servitude to other humans and realize the rule of God on earth. This is the greatest of all human tasks and one should not apologize for using force when necessary. God knows that evil must be confronted in this way. (Perhaps this attitude is not so different from the actions of Western powers fighting to spread civilization, democracy, and/or human rights.) Qutb relates the “greater jihad” to this by describing it as the inner battle of the warrior to purify himself of personal desires and any other obstacles to his serving God and establishing God’s authority on earth.

In the present situation jihad takes effectively the form of revolution, though Qutb does not use this term. (He may be influenced by Mawdudi’s book, Jihad in Islam, which explicitly calls it “revolutionary struggle”, at least in the English translation.) Individuals or groups of Muslims must come together to organize their lives on the basis of Islam, thus giving birth to a new society and isolating themselves psychologically, though not physically, from the jahili society around them. These groups will for a long time devote themselves to studying and internalizing the basic Muslim creed, there is no god but God. This is what Muhammad did for thirteen years in Mecca, before any attempt to establish an Islamic society was made. Soon enough, the Muslim group will be attacked by the jahiliyya and have to respond in ways that probably include violence until it replaces or at least holds its own against the jahiliyya. In the early stages, violence is to be avoided except for self-defence though later it may be initiated, as mentioned above. All of this according to Qutb is based on the example of the Prophet’s actions in Mecca and Medina and represents a realization of the second part of the creed, “Muhammad is the Messenger of God.”

10. Human History

Qutb explicitly rejects the Enlightenment idea of continuous human progress, at least in the moral area. Rather, in accordance with the traditional Muslim view, history is characterized by a series of prophetic missions, often representing moral high points, followed by decline. The first prophet was the first man, Adam. Although he and his wife disobeyed God and were expelled from Paradise, they repented and were pardoned; their pure fitra was re-established though they now lived in a world of physical and moral struggle. Many of the ensuing prophets preached to peoples who rejected them and were destroyed by God, but some, in particular Ibrahim (Abraham), Musa (Moses), Daud (David), and ‘Isa (Jesus) left continuing communities, though these communities changed the revelations they had received. Each of the messengers taught the same truths about God and the universe, though in increasingly advanced forms as befit their societies’ development, until the human race reached its maturity and Muhammad brought the final revelation and most complete and universal message, confirming but superseding the previous messages. The high point of human moral and social history was the community in Medina under the prophet and his immediate successors. The Muslim community continued for some twelve centuries, often prospering politically and culturally though declining morally.

In the West, a corrupted form of Christianity was imposed on people and this eventually led to a rebellion against religion and to the anti-religious philosophies (“Positivism”, “Dialectical Materialism”, etc.) so prevalent by the twentieth century. The West also began to attack the Muslim world militarily during the medieval crusades and this crusading continued later in the form of Western imperialism. This is a common idea among Islamists today, who regularly refer to Westerners as crusaders. As a result of Western imperialism, Muslim societies began to adopt Western ways and abandoned the Shari’a, often without admitting it, so that by Qutb’s time there was no longer a truly Islamic society anywhere. The whole world is in a state of jahiliyya, and this jahiliyya, because of its material advancement and sophistication, is deeper than previous ones. Although the previous wave of Islam has left some traces, such as the idea of the unity of the human race, that might ease the rebirth of Islam, this will happen only by God’s will working through Islamic activists. A new Islamic society will not be morally better than the “unique Qur’anic generation” except (one may note, though Qutb does not say) that its moral status will be linked to much better technology.

11. Death, Judgment, Martyrdom

Qutb held to the traditional view that death is followed by resurrection on the Last Day, by divine judgment on the basis on one’s action, and a final abode in paradise or hell. This, finally, is the greatest motive for service to God in this life. How God will raise people to life after they are dead is one of the divine secrets that human reason cannot understand, just as it cannot understand the secret of life generally. He seems to take the Qur’anic descriptions of judgment, heaven, and hell, at face value, sometimes analysing the language and literary force of the accounts. These scenes are related to this world since worldly actions lead to them and worldly joy and suffering foreshadow them. They also widen the individual’s perspective beyond the bounds of this life. He also held to the common view that God has fixed the date of each person’s death, a good reason to risk martyrdom in revolutionary action.

The situation of martyrs, those who die in jihad, is distinctive. The Qur’an says, “Do not say of those who are killed in the path of God, ‘They are dead.’ They are alive . . .” (Qur’an 2:154; 3:169). Qutb says that they are alive in the sense that they continue to be an active force directing the community, but that they also may be more literally alive on another level of existence that we cannot conceive of. Toward the end of Milestones, he says that martyrs receive three rewards: contentment and freedom from fear and sorrow, praise from angels and humans and favorable accounting in the final judgment (I have seen no mention of 72 virgins, however). Qutb is considered a martyr by many, probably most, Muslims. It is reported that on learning that he was to be executed he praised God for earning martyrdom. Both Zaynab al-Ghazali and Qutb’s sister, Hamida, claimed to have had visions just after his death assuring them that he is in paradise.

12. Qutb’s Legacy

Qutb’s ideas, strengthened by his status as a martyr, have had considerable influence among Muslims. His close linking of belief in one God with the need for the rule of a divinely derived law, and his insistence on a clear line between Islam and non-Islam, has strengthened Islamism generally. His understanding of jahiliyya has broadened the scope and depth of the struggle. His conceptualization of the movement as one for “liberation” resonates with many people, as does his view that all forms of activity should be service to God. His understanding of jihad and his own martyrdom has strengthened the willingness for both violence and self-sacrifice. One young man, who was moved by his execution to join an Islamist cell, was Ayman al-Zawahiri, who later became a leader in the radical group Tanzim al-Jihad, and still later leader of al-Qaeda. Within the Muslim Brothers organization, Qutb’s legacy has been ambivalent, a threat to their ability to function with some freedom, but not possible to ignore. In 2009, his ideas were at the forefront of a debate between those who wanted less accommodation to secular society and those who wanted more.

Those who particularly claim to follow his legacy, mostly outside the Brothers, have commonly been called Qutbists or Qutbians. They include the so-called Takfir wa Hijra (the label refers to their condemnation of society and separation from it), Jama‘a Islamiyya (Islamic Group), and Tanzim al-Jihad (Jihad Organization) in Egypt, and al-Qaeda. (It is not clear where “Islamic State” or ISIS stands on Qutb.) They tend to simplify Qutb’s ideas or take them to extremes that he might not have accepted. This article considers their interpretations of some of Qutb’s ideas.

Qutb’s idea of jahiliyya is a fairly easy idea to misunderstand. It has often been interpreted as takfir, the declaration of individuals as unbelievers or apostates, usually applied to enemies or government representatives. Jama‘a Islamiyya and Tanzim al-Jihad spoke more of kufr than jahiliyya. They considered Egyptian society as a whole to be Muslims and only the leaders of society to be kafirs. On this assumption, some of the Tanzim al-Jihad members assassinated the Egyptian president in 1981, hoping by this to spark a revolt and overthrow the government, something that did not happen. On Qutb’s view of jahiliyya, this effort would have been hopelessly misguided and premature.

The leader of the so-called Takfir wa Hijra group, who had reportedly studied Qutb’s writings in prison, accepted the claim that the whole Egyptian society was jahili, but with a more extreme interpretation than Qutb’s. He claimed that any of its members who left his group were abandoning Islam and that the standard Friday prayers were illicit in a jahili society. He also tried to isolate the group physically from society more than Qutb called for. Outsiders have interpreted its position as takfir and apparently insiders have too, since they came to accept the label.

The distinction between the “near enemy” (their own rulers) and the “far enemy” (for example, Israel and the United States) made by the Jama‘a Islamiyya and Tanzim al-Jihad, and their choice to attack the “near enemies” first, does owe something to Qutb’s idea of jahiliyya, since this idea removes Egyptian society from the category of Islamic. Al-Qaeda’s view of the world-wide struggle also seems to fit Qutb’s idea, though al-Qaeda changed the priority to the “far enemy”. Qutb might have accepted this as a practical example of flexibility after the attack on the “near enemy” failed.

Qutb called for a long period of preparation before engaging in jihad, but Tanzim al-Jihad and Jama‘a Islamiyya advocated immediate action. While al-Qaeda trains its recruits militarily and indoctrinates them, it does not appear to provide the sort of long term spiritual preparation Qutb had in mind. The leader of Takfir wa-Hijra appreciated the need for a long period of preparation, which is one of the reasons he sought to isolate the group. He hoped to build a model community that would eventually be strong enough to bring down the government. Unfortunately for them, police arrested some of the group and the group in return kidnapped a former government minister, whom they killed when the government refused to release the prisoners. The government then cracked down and succeed in capturing and executing the group’s leaders.

While Qutb defended the need for, and almost the inevitability of, violence in certain circumstances, this was to counter those who downplayed it, often for apologetic reasons. It is doubtful (though impossible to know) whether Qutb would have approved of the terrorist activities of the Qutbist groups. For the most part, they do not make sense if jahiliyya is as deeply rooted as Qutb claims and, in any case, Qutb accepted the traditional fiqh view that non-combatants should not be targeted. Also, revenge has often been a motive for violent actions, but Qutb appears to have rejected that motive. Perhaps the most important contribution of Qutb’s theories is that they remove the legitimacy from the existing authorities for his followers and make the followers look ultimately like “paper tigers.”

Qutb has been criticized by traditional scholars on particular points of fiqh and history and generally for making judgments about religion without the sort of training they consider necessary. Also, Sunnis have generally taken the position that for this worldly purpose a person is to be treated as Muslim if he is outwardly one, whatever his behaviour, and likewise, the government is to be treated as Muslim as long as the rulers are outwardly so. Many see Qutb’s views about jahiliyya and jihad as violations of this.

Many who are not radical Islamists still appreciate many of Qutb’s ideas and ultimate goals. Often it is argued that his extreme views were the result of his imprisonment and torture and that, had he lived longer, his ideas and activities would have developed in a more moderate direction. They also like to call attention to his earlier works, which contain less extreme views than those discussed in this article.

13. Final Remarks: Aesthetics, Harmony, and
Essentialism

There is a strongly aesthetic dimension to Qutb’s writing, and one could say that its master theme is harmony. God’s universe is a perfectly harmonious system into which everything fits beautifully and practically. This universe is friendly to life, and human life can be in full harmony with it and blessed. Disharmony comes when humans act in ways that contravene the ways God has set out for them. The beauty of God’s harmony makes the disharmony introduced by humans all the worse, like a beautiful painting disfigured. Hence the horror of jahiliyya and seriousness of the effort to end it.

Connected with this is the resolutely essentialist nature of Qutb’s thinking. Everything is essentialized, including nature, humanity, gender, Islam, the West, jahiliyya, Shari’a, belief, and unbelief. Perhaps God is a partial exception, since His essence is unknowable and His freedom to produce miracles may break the regularities on which human essentialism depends. A major aspect of this essentialism is the dichotomously “Manichean” way in which he treats good and evil. As mentioned above, there is no mid-term between guidance and error, faith and unbelief, tawhid and shirk, or between Islam and jahiliyya or Shari’a and human legislation, Although the interpretation of the Shari’a may require human effort (ijtihad), and its application may vary with circumstances, the difference in principle between divinely sourced and humanly sourced is stark.

This combination of aesthetics, essentialism, and “Manicheism,” while very much open to criticism from scientists and philosophers, is undoubtedly one of the keys to the power of his ideology. The strong contrast between good and evil, the sense that evil is currently in charge in the world though good is in ultimate control, and the conviction that something can be done must and must be done at any cost to change this situation has characterized and driven many a revolutionary ideology.

14. References and Further Reading

a. Primary Sources

  • Qutb, Sayyid, In the Shade of the Qur’an (Fi zilal al-Qur’an), 18 vols, Translated & Edited by: M.A. Salahi & A.A Shamis, Leicester, UK: The Islamic Foundation, 1999-2005.
    • Qutb’s massive and popular commentary on the Qur’an. Much of it was written before his most radical period but the first 13 (of 30) parts were revised during that period.
  • Qutb, Sayyid, The Islamic Concept and its Characteristics (Khasa’is al-tasawwur al-islami wa-muqawwimatuhu), trans. Mohammed M. Siddiqui. Indianapolis: American Trust Publications, 1991.
    • The most “philosophical” of Qutb’s late works, used considerably for this article. It is the first of two volumes on the subject; the second has not been translated into English.
  • Qutb, Sayyid, Basic Principles of the Islamic Worldview, trans. Rami David. North Haledon, N.J.: Islamic Publications International IPI, 2006.
    • A later translation of the same work as above.
  • Qutb, Sayyid, Islam: The Religion of the Future (Al-mustaqbal li-hadha al-din), translator not given. Beirut and Damascus: The Holy Koran Publishing House, n.d.
    • A shorter book stating main point and emphasizing the need of humanity for Islam. Comments on quotes from Alexis Carrel and John Foster Dulles.
  • Qutb, Sayyid, Milestones (Ma‘alim fi al-tariq), trans. S. Badrul Hasan [?]. Kuwait: International Islamic Federation of Student Organizations, 1978. Also, Lahore: Kazi Publications, nd. The title is sometimes translated “Signposts”.
    • Qutb’s best known radical work, a handbook for Islamic revolution.
  • Qutb, Sayyid, Milestones, “revised translation”, translator not given. Indianapolis: American Trust Publications, 1990.
    • Claims to provide “a fresh editing and rereading” but I cannot confirm that does so from what I have read of it.
  • Qutb, Sayyid, This Religion of Islam (Hadha al-din), translator not given. Kuwait: International Islamic Federation of Student Organizations, 1972.
    • Summarizes the characteristics of the Islamic manhaj and its positive effect on the world in the past. Relatively optimistic.
  • [Qutb, Sayyid] Sayyid Qutb and Islamic Activism: A translation and critical analysis of Social Justice in Islam (Al-‘adala al-ijtima‘iyya fi al-islam). By William Shepard, Leiden: Brill, 1996.
    • Last edition of Qutb’s major work on Islamic social and political teachings. Comparisons are made with earlier editions.
  • The Sayyid Qutb Reader, ed. Albert J. Bergesen. Routledge, 2007.
    • Includes an introduction to Qutb’s career and ideas, and selections mainly from the radical parts of In the Shade of the Qur’an , along with some from Milestones, Social Justice in Islam, and A Child from the Village (autobiographical account of his childhood village, written before he became Islamist).

b. Secondary Sources

  • Abu-Rabi‘, Ibrahim, Intellectual Origins of Islamic Resurgence in the Modern Arab World. Albany: SUNY Press, 1996.
    • Chapter 3 deals with the Muslim Brothers and chapters 4 to 6 cover Qutb’s pre-Islamist, early Islamist and later Islamist thinking.
  • Calvert, John, Sayyid Qutb and the Origins of Radical Islamism. New York: Columbia University Press, 2010.
    • Excellent study of Qutb’s activities and writings during both is secularist and Islamist period; with helpful information on the social and political background and a survey of later “Qutbists”.
  • Carré, Olivier, Mysticism and Politics: A Critical Reading of Fî Zilal al-Qur’an by Sayyid Qutb (1906-1966), Leiden, Boston: Brill, 2003.
    • An in-depth study of Qutb’s Qur’an commentary. Includes selections from the text.
  • Haddad, Yvonne Y., ‘Sayyid Qutb: Ideologue of Islamic Revival’, ch. 4 in Voices of Resurgent Islam, ed. J. Esposito. New York and Oxford: Oxford U. P., 1983.
    • Includes a discussion of Qutb’s main concepts.
  • Kepel, Gilles, Muslim Extremism in Egypt: The Prophet and the Pharoah. Berkeley & Los Angeles, 1986 and Berkeley: University of California Press, 2003.
    • Chapters 1 and 2 discuss Qutb’s last years and Milestones. The rest of the book deals with later radical groups in Egypt.
  • Musallam, Adnan, From Secularism to Jihad: Sayyid Qutb and the Foundations of Radical Islamism. Praeger, 2005.
    • Thoughtful account of the whole of Qutb’s life, career and writings, especially good on the earlier years. Also deals with Qutb’s influence on later radicals.
  • Shepard, William, “Sayyid Qutb’s doctrine of Jahiliyya “, International Journal of Middle East Studies 35/4 (Nov. 2003): 521-545.
    • Discusses the background to and components of this doctrine.
  • Shepard, W., “Islam as a ‘System’ in the Later Writings of Sayyid Qutb”, Middle Eastern Studies 25/1 (January 1989): 31-50.
    • Discusses key terms such as tasawwur and manhaj.
  • Toth, James. Sayyid Qutb: The Life and Legacy of a Radical Islamic Intellectual. Oxford: Oxford UP, 2013.
    • A good study of Qutb’s life and ideas with a lot of interesting information.

Author Information

William E. Shepard
Email: w.shepard@snap.net.nz
University of Canterbury
New Zealand

Set Theory

Set Theory is a branch of mathematics that investigates sets and their properties. The basic concepts of set theory are fairly easy to understand and appear to be self-evident. However, despite its apparent simplicity, set theory turns out to be a very sophisticated subject. In particular, mathematicians have shown that virtually all mathematical concepts and results can be formalized within the theory of sets. This is considered to be one of the greatest achievements of modern mathematics. Given this achievement, one can claim that set theory provides a foundation for mathematics.

The foundational role of set theory and its mathematical development have raised many philosophical questions that have been debated since its inception in the late nineteenth century. For example, here are three: Does infinity exist, and if so, are there different kinds of infinity? Is there a mathematical universe? Are all mathematical problems solvable?

Before pursuing the philosophical issues concerning set theory, one should be familiar with a standard mathematical development of set theory. This article presents such a development.

In the late nineteenth century, the mathematician Georg Cantor (1845–1918) created and developed a mathematical theory of sets. This theory emerged from his proof of an important theorem in real analysis. In this proof, Cantor introduced a process for forming sets of real numbers that involved an infinite iteration of the limit operation. Cantor’s novel proof led him to a deeper investigation of sets of real numbers and to his theory of abstract sets. Cantor’s creation now pervades all of mathematics and offers a versatile tool for exploring concepts that were once considered to be ineffable, such as infinity and infinite sets.

Sections 1 and 2 below describe the “naïve” principles of set theory that were used and developed by Cantor. Then, Section 3 describes a more sophisticated (axiomatic) approach to set theory that arose from the discovery of Russell’s paradox. After identifying the Zermelo-Frankel axioms of set theory, Section 4 discusses Cantor’s well-ordering principle and examines how Cantor used the well-ordering principle to develop the ordinal and cardinal numbers. Section 5 considers controversies concerning the well-ordering principle and its equivalent, the axiom of choice. This is followed by introducing the cumulative hierarchy of sets, Kurt Gödel’s universe of constructible sets, and Paul Cohen’s method of forcing in Sections 6, 7, and 8, respectively. The latter two topics, explored in Sections 7 and 8, can be used to show that certain questions are unresolvable when assuming the Zermelo-Frankel axioms (with or without the axiom of choice). The next two sections address further developments in set theory that are intended to settle these and other unresolved questions; namely, Section 9 discusses large cardinal axioms, and Section 10 investigates the axiom of determinacy.

Table of Contents

  1. On the Origins
  2. Cantor’s Development of Set Theory
    1. Russell’s Paradox
  3. The Zermelo-Fraenkel Axioms
    1. The Axioms
    2. Classes
  4. Cantor’s Well-Ordering Principle
    1. Ordinal Numbers
    2. Cardinal Numbers
  5. The Axiom of Choice
    1. On Zermelo’s Proof of the Well-Ordering Principle
    2. Banach-Tarski Paradox
  6. The Cumulative Hierarchy
  7. Gödel’s Constructible Universe
  8. Cohen’s Forcing Technique
  9. Large Cardinal Axioms
  10. The Axiom of Determinacy
  11. Concluding Remarks
  12. References and Further Reading
    1. Primary Sources
    2. Secondary Sources
    3. Internet Sources

1. On the Origins

Let us first discuss a few basic concepts of set theory. A set is a well-defined collection of objects. The items in such a collection are called the elements or members of the set. The symbol “\in” is used to indicate membership in a set. Thus, if A is a set, we write x \in A to say that “x is an element of A,” or “x is in A,” or “x is a member of A.” We also write x \notin A to say that x is not in A. In mathematics, a set is usually a collection of mathematical objects, for example, numbers, functions, or other sets.

Sometimes a set is identified by enclosing a list of its elements by curly brackets; for example, a set of natural numbers A can be identified by the notation

A = \{1,2,3,4,5,6,7,8,9\}. 

More typically, one forms a set by enclosing a particular expression within curly brackets, where the expression identifies the elements of the set. To illustrate this method of identifying a set, we can form a set B of even natural numbers, using the above set A, as follows:

B = \{n \in A : n \text{ is even}\}. 

which can be read as “the set of n \in A such that n is even.” Of course,

\{n \in A : n is even\} = \{2,4,6,8\}. 

It is difficult to identify the genesis of the set concept. Yet, the idea of a finite collection of objects has existed for as long as the concept of counting. Indeed, mathematicians have been investigating finite sets and methods for measuring the size of finite sets since the beginning of mathematics. For example, the above two sets

A=\{1,2,3,4,5,6,7,8,9\}

B=\{2,4,6,8\} 

are finite sets. As every element in B is an element in A, the set B is said to be a subset of A, denoted by B \subseteq A. Since there are elements in A that are not in B, we say that B is a proper subset of A. Moreover, the number of elements in B is strictly smaller than the number of elements in A. Thus, one can say, “the whole A is greater in size than its proper part B.”

Infinite sets lead to an apparent contradiction. Consider the infinite sets:

C=\{0,1,2,3,\ldots \}

D=\{1,3,5,7, \ldots \}. 

We view the sets C and D as existing entities that both contain infinitely many elements. Thus, C and D are “completed infinities.” Observe that every element in D is in C, and that D is a proper subset of C. However, if, as many mathematicians once believed, “infinity cannot be greater than infinity,” then the whole C is not greater in size than its proper part D. This counterintuitive result was viewed by many early prominent mathematicians as being contradictory, as it appeared to conflict with the well-understood behavior of finite sets. These mathematicians thus concluded that the concept of a “completed infinity” should not be allowed in mathematics.

For this reason, before Cantor, a majority of mathematicians considered infinite collections to be mathematically illicit objects. Cantor was the first mathematician to view infinite sets as being legitimate mathematical objects that can coexist with finite sets. Clearly, the size of a finite set can be measured simply by counting the number of elements in the set. Cantor was the first to investigate the following question:

Can the concept of “size” be extended to infinite sets? 

Cantor addressed this question in the affirmative by using the concept of a function to measure and compare the sizes of infinite sets. Functions are widely used in science and mathematics. For sets A and B, we say that f is a function from A to B, denoted by f: A \rightarrow B, if and only if f is a relation (operation) that assigns to each element x in A, a single element f(x) in B. There are three important properties that a function might possess:

  • f: A \rightarrow B is an injection if and only if for each y in B there is at most one x in A such that f(x)=y.
  • f: A \rightarrow B is a surjection if and only if for each y in B there is at least one x in A such that f(x)=y.
  • f: A \rightarrow B is a bijection if and only if for each y in B there is exactly one x in A such that f(x)=y.

Observe that f: A \rightarrow B is an injection if and only if distinct elements in A are assigned to distinct elements in B; that is, for all x and a in A, if x \neq a, then f(x) \neq f(a). Also note that f: A \rightarrow B is a bijection if and only if f: A\rightarrow B is an injection and a surjection.

Cantor observed that two sets A and B have the same size if and only if there is a one-to-one correspondence between A and B, that is, there is a way of evenly matching the elements in A with the elements in B. In other words, Cantor noted that the sets A and B have the same size if and only if there is a bijection f: A \rightarrow B. In this case, Cantor said that A and B have the same cardinality. For an illustration, let \mathbb{N} = \{0, 1, 2, 3, 4, \ldots \} be the set of natural numbers and let E = \{0,2,4,6,8,\ldots\} be the set of even natural numbers. Now let f: \mathbb{N} \rightarrow E be defined by f(n)=2n. One can verify that f: \mathbb{N} \rightarrow E is a bijection and, thus, we obtain the following one-to-one correspondence between the set \mathbb{N} of natural numbers and the set E of even natural numbers:

Hence, each natural number n corresponds to the even number 2n, and each even natural number 2i is thereby matched with i \in \mathbb{N}. The bijection f: \mathbb{N} \rightarrow E specifies a one-to-one match-up between the elements in \mathbb{N} and the elements in E. Cantor concluded that the sets N and E have the same cardinality.

Cantor also defined what it means for a set C to be smaller, in size, than a set D. Specifically, he said that C has smaller cardinality (smaller size) than D if and only if there is an injection f: C \rightarrow D but there is no bijection g: C \rightarrow D. Cantor then proved that there is no one-to-one correspondence between the set of real numbers and the set of natural numbers. Cantor’s proof showed that the set of real numbers has larger cardinality than the set of natural numbers (Cantor 1874). This stunning result is the basis upon which set theory became a branch of mathematics.

The natural numbers 0, 1, 2, 3, \ldots are the whole numbers that are typically used for counting. The real numbers are those numbers that appear on the number line. For example, the natural number 2, the integer -3, the fraction 6/5, and all of the other rational numbers are real numbers. The irrational numbers, such as \sqrt{2} and \pi, are also real numbers. Again, let \mathbb{N} = \{0, 1, 2, 3, \ldots \} be the set of natural numbers, and let \mathbb{R} be the set of real numbers. If a set is either finite or has the same cardinality as the set of natural numbers, then Cantor said that it is countable. Since the set of real numbers \mathbb{R} is larger, in size, than the set of natural numbers \mathbb{N}, Cantor referred to the set \mathbb{R} as being uncountable.

After proving that the set of real numbers is uncountable, Cantor was able to prove that there is an increasing sequence of larger and larger infinite sets. In other words, Cantor showed that there are “infinitely many different infinites,” a result with clear philosophical and mathematical significance.

After his introduction of uncountable sets, in 1878, Cantor announced his Continuum Hypothesis (CH), which states that every infinite set of real numbers is either the same size as the set of natural numbers or the same size as the entire set of real numbers. There is no intermediate size. Cantor struggled, without success, for most of his career to resolve the Continuum Hypothesis. The problem persisted and became one of the most important unsolved problems of the twentieth century. After Cantor’s death, most set theorists came to believe that the Continuum Hypothesis is unresolvable.

Cantor’s profound results on the theory of infinite sets were counterintuitive to many of his contemporaries. Moreover, Cantor’s set theory violated the prevailing dogma that the notion of a “completed infinity” should not be allowed in mathematics. Thus, the outcry of opposition persisted. Influential mathematicians continued to argue that Cantor’s work was subversive to the true nature of mathematics. These mathematicians believed that infinite sets were dangerous fictional creations of Cantor’s imagination and that Cantor’s fictions needed to be eradicated from mathematics (Dauben 1979, page 1) (Dunham 1990, pp. 278-280). Nevertheless, Cantor’s theory of sets soon became a crucial tool used in the discovery and establishment of new mathematical results, for example, in measure theory and the theory of functions (Kanamori 2012). Mathematicians slowly began to see the utility of set theory to traditional mathematics. Accordingly, attitudes started to change and Cantor’s ideas began to gain acceptance in the mathematical community (Dauben 1979, pp. 247-248). The significance of Cantor’s mathematical research was eventually recognized. David Hilbert, a prominent twentieth century mathematician, described Cantor’s work as being

the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity. (Hilbert 1923)

Ultimately, Cantor’s theory of abstract sets would dramatically change the course of mathematics.

2. Cantor’s Development of Set Theory

In his development of set theory, Cantor identified a single fundamental principle, called the Comprehension Principle, under which one can form a set. Cantor’s principle states that, given any specific property \varphi(x) concerning a variable x, the collection \{x : \varphi(x)\} is a set, where \{x : \varphi(x)\} is the set of all objects x that satisfy the property \varphi(x). For example, let \psi(x) be the property that “x is an odd natural number.” The Comprehension Principle implies that

S = \{ x : \psi (x)\} = \{1,3,5,7,\ldots \} 

is a set. Employing the Comprehension Principle, one can form the intersection of two sets A and B using the property “x \in A and x \in B”; thus, the intersection of A and B is the set

A \cap B = \{x : x \in A and x \in B\}. 

One can also form the set

A \cup B = \{x : x \in A or x \in B\} 

which is called the union of A and B. Recall that one writes X \subseteq A to mean that X is a subset of A, that is, every element of X is also an element of A. Using the Comprehension Principle, one can form the power set of A, which is the set whose elements are all of the subsets of A, that is,

\wp(A) = \{ X : X \subseteq A\}. 

Thus, if A is a set and X \subseteq A, then X \in \wp(A). So, if A = \{1,2,3\} and B = \{3,4,5\}, then

A \cap B = \{3\},
A \cup B = \{1,2,3,4,5\}, and

\wp(A) = \{\varnothing,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}, 

where \varnothing denotes the empty set, that is, the set that contains no elements. The Comprehension Principle was an essential tool that allowed Cantor to form many important sets. Cantor’s approach to set theory is often referred to as naïve set theory.

Cantor’s set theory soon became a very powerful tool in mathematics. In the early 1900s, the mathematicians Émile Borel, René-Loius Baire, and Henri Lebesgue used Cantor’s set theoretic concepts to develop modern measure theory and function theory (Kanamori 2012). This work clearly demonstrated the great mathematical utility of set theory.

a. Russell’s Paradox

The philosopher and mathematician Bertrand Russell was interested in Cantor’s work and, in particular, Cantor’s proof of the following theorem, which implies that the cardinality of the power set of a set is larger than the cardinality of the set. First, recall that a function g: A \rightarrow B is a surjection (or is onto B) if for all y \in B, there is an x \in A such that g(x)=y.

Cantor’s Theorem. Let A be a set. Then there is no surjection f: A \rightarrow \wp(A). 

Proof. Suppose, for the sake of obtaining a contradiction, that there exists a surjection f: A \rightarrow \wp(A). Observe that, for all z \in A, f(z) \subseteq A. By the Comprehension Principle, let X be the set

X = \{x : x \in A and x \notin f(x)\}. 

Clearly, X \subseteq A. Thus, X \in \wp (A). As f is onto \wp(A), there is an a \in A such that f(a) = X. There are two cases to consider: either a \in X or a \notin X. If a \in X, then the definition of X implies that a \notin f(a). Since f(a) = X, we have that a \notin X, which is a contradiction. On the other hand, if a \notin X, then the definition of X implies that a \in f(a). Since f(a) = X, we see that a \in X, a contradiction. Thus, there is no surjection f: A \rightarrow \wp(A). This completes the proof.

In 1901, after reading Cantor’s proof of the above theorem, that was published in 1891, Bertrand Russell discovered a devastating contradiction that follows from the Comprehension Principle. This contradiction is known as Russell’s Paradox. Consider the property “x \notin x”, where x represents an arbitrary set. By the Comprehension Principle, we conclude that

A = \{x : x \notin x\} 

is a set. The set A consists of all the sets x that satisfy x \notin x. Clearly, either A \in A or A \notin A. Suppose A \in A. Then, the definition of the set A implies that A must satisfy the property A \notin A, which contradicts our supposition. Suppose A \notin A. Since A satisfies A \notin A, we infer, from the definition of A, that A \in A, which is also a contradiction.

There were similar paradoxes discovered by others, including Cantor (Dauben 1979), but Russell’s paradox is the easiest to understand. These paradoxes appeared to threaten Cantor’s fundamental principle that he used to develop set theory. Nevertheless, Cantor did not believe that these paradoxes actually refuted his development of set theory. He knew that the construction of certain collections can lead to a contradiction. Cantor referred to these collections as “inconsistent multiplicities.” Today, such collections are called proper classes, and the paradoxes can be used to prove that they are not sets.

3. The Zermelo-Fraenkel Axioms

Over time, it became clear that, to resolve the paradoxes in Cantor’s set theory, the Comprehension Principle needed to be modified. Thus, the following question needed to be addressed:

How can one correctly construct a set? 

Ernst Zermelo (1871–1953) observed that to eliminate the paradoxes, the Comprehension Principle could be restricted as follows: Given any set A and any property \psi (x), one can form the set \{x \in A : \psi (x)\}, that is, the collection of all elements x \in A that satisfy \psi (x), is a set. Zermelo’s approach differs from Cantor’s method of forming a set. Cantor declared that for every property one can form a set of all the objects that satisfy the property. Zermelo adopted a different approach: To form a set, one must use a property together with a set.

Zermelo also realized that in order to more fully develop Cantor’s set theory, one would need additional methods for forming sets. Moreover, these additional methods would need to avoid the paradoxes. In 1908, Zermelo published an axiomatic system for set theory that, to the best of our knowledge, avoids the difficulties faced by Cantor’s development of set theory. In 1930, after receiving some proposed revisions from Abraham Fraenkel, Zermelo presented his final axiomatization of set theory, now known as the Zermelo-Fraenkel axioms and denoted by ZF. These axioms have become the accepted formulation of Cantor’s ideas about the nature of sets.

a. The Axioms

As noted by Zermelo, to avoid paradoxes, the Comprehension Principle can be replaced with the principle: Given a set A and a property \varphi (x) with a variable x, the collection \{x \in A : \varphi (x)\} is a set. However, this raises a new question: What is a property? The most favored way to address this question is to express the axioms of set theory in the formal language of first-order logic, and then declare that its formulas designate properties. This language involves variables and the logical connectives \wedge (and), \vee (or), \neg (not), → (if … then …), and ↔ (if and only if), together with the quantifier symbols \forall (for all) and \exists (there exists). In addition, this language uses the relation symbols = and \in (as well as \neq and \notin). In this language, the variables and quantifiers range over sets and only sets. A formula constructed in this formal language is referred to as a formula in the language of set theory. Such formulas are used to give meaning to the notion of “property.”

We now illustrate the expressive power of this set theoretic language. The formula \exists x(x \in A) asserts that “the set A is nonempty,” and \forall x(x \notin A) states that “A has no elements.” Moreover \neg \exists x \forall y(y \in x) states that “it is not the case that there is a set that contains all sets as elements.” In addition, one can translate English statements, which concern sets, into the language of set theory. For example, the English sentence “the set A contains at least two elements” can be translated into the language of set theory by \exists x \exists y((x \in A \wedge y \in A) \wedge x \neq y).

There is another quantifier, called the uniqueness quantifier, that is sometimes used. This quantifier is written as \exists ! x \varphi (x) and it means that “there exists a unique x satisfying \varphi (x).” This is in contrast with \exists x \varphi(x), which simply states that “at least one x satisfies \varphi (x).” The uniqueness quantifier is used as a convenience, as the assertion \exists !x \varphi (x) can be expressed in terms of the other quantifiers \exists and \forall; namely, it is equivalent to the formula

\exists x \varphi (x) \wedge \forall x \forall y ((\varphi (x) \wedge \varphi (y)) \rightarrow x=y). 

The above formula is equivalent to \exists!x \varphi (x) because it asserts that “there is an x such that \varphi(x) holds, and any sets x and y that satisfy \varphi (x) and \varphi(y) must be the same set.”

The Zermelo-Fraenkel axioms are listed below. Each axiom is first stated in English and then written in logical form. After each logical form, there is a discussion of the axiom and some of its consequences. When reading these axioms, keep in mind that, in Zermelo-Fraenkel set theory, everything is a set, including the elements of a set. Also, the notation \vartheta (x, \ldots, z) means that x, \ldots, z are free variables in the formula \vartheta and that \vartheta is allowed to contain parameters (free variables other than x, \ldots, z) that represent arbitrary sets.

a)

Extensionality Axiom. Two sets are equal if and only if they have the same elements. 

\forall A \forall B ( A = B \leftrightarrow \forall x ( x \in A \leftrightarrow x \in B)). 

The extensionality axiom is essentially a “definition” that states that two sets are equal if and only if they have exactly the same elements.

b)

Empty Set Axiom. There is a set with no elements. 

\exists A \forall x ( x \notin A). 

The empty set axiom states that there is a set which has no elements. Since the extensionality axiom implies that this set is unique, we let \varnothing denote the empty set.

c)

Subset Axiom. Let \varphi(x) be a formula. For every set A, there is a set S that consists of all the elements x \in A such that \varphi(x) holds. 

\forall A \exists S \forall x ( x \in S \leftrightarrow ( x \in A \wedge \varphi (x))). 

(The variable S is assumed not to appear in the formula \varphi (x).) The subset axiom, also known as the axiom of separation, asserts that any definable sub-collection of a set is itself a set, that is, for any formula \varphi(x) and any set A, the collection \{x \in A : \varphi(x)\} is a set. Clearly, the subset axiom is a limited form of the Comprehension Principle. Yet, it does not lead to the contradictions that result from the Comprehension Principle. The subset axiom is, in fact, an axiom schema since it yields infinitely many axioms-one for each formula \varphi.

d)

Pairing Axiom. For every u and v, there is a set that consists of just u and v. 

\forall u \forall v \exists P \forall x ( x \in P \leftrightarrow ( x =u \vee x = v)). 

The pairing axiom states that, for any two sets u and v, the set \{u, v\} exists. Thus, by the extensionality axiom, the set \{u, u\} = \{u\} exists.

e)

Union Axiom. For every set F, there exists a set U that consists of all the elements that belong to at least one set in F. 

\forall F \exists U \forall x ( x \in U \leftrightarrow \exists C (C \in F \wedge x \in C)). 

The union axiom states that, for any set F, there is a set U whose elements are precisely those elements that belong to an element of F, that is, x \in U if and only if x \in A for some A \in F. The extensionality axiom implies that the set U is unique; it is often denoted by \bigcup F. For example, consider the set \{A,B\}. Then

\bigcup \{A,B\} = \{x : x belongs to a member of \{A,B\}\} = \{x : x \in A or x \in B\} = A \cup B. 

For another example, let F = \{ \{a,b,c\},\{e,f\},\{e,c,d\} \}. Then \bigcup F = \{a,b,c,d,e,f\}.

f)

Power Set Axiom. For every set A, there exists a set P that consists of all the sets that are subsets of A. 

\forall A \exists P \forall x ( x \in P \leftrightarrow \forall y( y \in x \rightarrow y \in A)). 

The power set axiom states that, for any set A, there is a set, which we denote by \wp(A), such that for any set B, B \in \wp(A) if and only if B \subseteq A.

g)

Infinity Axiom. There is a set I that contains the empty set as an element and whenever x \in I, then x \cup \{x\} \in I. 

\exists I ( \varnothing \in I \wedge \forall x (x \in I \rightarrow x \cup \{ x \} \in I)). 

The infinity axiom ensures the existence of at least one infinite set. For any set x, the successor of x is defined to be the set x^{+} = x \cup \{x\}. Thus, the axiom of infinity asserts that there is a set I such that \varnothing \in I and if x \in I, then x^{+} \in I. Note that \varnothing^{+} = \{\varnothing\}, and that \{\varnothing\}^{+} = \{\varnothing,\{\varnothing\}\}. It follows that the set I contains each of the sets

\varnothing; \{\varnothing\}; \{\varnothing, \{\varnothing \}\}; \{\varnothing, \{\varnothing, \{\varnothing \}\}\}; \ldots. 

One can show that any two of the sets in the above list (separated by a semi-colon) are distinct. Hence, the set I contains an infinite number of elements; in other words, I is an infinite set. So, the infinity axiom simply states that infinite sets exist and are legitimate mathematical objects. The infinity axiom is a key tool that is used to develop the set of natural numbers \mathbb{N} and to prove that \mathbb{N} is well-ordered, that is, every nonempty set of natural numbers has a least element.

h)

Replacement Axiom. Let \psi (x, y) be a formula. For every set A, if for each x \in A there is a unique y such that \psi (x, y), then there is a set S that consists of all of the elements y such that \psi (x, y) for some x \in A. (Below, \exists! is the uniqueness quantifier.) 

\forall A (\forall x ( x \in A \rightarrow \exists ! y \psi (x,y)) \rightarrow \exists S \forall y( y \in S \leftrightarrow \exists x (x \in A \wedge \psi(x, y)))). 

(The variable S is assumed not to appear in the formula \psi (x, y).) The replacement axiom states that for every set A, if for each x \in A there is a unique y such that \psi(x,y), then the collection \{y : \exists x (x \in A \wedge \psi(x,y))\} is a set; that is, a “functional image of a set, is a set.” The replacement axiom is a special form of Cantor’s Comprehension Principle that plays a critical role in modern set theory. However, the replacement axiom does not lead to the contradictions that follow from the Comprehension Principle. Like the subset axiom, the replacement axiom is an axiom schema. Accordingly, there are infinitely many Zermelo-Fraenkel axioms.

i)

Regularity Axiom. Each nonempty set A contains an element that is disjoint from A. 

\forall A ( A \neq \varnothing \rightarrow \exists x ( x \in A \wedge \neg \exists y ( y \in x \wedge y \in A))). 

The regularity axiom, also known as the axiom of foundation, states that, for any nonempty set A, there is a set x \in A such that A \cap x = \varnothing. The regularity axiom rules out the possibility of a set belonging to itself. In standard mathematics, there are no sets that are members of themselves. For example, the set of natural numbers is not a natural number. The regularity axiom eliminates collections that are not relevant for standard mathematics. The regularity and pairing axioms imply that if a \in b, then b \notin a. To see this, suppose that a \in b. Then it follows, from regularity, that a \cap \{a,b\} = \varnothing. So b \notin a.

The Zermelo-Fraenkel axioms are now the most widely accepted answer to the question: How can one correctly construct a set? Of course, these axioms are more restrictive than Cantor’s Comprehension Principle; however, no one, in over 100 years, has been able to derive a contradiction from these axioms. Moreover, all of the classic results (excluding the paradoxes) that were derived using Cantor’s naïve set theory can be derived from the Zermelo-Fraenkel axioms.

It is a remarkable fact that essentially all mathematical objects can be defined as sets within Zermelo-Fraenkel set theory. For example, functions, relations, the natural numbers, and the real numbers can be defined within Zermelo-Fraenkel set theory. Hence, effectively all theorems of mathematics can be considered as statements about sets and proven from the Zermelo-Fraenkel axioms.

b. Classes

The argument used in Russell’s Paradox can be applied to prove, in ZF, that there is no set that contains all sets (as elements). As every set is equal to itself, the collection \{x : x = x\} contains every set, but this collection is not a set. Thus, given a formula \varphi(x), one cannot necessarily conclude that the collection \{x : \varphi(x)\} is a set. However, in set theory, it is convenient to be able to discuss such collections. They cannot be called sets. Instead, a collection of the form \{x : \varphi(x)\} is called a class. The collection \{x : x = x\} is a class that is not a set; for this reason, it is called a proper class.

When can one prove that a class is a set? Let us say that a class \{x : \varphi(x)\} is bounded if and only if there is a set A such that for all x, if \varphi(x), then x \in A. Using the subset axiom, one can prove that a bounded class is a set. It follows that the class \{x : x = x\} is not bounded.

In the Zermelo-Fraenkel axioms, there is no explicit mention of classes. However, there are alternative axiomatizations of set theory that extend ZF by including classes as objects in the language, that is, these axiom systems give classes a formal state of existence. The most common such axiomatic treatment of classes is denoted by NBG (von Neumann–Bernays–Gödel). The NBG system uses a formal language that has two different types of variables: capital letters denote classes and lowercase letters denote sets. In addition, classes can contain only sets as elements. So, a class that is not a set cannot belong to a class. Thus, a class X is a set if and only if \exists Y (X \in Y). In the NBG system, sets satisfy all of the ZF axioms, and the intersection of a class with a set is a set, that is, X \cap y is a set. The NBG system also has the class comprehension axiom:

\exists X \forall y (y \in X \leftrightarrow \varphi (y)) 

where the formula \varphi(y) can contain set parameters and/or class parameters (with other restrictions). Thus, the class comprehension axiom asserts that \{x : \varphi(x)\} is a class.

The NBG system is a conservative extension of ZF; that is, a sentence with only lowercase (set) variables is provable in NBG if and only if it is provable in ZF. The Zermelo-Fraenkel system has a clear advantage over NBG, namely, the simplicity of working with only one type of object (sets) rather than two types of objects (sets and classes). The Zermelo-Fraenkel axiomatic system is the standard system of axioms for modern set theory.

4. Cantor’s Well-Ordering Principle

As proposed by Cantor, two sets A and B have the same cardinality if and only if there is a bijection f: A \rightarrow B. When A is a finite set, there is a unique natural number, denoted by |A|, that identifies the number of elements in A. In this case, we say that |A| is the cardinality of A. For example, if A = \{3,5,7,2\}, then |A| = 4. Clearly, the cardinality of a finite set identifies the number of elements that are in the set. Moreover, if A and B are both finite sets, then one can prove that

|A| = |B| if and only if there exists a bijection f: A \rightarrow B.

(\Delta) 

With this understanding, Cantor asked the following question:

Are there values that can represent the size of infinite sets and satisfy (\Delta)?

In other words, given two infinite sets A and B, can one assign values |A| and |B| such that

|A| = |B| if and only if there exists a bijection f: A \rightarrow B? 

Cantor answered this question, in the affirmative, by developing the transfinite ordinal numbers, which are “infinite numbers” in the sense that they are larger than all of the natural numbers, and are well-ordered just like the natural numbers. Cantor believed that each infinite set can be assigned a specific ordinal number and that this ordinal number would measure the size of the set. Cantor realized that, in order to successfully apply his theory of ordinal numbers, he needed an additional principle. In 1883, he proposed the following principle.

Well-Ordering Principle: It is always possible to bring any well-defined set into the form of a well-ordered set. 

A relation \leq on a set X is a well-ordering of X if and only if it is a total ordering in which every non-empty subset of X has a least element, where it is assumed that the relation \leq does not apply to any elements that are not in X. If a set can be well-ordered, then one can generalize the concepts of induction and recursion, similar to mathematical induction, on the elements of the set. Given any infinite set, Cantor used the well-ordering principle to identify an ordinal number that measures the size of the set. Such an ordinal is called a cardinal number.

a. Ordinal Numbers

The natural numbers are often used for two purposes: to indicate the position of an element in a sequence and to identify the size of a finite set. In other words, a natural number can be used to identify a position (first, second, third, …) and it can be used to identify a size (one, two, three, …). Cantor extended the natural numbers by introducing the concepts of transfinite position and transfinite size. Suppose that we want to count the number of real numbers. As noted in Section 1, Cantor proved that the set of real numbers is uncountable. Thus, if we attempted to assign each real number to exactly one of the natural numbers 0, 1, 2, 3, \ldots, then we would not have enough natural numbers to complete this task. However, suppose that we add some new numbers, called transfinite ordinals, to our stock of numbers. Clearly, we need an ordinal that will identify the first position that occurs after all of the natural numbers. Cantor denoted this ordinal by the Greek letter \omega. That is, Cantor proposed the following “position” sequence

0, 1, 2, 3, 4, \ldots, \omega.

(1) 

Observe the following:

  • By starting with 0 and repeatedly adding 1, we obtain all of the natural numbers.
  • Every natural number greater than 0 has an immediate predecessor; for example, 5 has 4 as its immediate predecessor.

By contrast, the ordinal number \omega cannot be obtained by repeatedly adding 1 to 0 and it does not have an immediate predecessor. For these reasons, we say that \omega is a limit ordinal.

We can continue the sequence (1) by repeatedly adding to \omega. By doing so, we obtain the following position sequence:

0, 1, 2, 3, 4, \ldots, \omega, \omega+1, \omega+2, \omega+3, \ldots

(2) 

The process for constructing (1) and (2) can be repeated endlessly. In this way, we obtain the ordered sequence of all of the ordinals:

0, 1, 2, 3, 4, \ldots, \omega, \omega+1, \omega+2, \ldots ,\omega+\omega,(\omega+\omega)+1,(\omega+\omega)+2, \ldots

(3) 

where \omega+\omega is a limit ordinal which is usually represented by 2 \cdot \omega. An ordinal of the form \alpha+1 is called a successor ordinal. An ordinal \delta > 0 that is not a successor ordinal is called a limit ordinal. Cantor used the ordinals to measure the “length” of a well-ordered set.

The natural numbers 0, 1, 2, 3, 4, \ldots are sometimes called finite ordinals. Every nonempty subset of the natural numbers has a least element. Similarly, every nonempty set of ordinals has a least element with respect to the ordering in (3). The ordinal numbers are a generalized extension of the natural numbers. One can define the operations of addition, multiplication, and exponentiation on the ordinal numbers. These operations satisfy some (but not all) of the arithmetic properties that hold on the natural numbers, for example, addition is associative (Cunningham 2016).

The set of predecessors of an ordinal is the set of all of the ordinals that come before it in the list (3); for example, the set of predecessors of \omega and \omega+1 are the respective sets

\mathbb{N} = \{0, 1, 2, 3, 4, \ldots\}, N’ = \{0, 1, 2, 3, 4, \ldots , \omega \}.
(4)

The ordinals \omega and \omega+1 represent different positions in the list (3); but, the sets \mathbb{N} and N’ in (4) have the same cardinality. Note that the cardinality of \mathbb{N} is larger than any finite set, that is, for any natural number n, the set \mathbb{N} has cardinality larger than the set \{0, 1, 2, \ldots, n\}. For this reason, we say that \omega is a cardinal number.

For any two ordinals \alpha and \beta, we say that \alpha < \beta if and only if \alpha appears before \beta in the list (3). For each ordinal \gamma, let Pred(\gamma) = \{\alpha : \alpha < \gamma\} be the set of predecessors of \gamma. One can prove, in ZF, that Pred(\gamma) is a set. In contemporary set theory one usually defines the ordinals so that, for each ordinal \gamma, \gamma = Pred(\gamma); that is, each ordinal is defined to be the set of its predecessors. Specifically, a set \gamma is said to be an ordinal if and only if \gamma is well-ordered by the membership relation and is transitive, that is, every element in \gamma is a subset of \gamma. Thus, if \alpha < \beta, then \alpha \in \beta and \alpha \subseteq \beta. For example, \omega = \{0, 1, 2, 3, 4, \ldots\} is an ordinal if the integers (the finite ordinals) are defined as follows:

  • 0 = \varnothing,
  • 1 = \{0\},
  • 2 = \{0,1\},
  • 3 = \{0,1,2\},
  • 4 = \{0,1,2,3\}.

This approach is due to Von Neumann (Kunen 2009), and such ordinals can be called Von Neumann ordinals. The collection of all ordinals is a proper class (see Cunningham 2016).

b. Cardinal Numbers

An ordinal number \kappa is said to be a cardinal if and only if, for all \alpha < \kappa, the set Pred(\alpha) has smaller cardinality than Pred(\kappa). It follows that the natural numbers are all cardinals. As noted above, \omega is the first transfinite cardinal, which is often denoted by \aleph_{0}. The next transfinite cardinal, after \aleph_{0}, is designated by \aleph_{1}. This process can be continued to produce the following sequence of finite and transfinite cardinals:

0, 1, 2, 3, 4, \ldots, \aleph_{0}, \aleph_{1}, \ldots, \aleph_{\omega}, \aleph_{\omega+1}, \ldots, \aleph_{2 \cdot \omega}, \ldots, \aleph_{\omega \cdot \omega}, \ldots

(5) 

where the transfinite cardinal numbers in (5) are indexed by the ordinal numbers. Thus, the collection of all the cardinal numbers is a proper class. A cardinal \aleph_{\beta} is called a successor cardinal if and only if \beta is a successor ordinal; otherwise, it is called a limit cardinal. One can prove, in ZF, that, for every cardinal \kappa, there is an ordinal \alpha such that \kappa = \aleph_{\alpha} (Cunningham 2016). Thus, every cardinal appears on the list (5). One can define the operations of addition, multiplication, and exponentiation on the cardinals (exponentiation requires the well-ordering principle). These particular operations are not the same as the corresponding operations on the ordinal numbers (Cunningham 2016).

Cantor used the cardinal numbers to measure the “size” of sets. The well-ordering principle implies that every set A can be assigned a (unique) cardinal number that measures its size. This cardinal number is usually denoted by |A|, and is called the cardinality of A. Cantor’s Theorem implies that, for any set A, |A| < |\wp(A)|. The operation of cardinal exponentiation allowed Cantor to prove that the cardinality of \mathbb{R}, the set of real numbers, is equal to 2^{\aleph_{0} }, that is, |\mathbb{R}| = 2^{\aleph_{0}}. Since \aleph_{1} is the first cardinal greater than \aleph_{0}, Cantor was able to express the Continuum Hypothesis in terms of the equation 2^{\aleph_{0}} = \aleph_{1}. Moreover, assuming the well-ordering principle, one can conclude that a set A is countable if and only if |A| \leq \aleph_{0} and that a set B is uncountable if and only if \aleph_{1} \leq |B|.

Infinite cardinals come in two distinct forms: regular or singular. An infinite cardinal \kappa is said to be a regular cardinal if and only if \kappa is not the union of a set consisting of less than \kappa many smaller cardinals. Thus, if \kappa is a regular cardinal, S is a set of cardinals smaller than \kappa, and |S| < \kappa, then \kappa \neq \bigcup S. Assuming the well-ordering principle, it follows that each successor cardinal is a regular cardinal. When a cardinal is not regular, it is called a singular cardinal. One can show that an infinite cardinal \kappa is singular if and only if there exists an ordinal \beta < \kappa and a function f: Pred(\beta) → Pred(\kappa) such that for all \gamma < \kappa there is an ordinal \alpha < \beta such that \gamma < f(\alpha). It follows that \aleph_{\omega} is a singular cardinal.

5. The Axiom of Choice

At the third International Congress of Mathematicians at Heidelberg in 1904, Julius König submitted a proof that the well-ordering principle is false; in particular, he presented an argument showing the set of real numbers cannot be well-ordered. On the next day, Ernst Zermelo identified an error in König’s purported proof. Shortly after the Heidelberg congress, Zermelo (Moore 2012) discovered a proof of the following theorem, which implies that the error found in König’s proof cannot be removed.

Well-Ordering Theorem: Every set can be well-ordered 

In his clever proof of the well-ordering theorem, Zermelo formulated and applied the following principle, which he was the first to identify.

Axiom of Choice (AC). Let T be a set of nonempty sets. Then there is a function F such that, for each set A in T, F(A) \in A. 

The function F mentioned in AC is called a choice function for the set T. Informally, the axiom of choice asserts that, for any collection of nonempty sets, it is possible to uniformly choose exactly one element from each set in the collection. When T is a finite set, one can prove, in ZF, that there exists a choice function. Today, mathematicians use the axiom of choice when the set T is infinite and it is not clear how to define or construct a desired choice function.

Zermelo applied the axiom of choice to establish the well-ordering theorem. The well-ordering theorem validates both Cantor’s well-ordering principle and that every set can be assigned a cardinal number that measures its size.

a. On Zermelo’s Proof of the Well-Ordering Principle

Zermelo’s proof of the well-ordering theorem is the first mathematical argument that explicitly invokes the axiom of choice. As a result, the proof can be viewed as an important moment in the development of modern set theory. For this reason, we now present a summary of this proof. Let A be a nonempty set and let T be the set of all nonempty subsets of A; that is, let

T = \{ X \in \wp (A) : X \neq \varnothing \}. 

Let \gamma be a choice function for T. Call a set X \in T a \gamma-set if and only if there is a well-ordering \leq of X such that, for each a \in X,

\gamma(\{z \in Aza\}) =a . 

Thus, each element a \in X is the element that the choice function \gamma selects from the set of all elements in A that do not (strictly) precede a in the ordering \leq. For example, if w = \gamma(A), then one can show that \{w\} is a \gamma-set. Thus, \gamma-sets exist. Let X be a \gamma-set with well ordering \leq and let Y be a \gamma-set with well-ordering \leq’. In his proof, Zermelo showed that either X \subseteq Y and \leq’ continues \leq or Y \subseteq X and \leq continues \leq’, where we say that \leq’ continues \leq when the order \leq’ only adds new elements that are greater than all of the elements ordered by \leq. Zermelo also showed that the union of all of the \gamma-sets is a \gamma-set and that this union equals A. Therefore, A can be well-ordered.

Essentially, the axiom of choice states that one can make infinitely many arbitrary choices. As noted above, Cantor’s acceptance of infinite sets led to a dispute among some of Cantor’s contemporaries. Similarly, Zermelo’s axiom of choice incited further controversy concerning the infinite. The main objection to the axiom of choice was the obvious one: How can the existence of a choice function be justified when such a function cannot be defined or explicitly constructed? Surprisingly, many of the axiom’s severest critics had unwittingly applied the axiom in their own work. In the decades following its introduction, the axiom of choice gained acceptance among most mathematicians; in part, this was because the axiom of choice is a very useful principle whose deductive strength is required to prove many important mathematical theorems (Moore 2012). Moreover, the axiom of choice is equivalent to a number of seemingly unrelated principles in mathematics. For example, in ZF, the axiom of choice is equivalent to Zorn’s lemma, the well-ordering theorem, and the comparability theorem (see Cunningham 2016).

The Zermelo-Fraenkel system of axioms is denoted by ZF and the axiom of choice is abbreviated by AC. The axiom of choice is not one of the axioms in ZF. The result of adding the axiom of choice to the system ZF is denoted by ZFC.

There were many unsuccessful attempts to prove the axiom of choice assuming only the axioms in ZF. As a result, mathematicians began to doubt the possibility of proving the axiom of choice from the axioms in ZF and, eventually, it was shown that such a proof does not exist. The combined work of Kurt Gödel, in 1940, and Paul Cohen, in 1963, confirmed that the axiom of choice is independent of the Zermelo-Fraenkel axioms, that is, AC cannot be proven or refuted using just the axioms in ZF. Nevertheless, the axiom of choice is a powerful tool in mathematics and there are many significant theorems that cannot be established without it. Consequently, mathematicians typically assume the axiom of choice and often cite it when they use it in a proof.

b. Banach-Tarski Paradox

Set theory frequently deals with infinite sets. Moreover, as we have seen, there are times when infinite sets have properties that are unlike those of finite sets. Such properties of infinite sets can appear to be counter-intuitive or paradoxical, because they conflict with the behavior of finite sets or with our limited intuition. Cantor proved a theorem that illustrates this fact. Let I denote the unit interval \lbrack 0,1 \rbrack, that is, the set of all real numbers x such that 0 \leq x \leq 1. Let S denote the unit square in the plane, that is, the set of all ordered pairs (x,y) such that such that 0 \leq x \leq 1 and 0 \leq y \leq 1. The sets I and S appear in the following figure:


Cantor initially believed that the set of points in the two-dimensional square S must have cardinality much larger than the set of points in the one-dimensional interval I. Then he discovered a proof showing that his initial intuition was wrong. Cantor’s theorem below, which can be proven without the axiom of choice, shows the sets I and S have the same cardinality.

Theorem (Cantor). There exists a bijection f: I \rightarrow S. 

One can use the bijection f: I \rightarrow S to proclaim that one can, theoretically, disassemble all of the points in the interval I and then reassemble these points to obtain the unit square S. This, of course, is counter-intuitive, as we know that one cannot cut-up a 1-foot piece of thread and then put the pieces together to obtain a square-foot piece of fabric. Thus, there are infinite abstract objects that do not behave in the same way as finite concrete objects.

We now present a theorem due to Stefan Banach and Alfred Tarski (1924). The proof of this theorem uses the axiom of choice, in an essential manner, to prove another counter-intuitive result. Some have claimed that this theorem thus refutes the axiom of choice. First, we identify some terminology. In three-dimensional space, a unit ball is a set of points of distance less than or equal to 1 from a fixed central point.

Theorem (Banach, Tarski). A unit ball in three-dimensional space can be split into five pieces that can be rigidly moved, rotated, and put back together to form two unit balls. 

The Banach–Tarski Theorem is often referred to as a paradox because it is counter-intuitive; for example, the theorem implies that, theoretically, one can split a solid glass ball into five pieces and then use the pieces to create two new glass balls of the same size as the original. However, in the proof of the theorem, the five pieces that are formed are not solids that have a measurable volume; they are five complex infinite sets of points. We repeat: there are infinite abstract objects that do not behave in the same way as finite concrete objects.

The conclusion of the Banach–Tarski Theorem does not refute the axiom of choice, and Cantor’s above theorem does not render the axioms of set theory false. Ever since the ancient Greeks, there have been results in mathematics that were once viewed as being counter-intuitive. Such results eventually become better understood and, as a result, become more intuitive themselves.

6. The Cumulative Hierarchy

Zermelo’s 1904 proof of the well-ordering theorem resembles von Neumann’s 1923 proof of the transfinite recursion theorem, a powerful tool in set theory. A formula \varphi(g,u) is said to be functional if and only if \forall g \exists ! u \varphi (g,u); that is, for all g, there is a unique u such that \varphi(g,u). Given a functional formula, \varphi(g,u), consider the class of ordered pairs

F = \{(g,u)\varphi(g,u)\}. 

Since \varphi(g,u) is functional, one can view F as a class function (that is, a functional class), and thus, F(x) is a set whenever x is a set. Let F|A denote the function obtained by restricting the domain of F to the set A. The replacement axiom implies that F|A is a set whenever A is a set.

Transfinite Recursion Theorem: Let \varphi(g,u) be a functional formula. Then there is a class function H such that, for all ordinals \beta, \varphi(H|\beta,H(\beta)). 

The transfinite recursion theorem is used to define what is commonly known as the cumulative hierarchy of sets and usually denoted by \{V_{\beta} : \beta \text{ is an ordinal}\}, which satisfies (see figure below)

  • V_{0} = \varnothing,
  • V_{\gamma + 1} = \wp (V_{\gamma}), for any ordinal \gamma,
  • V_{\beta} = \bigcup \{V_{\alpha} : \alpha < \beta\}, for any limit ordinal \beta.

 


One obtains \{V_{\beta} : \beta \text{ is an ordinal}\} by repeatedly applying the power set operation at successor ordinals and by taking the union of all the previous sets at limit ordinals. In particular, V_{0} = \varnothing and

V_{1} = \wp (V_{0})= \{ \varnothing,\{ \varnothing \} \}, \ldots , V_{\omega} = \bigcup \{ V_{n} : n < \omega\}, \ldots

 
The regularity axiom implies that for every set x, there exists an ordinal \alpha such that x \in V_{\alpha}. For this reason, the proper class V = \bigcup \{V_{\beta} : \beta \text{ is an ordinal}\} is called the universe of sets. It follows that each set V_{\beta} is in V and that all of the axioms in ZF are true in V. In addition, as one ascends the “ordinal spine,” one obtains sets V_{\gamma} of ever greater complexity that become better and better approximations to V (see above figure). This is confirmed by the reflection principle (see below) which, in essence, asserts that any statement that is true in V, is also true in some set V_{\beta}.

Let \varphi (v_{1}, \ldots , v_{n}) be a formula in the language of set theory with free variables v_{1}, \ldots , v_{n}. For any ordinal \alpha and x_{1}, \ldots , x_{n} \in V_{\alpha}, we write

(V_{\alpha}, \in) \vDash \varphi (x_{1}, \ldots , x_{n}) 

to mean that \varphi(x_{1}, \ldots ,x_{n}) is true in V_{\alpha}. The following theorem of ZF, due to Azriel Levy (Levy 1960) and Richard Montague (Montague 1961), implies that any specific truth that holds in V likewise holds in some initial segment V_{\beta} of V; in fact, it holds in unboundedly many initial segments.

Reflection Principle: Let \varphi(v_{1}, \ldots, v_{n}) be a formula and let \alpha be an ordinal. Then there is an ordinal \beta > \alpha such that, for all x_{1}, \ldots , x_{n} \in V_{\beta}, \varphi (x_{1}, \ldots ,x_{n}) is true in V if and only if (V_{\beta}, \in) \vDash \varphi (x_{1}, \ldots, x_{n}). 

As a corollary, for any finite number of formulas that hold in V, the reflection principle implies that all of these formulas also hold in some V_{\beta}. As noted before, there are an infinite number of axioms in ZF. Montague (Montague 1961) used the reflection principle to conclude that if ZF is consistent, then ZF is not finitely axiomatizable. Hence, ZF is not equivalent to any finite number of the axioms in ZF. This follows from Gödel’s second incompleteness theorem (see Kunen 2011, page 8), which implies that, if ZF is consistent, then one cannot prove, in ZF, the existence of a set model of ZF, that is, a set M such that (M,\in) \vDash \varphi, for every axiom \varphi in ZF.

7. Gödel’s Constructible Universe

As we have seen, the cumulative hierarchy of sets is constructed in stages. At successor stages, one adds all possible subsets of the previous stage and, at limit stages, one takes the union of all of the previously produced sets. To prove that the axiom of choice and the Continuum Hypothesis are consistent with ZF, Kurt Gödel (1938) constructed the “inner model” L of V commonly known as the universe of constructible sets. As we will see, L is a subclass of V. The idea behind Gödel’s construction of L is to modify the cumulative hierarchy structure so that the end result will produce a (smaller) class that satisfies ZF. For any set X, define D(X) to

D(X) = \{A \subseteq X: A is definable over (X,\in)\} 

where A is definable over (X,\in) means that there are x_{1},\ldots,x_{n} in X and a formula \varphi(v,x_{1},\ldots,x_{n}) such that, for all a in X,

a \in A if and only if (X,\in) \vDash \varphi (a,x_{1},\ldots,x_{n}). 

One can show, in ZF, that D is a class function (Moschovakis 2009, 8D). Using the transfinite recursion theorem and the “definable subset” operation D, Gödel defined the class \{L_{\beta} : \beta \text{ is an ordinal}\} by applying the operation D at successor ordinals and by taking the union of all of the previous sets at limit ordinals. The class \{L_{\beta} : \beta\text{ is an ordinal}\} satisfies the following (see figure below):

  • L_{0} = \varnothing,
  • L_{\gamma + 1} = D(L_{\gamma}), for any ordinal \gamma,
  • L_{\beta} = \bigcup \{L_{\alpha} : \alpha < \beta\}, for any limit ordinal \beta.

Consequently, at each successor stage of the construction, one extracts only the definable subsets of the previous stage. The proper class L = \bigcup\{L_{\beta} : \beta\text{ is an ordinal}\} is called the universe of constructible sets.

Assuming ZF, Gödel proved that L satisfies ZF, the axiom of choice, and the Continuum Hypothesis (Gödel 1990). Thus, if ZF is consistent, then so is the theory ZF+AC+CH. This result does not prove that the axiom of choice and the Continuum Hypothesis are true in V, but it does show that one cannot prove, in ZF, that either AC or CH is false.

The proper class L (with the \in relation restricted to L) is called an inner model, because it is a transitive class (a class that includes all of the elements of its elements), contains all of the ordinals, and satisfies all of the axioms in ZF.

Gödel’s notion of a constructible set has led to interesting and fruitful discoveries in set theory. By generalizing Gödel’s definition of L, contemporary set theorists have defined a variety of inner models that have been used to establish new consistency results (Kanamori 2003, pp. 34-35). Each of these inner models contains L as a subclass, and to understand the structure of these inner models, one must be familiar with the above definition of Gödel’s constructible sets. Moreover, a penetrating investigation into the structure of L has led researchers to discover many fascinating results about L and its relationship to the universe of sets V (Jech 2003).

8. Cohen’s Forcing Technique

In 1963, the mathematician Paul Cohen introduced an extremely powerful method, called forcing, for the construction of models of Zermelo-Fraenkel set theory. A model M of set theory is a transitive collection of sets in which the ZF (ZFC) axioms are all true, denoted by M \vDash ZF (M \vDash ZFC).

As discussed in section 7, Gödel showed that one cannot prove, in ZF, that either AC or CH is false. Cohen used his forcing technique to construct a model of ZFC in which the Continuum Hypothesis is false. Hence, one cannot prove, in ZFC, that CH is true. Thus, if ZFC is consistent, then CH is undecidable in ZFC. Cohen (1963) also showed that his technique of forcing can be used to produce a model of set theory in which ZF holds and the axiom of choice is false. Thus, AC is not provable in ZF. So, if ZF is consistent, then AC is undecidable in ZF.

Cohen’s idea was to start with a given set model M of ZFC (the ground model) and extend it by adjoining a “generic” set G to M where G \notin M. The resulting model M[G] (a generic extension of M) includes M, contains G, and satisfies ZFC. Cohen showed how to find a set G so that CH fails in M[G]. In a similar manner, Cohen was able to add a new set G to M such that there is an inner model of M[G] in which ZF holds and the axiom of choice is false. For his work, Cohen was awarded the Fields Medal in 1966. This award is considered to be the “Nobel Prize” of mathematics. Gödel stated that Cohen’s forcing method was “the greatest advance in the foundations of set theory since its axiomatization” (Kanamori 2003, page 32).

The discussion in the previous paragraph about M is neither complete nor entirely correct. In order to prove that the desired generic set G exists, Cohen, in fact, had to assume that M is a countable transitive set model of ZFC. Let us do the same. A partial order is a pair (P,\leq) such that P \neq \varnothing and \leq is a relation on P which is reflexive, antisymmetric, and transitive. By varying (P,\leq), one can obtain generic extensions that satisfy a wide variety of statements that are consistent with ZFC. Let (P,\leq) \in M be a partial order that is definable in M, and suppose that, in M, the definition of (P,\leq) and its properties are based only on the fact that M \vDash ZF. Since M is countable, there exists a generic set G \subseteq P (Kunen 2012, Lemma IV.2.3). Let us presume that (P,\leq) has the properties required to ensure that M[G] \vDash \varphi, where \varphi is a sentence in the language of set theory; for example, \varphi could be “not CH.” Hence, M[G] \vDash ZFC +~\varphi. Thus,

if M is a countable transitive set model of ZFC, then ZFC +~\varphi is consistent.

(6) 

To conclude that ZFC +~\varphi is consistent, it appears that one must first show that there exists a countable transitive set model of ZFC. However, by Gödel’s second incompleteness theorem, one cannot prove, in ZFC, that such a set model exists (unless ZFC is inconsistent). Is there a way around this difficulty? Note that there are finitely many axioms in ZFC such that if just these axioms hold in M, then one can still prove that M[G] \vDash \varphi (Kunen 2011).

We now discuss how the above argument used to establish (6) can be modified to correctly conclude that ZFC +~\varphi is consistent. Let T be a finite set of axioms in ZFC. Using the reflection principle, one can prove, in ZFC, that

there is a countable transitive set model M in which the axioms in T are true.

(7) 

For any finite set S of axioms in ZFC, the forcing method shows that there is a finite set T of axioms in ZFC such that S \subseteq T and

if M is a countable transitive set model in which the axioms in T hold, then there is a generic extension M[G] in which \varphi and the axioms in S hold.

(8) 

Since T is a finite set of axioms, we conclude from (7) that there is a countable transitive set model M that satisfies all of the axioms in T. Therefore, by (8), there is a generic extension M[G] that satisfies \varphi and all of the axioms in S. Since proofs are finite, we conclude that, in ZFC, one cannot prove \neg \varphi. Hence, ZFC +~\varphi is consistent, assuming that ZFC is consistent.

Cohen’s forcing technique is very versatile and has been used to show that there are many statements, both in set theory and in mathematics, that are undecidable (or unprovable) in ZF and ZFC. For example, in mathematics, the Hahn–Banach theorem is a crucial tool used in functional analysis. The proof of this theorem uses the axiom of choice. The forcing method has been used to show that Hahn–Banach theorem is not provable in ZF alone (Jech 1974). Moreover, using forcing results and the universe of constructible sets, Saharon Shelah (1974) has shown that a famous open problem in abelian group theory (Whitehead’s Problem) is undecidable in ZFC.

As suggested earlier, since essentially all mathematical concepts can be formalized in the language of set theory, set theory offers a unifying theory for mathematics. Thus, the theorems of mathematics can be viewed as assertions about sets. Moreover, these theorems can also be proven from ZFC, the Zermelo-Fraenkel axioms together with the axiom of choice. Cohen’s forcing method clearly shows that ZFC is an incomplete theory, as there are statements that cannot be resolved in it. This motivates the following question:

What path should be taken to try to settle the Continuum Hypothesis and other undecided statements in mathematics? 

In contemporary set theory, the most common answer to this question is called Gödel’s Program:

Search for new axioms, which, when added to ZFC, will determine the truth or falsity of unresolved statements. 

This program was inspired by an article of Gödel’s in which he discusses the mathematical and philosophical aspects of mathematical statements that are independent of ZFC (Gödel 1947). Sections 9 and 10 will discuss two directions that this program has taken: large cardinal axioms and determinacy axioms.

9. Large Cardinal Axioms

Roughly, a large cardinal axiom is a set-theoretic statement that asserts the existence of an uncountable cardinal \kappa that satisfies a particular property that implies that there is a set M such that (M,\in) is a model of ZFC; such a \kappa is called a large cardinal. Gödel’s second incompleteness theorem implies that, in ZFC, one cannot prove the existence of large cardinals. Thus, a large cardinal axiom is a “new axiom.” Most modern set theorists believe that the standard large cardinal axioms are consistent with ZFC.

Assuming ZFC, let us say that a cardinal \kappa is a strong limit cardinal if and only if, for every cardinal \lambda, if \lambda < \kappa, then 2^{\lambda} < \kappa. A cardinal \kappa is said to be inaccessible if and only if \kappa is uncountable, regular, and a strong limit cardinal. Recall that a cardinal \kappa is regular if \kappa is not the union of fewer than \kappa many sets of size each less than \kappa. If \kappa is an inaccessible cardinal, then, in ZFC, one can prove that (V_{\kappa},\in) is a model of ZFC (Kanamori 2003). Hence, such a \kappa is an example of a large cardinal and so, the statement “there exists an inaccessible cardinal” is a large cardinal axiom.

There are other large cardinal axioms. The description of these large cardinal axioms usually involves the concept of an elementary embedding of the universe, that is, a nontrivial truth preserving transformation from (V,\in) into (M,\in) where M is a transitive subclass of V. A theorem of Kenneth Kunen (Jech 2003) shows that there is no nontrivial elementary embedding of the universe V into itself. Thus, for any nontrivial truth preserving transformation from (V,\in) into (M,\in) where M is a transitive subclass of V, M \neq V. More specifically, a large cardinal axiom can be expressed as asserting that there exists a nontrivial (class) function

j: V \rightarrow M 

such that for each formula \varphi(v_{1},v_{2},\ldots,v_{n}) (in the language of set theory) and for all elements x_{1},\ldots,x_{n} in V,

(V,\in) \vDash \varphi(x_{1},\ldots,x_{n}) if and only if (M,\in) \vDash \varphi(j(x_{1}),\ldots,j(x_{n})). 

Since the embedding j is not the identity, there must be a least ordinal \kappa such that \kappa < j(\kappa). This ordinal is called the critical point of j and is denoted by \kappa = crit(j). It follows that \kappa is a cardinal; indeed, \kappa is the large cardinal that is confirmed by the existence of the embedding j.

A cardinal \kappa is said to be measurable if and only if there exists an embedding j: V \rightarrow M such that \kappa is the critical point of j. In this case, one can prove that V_{\kappa+1} \subseteq M. Therefore, there is some resemblance between M and V. Increasingly stronger large cardinal axioms demand a greater agreement between M and V. For example, if one requires that V_{\kappa+2} \subseteq M, then one obtains a stronger large cardinal axiom. For another example, a cardinal \kappa is said to be superstrong if and only if there is a transitive class M and a nontrivial elementary embedding j: V \rightarrow M such that \kappa = crit(j) and V_{j(\kappa)} \subseteq M. Even stronger large cardinal axioms are obtained by requiring greater and greater resemblance between M and V (Woodin 2011).

Large cardinal axioms are statements that assert the existence of large cardinals. These axioms are widely viewed as being very promising new axioms for set theory. Large cardinal axioms do not resolve the Continuum Hypothesis but they have led mathematicians to formulate conditions under which Cantor’s hypothesis is false (Woodin 2001, p. 688). As already mentioned, one cannot prove, in ZFC, that large cardinals exist. Yet, there is very strong evidence that their existence cannot be refuted in ZFC (Maddy 1988).

10. The Axiom of Determinacy

Descriptive set theory has its origins, in the early 20th century, with the theory of real-valued functions and sets of real numbers developed by Borel, Baire, and Lebesgue. These analysts, respectively, introduced

  • the hierarchy of Borel sets of real numbers,
  • the Baire hierarchy of real-valued functions,
  • Lebesgue measurable sets of real numbers.

Descriptive set theory extends the work of these mathematicians (Moschovakis 2009). Recall that \omega = \{0,1,2,3,4,\ldots\} is the set of natural numbers. Let ^{\omega}\omega be the set of all functions from \omega to \omega. The set ^{\omega}\omega is denoted by \mathbb{R} and is called Baire Space. \mathbb{R} is often referred to the set of reals; and if x \in \mathbb{R}, then x is called a real. \mathbb{R} is regarded as a topological space by giving it the product topology, using the discrete topology on \omega. The space \mathbb{R} is homeomorphic to the set of irrational numbers which is a subspace of the set of real numbers (Moschovakis 2009).

Descriptive set theory is a branch of set theory that uses set theoretic tools to investigate the structure of definable sets and functions over \mathbb{R}. One can identify the level of complexity of such definable sets of reals (Moschovakis 2009). Thus, there is a natural hierarchy on the definable subsets of \mathbb{R}, which, in increasing order of complexity, is called the projective hierarchy.

As a result of Gödel’s and Cohen’s work, it has been shown that many questions in descriptive set theory are not decidable in axiomatic set theory. For example, in 1938, Gödel showed that in L, the universe of constructible sets, there are projective sets of reals that are not Lebesgue measurable. In 1970, using the method of forcing, Robert Solovay showed that if there is an inaccessible cardinal, then ZFC is consistent with the statement that every projective set is Lebesgue measurable. Thus, one can neither prove nor disprove, in ZFC, the Lebesgue measurability of projective sets. Hence, in ZFC, the theory of projective sets is incomplete. For this reason, modern descriptive set theory focuses on new axioms; one such axiom concerns infinite games.

Gale and Stewart (1953) introduced the general concept of an infinite game of perfect information and began the study of these games. Other mathematicians then pursued this subject and discovered that it can be used to resolve problems in descriptive set theory.

We now turn to a description of infinite games and strategies. For each A \subseteq \mathbb{R}, we associate a two-person infinite game on \omega with payoff A, denoted by G_{A}, where players I and II alternately choose natural numbers a_{i} in the order given in the diagram:


After completing an infinite number of moves, the players produce the real

x =a_{0},a_{1},a_{2},\ldots⟩. 

Player I is said to win if x \in A, otherwise player II is said to win. As each player is aware of all the previous moves before making a next move, the game is called a game of perfect information. The game G_{A} is said to be determined if and only if either player has a “winning strategy,” that is, a function that ensures the player will win the game regardless of how the other player makes his or her moves. The Axiom of Determinacy (AD) is a regularity hypothesis about such games that states: For all A \subseteq \mathbb{R}, the game G_{A} is determined.

In the theory ZF+AD, one can resolve many open questions about the sets of real numbers. For example, one can prove Cantor’s original form of the continuum hypothesis: Every uncountable set of real numbers has the same cardinality as the full set of real numbers.

Moreover, it has been shown that the axiom of choice implies that AD is false; that is, using the axiom of choice, one can construct a set of reals A such that the game G_{A} is not determined. Thus, the axiom of determinacy is incompatible with the axiom of choice. However, it is not clear that one can establish, without the axiom of choice, the existence of a set of reals A such that the game G_{A} is not determined (Moschovakis 2009). Moreover, there are weaker versions of AD that are compatible with ZF together with a weaker choice principle called the axiom of dependent choices.

Axiom of Dependent Choices (DC). Let R be a relation on a nonempty set A. Suppose that for all x \in A there is a y \in A such that R(x,y). Then there exists a function f: \omega \rightarrow A such that, for all n \in \omega, R(f(n),f(n+1)).

Many mathematicians working in descriptive set theory operate within the background theory ZF+DC and the following determinacy axiom: For every projective set A, the game G_{A} is determined. This axiom is denoted by PD (projective determinacy). Under the theory ZF+DC+PD, the classic open questions about projective sets have been successfully addressed (Moschovakis 2009). In particular, this theory implies that all projective sets are Lebesgue measurable.

Generalizing the construction of the inner model L, one can construct the inner model L(\mathbb{R}), the smallest inner model that contains all the ordinals and all the reals. The set \wp(\mathbb{R}) \cap L(\mathbb{R}) can be viewed as a natural extension of the projective sets. The determinacy hypothesis denoted by AD^{L(\mathbb{R})}, asserts that AD holds in L(\mathbb{R}). Since the inner model L(\mathbb{R}) contains all of the projective sets, the assumption AD^{L(\mathbb{R})} implies PD.

There are very deep results that connect determinacy hypotheses and large cardinal axioms. In 1988, Martin and Steel, working in ZFC, identified a large cardinal axiom that implies PD. By assuming a stronger large cardinal axiom, Woodin, within ZFC, was able to prove that AD^{L(\mathbb{R})} holds and so, L(\mathbb{R}) satisfies ZF+AD. Moreover, PD and AD^{L(\mathbb{R})}, individually, imply the consistency of certain large cardinal axioms (Kanamori 2003). Investigating the relationships between determinacy hypotheses and large cardinals has become an important component of modern set theory.

11. Concluding Remarks

Set Theory is a rich and beautiful branch of mathematics whose fundamental concepts permeate all branches of mathematics. It is a most extraordinary fact that all standard mathematical objects can be defined as sets. For example, the natural numbers and the real numbers can be constructed within set theory. In addition, algebraic structures, functional spaces, vector spaces, and topological spaces can be viewed as sets in the universe of sets V. Consequently, mathematical theorems can be regarded as statements about sets. These theorems can also be proven from ZFC, the axioms of set theory. Thus, mathematics can be embedded into set theory.

Since all of conventional mathematics can be developed within set theory, one can view certain results in set theory as being part of metamathematics, the field of study within mathematics that uses mathematical tools to investigate the nature and power of mathematics. For example, using the forcing technique and inner models, it has been shown that there are mathematical statements that cannot be proven or disproven in ZFC. Thus, when a particular mathematical statement is unresolved, set theory can sometimes show that there is neither a proof nor a refutation of the statement in ZFC. As noted above, this situation has inspired the search for new set theoretic axioms.

Of course, the fact that set theory offers a foundation for mathematics indicates that set theory is a very important branch of mathematics. However, the concepts and techniques developed within set theory demonstrate that, in itself, set theory is a deep and exciting branch of mathematics with significant applications to other areas of mathematics. This success has inspired some philosophers of mathematics to direct their attention to the philosophy of set theory and the search for new axioms (Maddy 1988a, 1988b, 2011).

12. References and Further Reading

a. Primary Sources

  • Banach, S. and Tarski, A. 1924. “Sur la décomposition des ensembles de points en parties respectivement congruentes,” Fund. Math., 6, pp. 244–277.
  • Cantor, Georg. 1874. “Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen,” Journal fur die reine und angewandte Mathematik (Crelle). 77, 258–262.
  • Cohen, Paul J. 1963. The independence of the axiom of choice. Mimeographed.
  • Cohen, Paul J. 1963a. “The independence of the continuum hypothesis I.” Proceedings of the U.S. National Academy of Sciences 50, 1143-48.
  • Cohen, Paul J. 1964. “The independence of the continuum hypothesis II.” Proceedings of the U.S. National Academy of Sciences 51, 105-110.
  • Cohen, Paul J. 1966. Set Theory and the Continuum Hypothesis, New York: Benjamin.
  • Cunningham, Daniel W. 2016. Set Theory: A First Course, New York: Cambridge University Press.
  • Dauben, Joseph W. 1979. Georg Cantor: his mathematics and philosophy of the infinite, Cambridge, Mass., Harvard University Press; reprinted: Princeton, Princeton University Press, 1990.
  • Dunham, William. 1990. Journey Through Genius: The Great Theorems of Mathematics (1st ed.). John Wiley and Sons.
  • Gale, D. and Stewart, F.M. 1953. “Infinite games with perfect information,“ Annals of Math. Studies, vol. 28, pp. 245–266.
  • Gödel, Kurt. 1947. “What is Cantor’s Continuum Problem?,” American Mathematical Monthly, vol. 54, pp. 515-525.
  • Gödel, Kurt. 1986. Collected Works, Volume I: Publications 1929–1936, (Solomon Feferman, editor-in-chief), Oxford University Press, New York.
  • Gödel, Kurt. 1990. Collected Works, Volume II: Publications 1938–1974, (Solomon Feferman, editor-in-chief), Oxford University Press, New York.
  • Gödel, Kurt. 1995. Collected Works, Volume III: Unpublished Essays and Lectures, (Solomon Feferman, editor-in-chief), Oxford University Press, New York.
  • Hilbert, David. 1923. On the infinite. Reprinted in the Philosophy of Mathematics: Selected Readings, 1983, edited by Paul Benacerraf and Hilary Putnam, pp. 83-201.
  • Jech, Thomas. 2003. Set theory. Third Edition, New York: Springer.
  • Jech, Thomas. 1973. The Axiom of Choice, North-Holland Publishing Company, Studies in logic and the foundations of mathematics, vol. 75, Amsterdam.
  • Kanamori A. 2003. The Higher Infinite. Perspectives in Mathematical Logic. Second edition. Berlin: Springer.
  • Kanamori A. 2012. Set theory from Cantor to Cohen, a book chapter in: Handbook of the History of Logic: Sets and Extensions in the Twentieth Century. Volume editor: Akihiro Kanamori. General editors: Dov M. Gabbay, Paul Thagard and John Woods. Elsevier BV.
  • Kunen, Kenneth. 2009. The Foundations of Mathematics. Studies in Logic, vol. 19. London: College Publications.
  • Kunen, Kenneth. 2011. Set Theory. Studies in Logic, vol. 34. London: College Publications.
  • Lévy, Azriel. 1960. “Axiom schemata of strong infinity in axiomatic set theory,” Pacific Journal of Mathematics, 10, pp. 223–238.
  • Maddy, Penelope H. 1988a. “Believing the axioms I.” The Journal of Symbolic Logic, 53(2), 481–511.
  • Maddy, Penelope H. 1988b. “Believing the axioms II.” The Journal of Symbolic Logic, 53(3), 736–764.
  • Maddy, Penelope H. 2011. Defending the axioms. On the philosophical foundations of set theory. Oxford: Oxford University Press.
  • Montague, Richard M. 1961. Fraenkel’s addition to the axioms of Zermelo. Essays on the foundations of mathematics, dedicated to A. A. Fraenkel on his seventieth anniversary, edited by Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson for The Hebrew University of Jerusalem, Magnes Press, Jerusalem, and North-Holland Publishing Company, Amsterdam, pp. 91–114.
  • Moore, Gregory H. 2012. Zermelo’s Axiom of Choice: Its Origins, Development, and Influence. Mineola, NY: Dover Publications. Reprint of the 1982 original published by Springer.
  • Moschovakis, Yiannis. 2009. Descriptive Set Theory, 2nd edition, vol. 155 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, 2009.
  • Solovay, Robert. 1970. “A model of set theory in which every set is Lebesgue measurable.” Annals of Mathematics, vol. 92, 1–56.
  • Shelah, Saharon. 1974. “Infinite abelian groups, Whitehead problem and some constructions.” Israel J. Math, vol. 18, 243–256.
  • Woodin, Hugh. 2001. “The Continuum Hypothesis, Part II.” Notices of the American Mathematical Society, vol. 48, no. 7.
  • Woodin, Hugh. 2011. Infinity, a book chapter in: Infinity: New Research Frontiers. Cambridge: Cambridge University Press.
  • Zermelo, Ernst. 2010. Collected Works. Gesammelte Werke. Volume I: Set Theory, Miscellania. Mengenlehre, Varia, edited by H.-D. Ebbinghaus and A. Kanamori, Springer, Berlin and Heidelberg, xxiv + 654 pp.

b.  Secondary Sources

  • Ebbinghaus, Heinz-Dieter. 2007. Ernst Zermelo. An Approach to His Life and Work. Berlin: Springer. In cooperation with Volker Peckhaus.
  • Enderton, Herbert B. 1977. Elements of Set Theory. New York: Academic Press.
  • Enderton, Herbert B. 2001. A Mathematical Introduction to Logic. 2nd edn. Burlington, MA: Harcourt/Academic Press.
  • Feferman, Solomon, Parsons, Charles and Simpson, Steven G. (Eds.). 2010. Kurt Gödel: essays for his centennial. Cambridge: Cambridge University Press.
  • Halmos, Paul R. 1974. Naïve  Set Theory. New York: Springer. Reprint of the 1960 edition published by Van Nostrand.
  • Hauser, Kai. 2006. “Gödel’s Program Revisited Part I: The Turn to Phenomenology.” Bulletin of Symbolic Logic, 12(4), 529–590.
  • Heller, Michael and Woodin, Hugh. (Eds.). 2011. Infinity: New Research Frontiers. Cambridge: Cambridge University Press.
  • Kanamori, Akihiro. 2012. “In praise of replacement.” Bulletin of Symbolic Logic, 18(1), 46–90.
  • Levy, Azriel. 2002. Basic Set Theory. Mineola, NY: Dover Publications. Reprint of the 1979 original published by Springer.
  • Moschovakis, Yiannis. 2006. Notes on Set Theory. 2nd edition. Undergraduate Texts in Mathematics. New York: Springer.
  • Potter, Michael. 2004. Set theory and Its Philosophy. New York: Oxford University Press.

c.  Internet Sources

Author Information

Daniel Cunningham
Email: cunnindw@buffalostate.edu
State University of New York Buffalo State
U. S. A.

Future Contingents

The riddle of the future bewilders human beings. On the one hand, we are inclined to think that future events are real in some sense, because we ask questions and make assertions about them. On the other hand, we are inclined to think that future events may depend on our choices, because we conceive of ourselves as free agents. These two inclinations seem to clash. If an event belongs to the future, then it is a fact that it will occur, and we cannot prevent it from occurring. Inversely, if we can prevent an event from occurring, then it cannot be a fact that it will occur. This apparent conflict is at the core of the debate on future contingents, a philosophical dispute that goes back to antiquity. Future contingents are sentences that concern future events that can occur or not occur. The question that started the debate—whether future contingents are true or false—is a question that has no clear answer, given that one may have different views about the truth and falsity of a sentence about the future. Yet an answer must be provided, and it cannot be just any answer. The constraints that define the problem of future contingents determine a restricted set of admissible answers, each of which gives rise to doubts, troubles, and complications.

Table of Contents

  1. The Problem
    1. Speaking about the Future
    2. The Sea Battle
    3. Bivalence, Excluded Middle, Fatalism
    4. Two Arguments
  2. Three Logical Options
    1. Neither Bivalence nor Excluded Middle
    2. Excluded Middle without Bivalence
    3. Both Bivalence and Excluded Middle
    4. Further Considerations
  3. Three Metaphysical Views
    1. Past, Present, and Future Entities
    2. No Future
    3. Many Futures
    4. One Future
  4. The Open Future
    1. Alternative Possibilities
    2. Indetermination
    3. Causal Power
    4. Other Definitions
  5. References and Further Reading

1. The Problem

a. Speaking about the Future

Tomorrow many things will happen. Some of them are things of which it seems correct to assert that they will happen, others are things of which it does not seem correct to assert that they will happen. For example, it seems correct to assert that the sun will rise. Alternatively, it does not seem correct to assert that exactly 3,245 pigeons will walk in Piazza San Marco.

The reason why in certain cases it seems correct to assert that things will go a certain way is that in those cases we take it to be true that things will go that way. As far as we know, the sun will rise tomorrow. Of course, we are not absolutely certain that it will. We might be wrong, due to unforeseen circumstances. However, the evidence that supports our prediction is solid.

Similarly, the reason why in certain cases it does not seem correct to assert that things will go a certain way is that in those cases we do not know whether things will go that way; that is, it may easily be false that things will go that way. We are not in a position to tell whether exactly 3,245 pigeons will walk in Piazza San Marco. As far as we know, the number of pigeons that will walk in Piazza San Marco may easily be bigger or smaller.

In this respect, assertions about the future resemble assertions about the past. The cases in which it seems correct to assert that things went a certain way are cases in which we take it to be true that things went that way. For example, it seems correct to assert that dinosaurs disappeared long time ago. Conversely, the cases in which it does not seem correct to assert that things went a certain way are cases in which we do not know whether things went that way. For example, it does not seem correct to assert that Caesar was annoyed by a mosquito while crossing the Rubicon.

More generally, the ordinary use of language suggests that assertions about the future, just like assertions about the past, can be correct or incorrect. Therefore, this suggests that future-tense sentences, like past-tense sentences, can be true or false. For example, “The sun will rise tomorrow” seems true. Conversely, “The sun will not rise tomorrow” seems false. Note that “The sun will rise tomorrow” does not express a necessary truth, that is, it is not a sentence such as “2+2=4.” Although unlikely, it is possible that it is false. Similarly, “The sun will not rise tomorrow” does not express a necessary falsity, that is, it is not a sentence such as “2+2=5.”

The problem discussed above, and that this article addresses, concerns future contingents; that is, sentences about future events that can occur or not occur. According to a line of thought that goes back to Aristotle, these sentences cannot be true or false. Hence, the linguistic analogy just considered is misleading: Assertions about the future are not like assertions about the past.

b. The Sea Battle

In chapter 9 of De Interpretatione, Aristotle asks whether it makes sense to say that a sentence about a future event that can occur or not occur is true or false. His answer is that it does not make sense, for if the sentence were true or false, then the event would be necessary or impossible:

Let us take, for example, a sea battle. It is requisite on our hypothesis that it should neither take place nor fail to take place tomorrow. These and other strange consequences follow, provided we assume in the case of a pair of contradictory opposites having universals for subjects and being themselves universal or having an individual subject, that one must be true, the other false, that there can be no contingency and that all things that are or take place come about in the world by necessity. (Aristotle, De interpretatione 18b23 ff)

Aristotle’s reasoning seems to be the following. Consider the sentences (1) and (2) as uttered today:

(1) There will be a sea battle tomorrow.

(2) There will not be a sea battle tomorrow.

If (1) were true, and (2) were false, then it would be settled today that there will be a sea battle tomorrow, so the sea battle would be necessary. Similarly, if (2) were true, and (1) were false, then it would be settled today that there will not be a sea battle tomorrow, so the sea battle would be impossible. Since the sea battle is contingent, that is, it is neither necessary nor impossible, this shows that (1) and (2) are neither true nor false.

For Aristotle, the claim that (1) and (2) are neither true nor false is consistent with the plausible assumption that the disjunction formed by (1) and (2) is true:

(3) Either there will be a sea battle tomorrow or there will not.

Aristotle seems to think that (3) expresses a necessary truth, although the same does not hold for (1) and (2) taken separately:

That every thing is or is not is necessary, and also that it will be or it will not be; however, certainly not that, taken separately, one or the other is necessary. I say for example that it is necessary that either there will be a sea battle tomorrow or there will not be a sea battle tomorrow, but it is neither necessary that a sea battle will occur tomorrow nor that it will not occur. Rather, it is necessary that it will occur or not. (Aristotle, De Interpretatione, 19a25-30)

Another aspect of Aristotle’s point is that the claim that (1) and (2) are neither true nor false does not reduce to the observation that we do not know whether there will be a sea battle tomorrow. Of course, we do not know whether there will be a sea battle tomorrow. The absence of truth or falsity that Aristotle ascribes to (1) and (2), however, is independent of our epistemic condition. The problem of future contingents concerns truth rather than knowledge. Compare (1) with “There was a sea battle yesterday.” We can easily imagine a situation in which one does not know whether a sea battle occurred the day before. Despite this, independently of whether one knows it or not, it seems right to say that “There was a sea battle yesterday” is either true or false. Its truth or falsity depends on what happened the day before. Aristotle suggests that (1) differs in this respect, because there is nothing that can make it true or false.

c. Bivalence, Excluded Middle, Fatalism

The problem of future contingents stems from the combination of three ingredients. Two of them are fundamental logical principles, namely, bivalence and excluded middle. The third is a controversial metaphysical doctrine, namely, fatalism.

Bivalence is the principle according to which truth and falsity are reciprocally exclusive and jointly exhaustive values. Classical logic relies on bivalence, in that it assumes that every sentence is true or false. If the letter p is used as a schematic expression that stands for any sentence, this assumption can be stated as follows:

(B) Either “p” is true or “p” is false.

For example, “p” can be replaced with “Snow is white,” “Snow is green,” or any other sentence.

Here, “any other sentence” includes not only simple sentences, such as those just considered, but also complex sentences, such as “Snow is not white,” “If snow is green, then it is not white,” and “Either snow is white or it is green.” The last three sentences are respectively a negation, a conditional, and a disjunction, in that they are formed by means of the connectives “not,” “if/then,” and “or.” In classical logic, complex sentences formed in this way are treated as truth functions of their constituents, which means that their truth or falsity is determined by the truth and falsity of their constituents. More precisely, the negation of a sentence is true if and only if the sentence is false, a conditional is true if and only if it is not the case that its antecedent is true and its consequent is false, and a disjunction is true if and only if at least one of its disjuncts is true. Thus, bivalence is consistent with the assumption that some connectives—such as “not,” “if/then,” and “or”—are truth-functional, that is, that the complex sentences formed by means of these connectives are truth functions of their constituents.

Excluded middle is the principle according to which every disjunction formed by a sentence and its negation is true. For instance:

(E) Either p or not-p

Classical logic justifies (E) in that it assumes that negation and disjunction are defined in the way explained. From that definition, it turns out that, no matter whether it is the case that p, one of the disjuncts of (E) must be true.

Finally, fatalism is the doctrine according to which nothing is contingent, that is, everything is either necessary or impossible:

(F) Either it is necessary that p or it is impossible that p

From (F) we get that if p, then it is necessary that p, and if not-p, then it is impossible that p. Suppose that p. Then the second disjunct of (F) is false, and hence the first must be true. Suppose that not-p. Then the first disjunct of (F) is false, and hence the second must be true. Note that here “necessary” and “impossible” are understood as “necessary given our past and our present” and “impossible given our past and our present,” that is, without taking into account what could happen if our past and our present were different. The problem of future contingents concerns future possibilities. It does not concern past or present possibilities.

The thesis that nothing is contingent is sometimes called “necessitarianism,” and the term “fatalism” often expresses the view that no one has free will, understood as the ability to do otherwise than what one actually does. However, even when a distinction is drawn between necessitarianism and fatalism, it is usually taken for granted that there is a close connection between them: If we are unable to do otherwise than we actually do, it is because what we do is necessary. In any case, independently of what “fatalism” means, (F) is controversial because it is at odds with free will. If nothing is contingent, then it is hard to see how one can be free to choose one course of action rather than another.

d. Two Arguments

The reasoning that emerges from the first quote in section 1.b suggests that bivalence entails fatalism. Suppose that (1) is either true or false. Assuming that the truth of (1) makes the sea battle necessary, and that the falsity of (1) makes the sea battle impossible, it follows that either it is necessary or it is impossible that there will be a sea battle. The argument may be phrased in schematic form as follows:

[BF]

(B) Either “p” is true or “p” is false.

(A1) If “p” is true, then it is necessary that p.

(A2) If “p” is false, then it is impossible that p.

So, (F) Either it is necessary that p or it is impossible that p.

[BF] is valid, in that its conclusion follows from its premises. Suppose that (B), (A1), and (A2) are true. Then one of the disjuncts of (B) is true. This means that either the antecedent of (A1) or the antecedent of (A2) is true, hence that either the consequent of (A1) or the consequent of (A2) is true. So (F) must be true. If one accepts the premises of a valid argument, one is compelled to accept its conclusion. Therefore, one cannot accept (B), (A1), and (A2) without accepting (F). By contraposition, if one takes (F) to be false, one must think that there is something wrong in the premises of [BF]. Aristotle thinks that the mistake lies in (B), as he takes (A1) and (A2) to be true.

Since (B) and (E) are distinct logical principles, rejecting (B) does not amount to rejecting (E). Aristotle is clearly aware of this fact, as shown by the second quote in section 1.2. However, there is another fact that he does not take into account, namely, that if one grants two apparently innocuous assumptions about truth and falsity, one can get bivalence from excluded middle. The argument is the following:

[EB]

(E) Either p or not-p.

(A3) If p, then “p” is true.

(A4) If not-p, then “p” is false.

So, (B) Either “p” is true or “p” is false.

[EB] is valid, as is [BF]. Here, again, the first premise is a disjunction, the second and third premises are conditionals in which the two disjuncts occur as antecedents, and the conclusion is a disjunction formed by the two consequents. This means that if (E), (A3), and (A4) are true, then (B) must be true.

Now the problem of future contingents becomes evident. According to [BF], bivalence entails fatalism. According to [EB], excluded middle entails bivalence. Therefore, from the combination of [EB] and [BF] we get that excluded middle entails fatalism. Since fatalism is unacceptable—or so assume Aristotle and many others after him—there must be something wrong with at least one of the premises of [BF] and [EB]. Determining which is the problem. Questions arise as to whether bivalence and excluded middle are sound logical principles, whether bivalence really entails fatalism, and whether excluded middle really entails bivalence. To solve the problem of future contingents is to provide satisfactory answers to these questions.

2. Three Logical Options

a. Neither Bivalence nor Excluded Middle

Now we will consider three distinct theses about bivalence and excluded middle, which constitute the main logical options available to solve the problem of future contingents. These three theses share two basic assumptions: One is that fatalism is wrong, and the other is that [BF] and [EB] are valid. Thus, they agree that (E) and (A1)-(A4) are not all true. If (E) and (A1)-(A4) were all true, on the second assumption it would follow that (F) is true, contrary to the first assumption.

The first option—option 1—is to deny both bivalence and excluded middle. According to this option, bivalence does not hold. Since (A1) and (A2) are true, if (B) were true, then (F) would be true. Excluded middle does not hold either, for (A3) and (A4) are just as true as (A1) and (A2). So, if (E) were true, then (B) would be true as well. In other terms, [BF] and [EB] are alike in that their first premise is false.

In the debate over future contingents, the theory that best expresses option 1 is Lukasiewicz’s three valued logic (Lukasiewicz 1970). This theory, which intends to provide a coherent interpretation of Aristotle, shares with classical logic the tenet of truth-functionality; that is, it takes for granted that the value of a complex sentence is determined by the values of its constituents. However, it differs from classical logic in that it contemplates three values instead of two: truth, falsity, and indeterminacy.

Lukasiewicz rejects bivalence because he thinks that some sentences are indeterminate. A sentence is indeterminate when the way things are does not make it true and does not make it false. For example, (1) is indeterminate, because no fact or event today can make it true or false.

Lukasiewicz also rejects excluded middle. In his logic, the negation of an indeterminate sentence is itself indeterminate. For example, (2) is indeterminate, for its truth would amount to the falsity of (1), and its falsity would amount to the truth of (1). Moreover, a disjunction is indeterminate if both its disjuncts are indeterminate. So (3) is indeterminate. In general, every disjunction formed by an indeterminate sentence and its negation turns out indeterminate.

The rejection of bivalence is an essential feature of any three-valued logic, for what defines such a logic is just the hypothesis that there are three values instead of two. The rejection of excluded middle, instead, is not essential in this sense. Assuming that there are three values, and that some connectives are truth-functional, there is no unique way to define those connectives. In particular, negation and disjunction could be so defined as to validate excluded middle.

However, it seems that there are no independent reasons for changing the definitions of negation and disjunction proposed by Lukasiewicz. First, it would make little sense to stipulate that the negation of an indeterminate sentence is true rather than indeterminate. Since (1) and (2) are about the same event, it is hard to see how (2) can be true if (1) is indeterminate. Second, it would make little sense to stipulate that a disjunction formed by two indeterminate sentences is true rather than indeterminate, because in that case, “Either there will be a sea battle tomorrow or it will rain tomorrow” would be true, which seems unreasonable.

On the other hand, from the perspective of a three-valued logic it would be impermissible to claim that some negations of indeterminate sentences are indeterminate while others are true, or that some disjunctions formed by indeterminate sentences are indeterminate while others are true. This would amount to giving up truth-functionality, which is essential to any such logic. To assume that “not” and “or” are truth functional is to assume that the value of a negation or a disjunction—no matter whether truth, falsity, or indeterminacy—solely depends on the value of its constituents.

Thus, although Lukasiewicz’s logic is not the only three-valued logic that we can imagine, it is reasonable to think that no other three-valued logic can provide a better account of future contingents. Accordingly, we assume that three-valued logic invalidates both bivalence and excluded middle.

One merit of option 1 is that it accepts [EB]. This is plausible, given that [EB] is valid and that (A3) and (A4) express principles about truth and falsity that seem evident. According to [EB], if one accepts (E), one must also accept (B). So, by contraposition, if one rejects (B), one must also reject (E).

The rejection of excluded middle, however, constitutes a flaw of option 1, for it is hard to believe that a disjunction formed by a sentence and its negation, such as (3), is not true. Even though we do not know what will happen tomorrow, it seems certain that either there will be a sea battle tomorrow or there will not.

Another problem that affects option 1—the assertion problem—derives from the rejection of bivalence. As we have seen in section 1.a, the ordinary use of language suggests that some assertions about the future are correct, and hence that some future contingents are true. For example, “The sun will rise tomorrow” seems true. If all future contingents are indeterminate, however, this sentence cannot be true, so it is not clear why one should assert it. Those who adopt option 1 must explain how we can make apparently correct assertions by using future contingents.

b. Excluded Middle without Bivalence

The second option—option 2—is to deny bivalence but accept excluded middle. According to this option, bivalence entails fatalism, but excluded middle does not entail fatalism, because excluded middle does not entail bivalence. In other words, the argument that does not work is [EB], for one can accept (E) without accepting (B). This is the most plausible reading of Aristotle, advocated by Boethius, Peter Auriol, and many other scholars.

To justify option 2, one must explain why [EB] does not work. That is, one must explain why (A3) and (A4) are not true. Supervaluationism, a theory elaborated by Thomason (1984) on the basis of ideas expressed by Prior (1967) and Van Fraassen (1966), provides one coherent explanation. Supervaluationism rests on the assumption that future-tense sentences can be evaluated as true or false relative to possible futures. For example, in some possible futures there will be a sea battle tomorrow, while in others there will be peace. (1) is true in a future of the first kind, while it is false in one of the second kind. According to supervaluationism, to ask whether a future-tense sentence is true or false is to ask whether it is true or false in any possible future. This idea can be phrased in a precise way if we define a “history” as a whole possible course of events, that is, a course of events that includes a possible future, and we assume that, for any future contingent “p,” uttered at a moment m, there is a set of accessible histories such that in each of them “p” is either true or false at m. Truth in the non-relative sense—truth simpliciter—is defined in terms of truth relative to histories: “p” is true at m if and only if it is true at m in all the histories of the set. Similarly, “p” is false at m if and only if it is false at m in all the histories of the set. The name of the theory comes from this idea. If we call “valuation” each attribution of value to a sentence relative to a history, we can call “supervaluation” an attribution of value to the sentence that takes into account all the valuations.

Supervaluationism draws a principled distinction between bivalence and excluded middle. Consider (1). Since (1) is true today in some histories and false today in other histories, (1) is neither true nor false today. The same goes for (2). In general, future contingents are neither true nor false, because they are true in some histories and false in others. Therefore, bivalence does not hold. Now consider (3). In every history, either the first disjunct is true today, or the second disjunct is true today. Consequently, (3) is true today. In general, a disjunction formed by a sentence and its negation is always true. Therefore, excluded middle holds.

Note that this account of excluded middle involves an essential duality with respect to truth-functionality. There is a sense in which (3) is a truth function of its constituents, the sense in which, for any history h, (3) is true in h if and only if one of its disjuncts is true in h. There is also a sense in which (3) is not a truth function of its constituents, the sense in which (3) is true simpliciter even though neither of its disjuncts is true simpliciter. Truth-functionality holds at the level of truth relative to histories, but not at the level of truth simpliciter. This makes supervaluationism a partially non-classical theory.

Now let us go back to (A3) and (A4). Supervaluationism provides a motivation for rejecting (A3). Suppose that “p” is a future contingent that is true at m in h. Then the antecedent of (A3) is true at m in h. Its consequent, however, is not true at m in h, because in order to be true at m in h, “p” should be true at m in all histories. Therefore, (A3) is not true at m in h. It follows that (A3) is not true at m. A similar reasoning motivates the rejection of (A4). Suppose that “not-p” is a future contingent that is true at m in h. Then the antecedent of (A4) is true at m in h. Its consequent, however, is not true at m in h, because “p” is not false at m in all histories. So (A4) is not true at m in h. It follows that (A4) is not true at m.

Although this explanation is consistent with the supervaluationist definition of truth, it is not entirely satisfactory, or so one might argue. The rejection of (A3) and (A4) speaks against supervaluationism, for (A3) and (A4) are very plausible assumptions. It seems trivial that “Snow is white” is true if snow is white, and that “Snow is white” is false if snow is not white. Just because it seems trivial, it should turn out true.

Independently of (A3) and (A4), the supervaluationist definition of truth may cause some perplexity. Some might contend that this definition mistakenly identifies truth with necessity. To say that “p” is true is not the same thing as to say that it is necessary that p, or so it appears. Imagine that Bob and Rob are at the racecourse and that Bob bets on Frisco. Bob and Rob are indeterminists, so they believe that it is possible that Frisco will win and that it is possible that Frisco will not win. In the middle of the race, Rob says to Bob: “Don’t worry, Frisco will win,” to which Bob replies, “I really hope that’s true.” Presumably, what Bob hopes is not that his philosophical convictions are false; that is, he does not hope that Frisco’s victory is necessary. To hope that Frisco will win is not the same thing as to hope that it is necessary that Frisco will win. It is consistent to hope that Frisco will win and think that it is possible that Frisco will not win. It thus seems that the truth of the sentence uttered by Rob does not amount to its truth in all histories.

The intuitive difference between the claim that “p” is true and the claim that it is necessary that p becomes even clearer when we consider retrospective attributions of truth. Suppose that Frisco really wins and that at the end of the race Bob exults: “You were right! It was true!” What Bob wants to say is that the sentence uttered by Rob during the race was true. However, the supervaluationist definition of truth entails that that sentence was neither true nor false, as it was false in some histories. This seems wrong, because the truth that Bob retrospectively attributes to the sentence uttered by Rob does not rule out its possible falsity. It is consistent to think that what Rob said was true and that, in the moment in which he said it, it was possible that Frisco would not win. Again, it seems that the truth of the sentence uttered by Rob does not amount to its truth in all histories.

Supervaluationism is not the only theory in line with option 2. Another theory, advocated by Belnap and others (Belnap, Perloff, and Xu 2001), implies that there is no such thing as truth simpliciter. Future contingents are true or false only relative to histories, because it is only relative to histories that they express a determinate content. Suppose that (1) is uttered today. Since at the moment of the utterance different futures are possible, each of which includes a different tomorrow, the word “tomorrow” in (1) does not denote a determinate moment, which means that (1) does not express a determinate content. Therefore, it makes no sense to ask whether (1) is true or false today. The only meaningful question that can be asked is whether (1) is true or false relative to a given history. This theory shares with supervaluationism the assumption that future contingents can be evaluated as true or false relative to possible futures, but does not identify truth simpliciter with truth in all histories, because it rejects the very idea of truth simpliciter.

MacFarlane (2003, 2008) has proposed a third theory. Just like Belnap and others, MacFarlane claims that there is no such thing as truth simpliciter. In this case, the motivation provided is that a parameter of evaluation other than the history has to be taken into account. According to MacFarlane, the value of a future contingent uttered at a given moment can vary depending on the context of assessment, that is, on the moment in which it is evaluated. Suppose that (1) is uttered today and that tomorrow there is a sea battle. Today, at the moment of the utterance, (1) is neither true nor false. Tomorrow, however, in the middle of the sea battle, (1) is true. Consequently, the same sentence, as uttered at a given moment, can have different values in different contexts of assessment.

Both theories reject bivalence: Future contingents are not true or false, because they are not true or false in some absolute sense. Moreover, they both preserve excluded middle, because they make it valid in a relative sense. For example, (3) is always true today, in that it is true today in every history or in any context of assessment. These two theories thus have much in common with supervaluationism.

Leaving specific problems aside, both theories considered run into the assertion problem, as they reject bivalence. If one claims that “The sun will rise tomorrow” is neither true nor false, independently of the motivation adopted, one has to explain why it seems correct to assert this sentence.

To conclude, option 2 differs from option 1 in that it saves excluded middle, which is a merit. Its main flaws are essentially two. One is that it must provide a plausible definition of truth that—among other things—enables us to explain what is wrong with [EB]. The other is that it must address the assertion problem, which it shares with option 1.

c. Both Bivalence and Excluded Middle

The third option—option 3—is to accept both bivalence and excluded middle. According to this option, excluded middle entails bivalence, but bivalence does not entail fatalism. In other terms, the argument that does not work is [BF], for one can accept (B) without accepting (F).

To justify option 3, one must explain why [BF] does not work, that is, it must be explained why (A1) and (A2) are not true. One way to do so is to endorse Ockham’s idea that one of the possible futures is the actual future, that is, the way things will actually go. In his Tractatus de praedestinatione et praescientia Dei respectu futurorum contingentibus, which aims to explain how divine foreknowledge is compatible with the contingency of events, Ockham draws a distinction between truth and determinate truth. The former is understood as truth in the actual future, the latter is understood as truth in all possible futures. According to Ockham, future contingents are true or false, even though they are not determinately true or determinately false (1978).

The distinction between truth and determinate truth—which has been defended by Von Wright (1984), Lewis (1986) and Horwich (1987), among others—can be illustrated by means of the two examples considered in section 2.b. Suppose, as before, that Rob says to Bob, “Don’t worry, Frisco will win!” and that Bob replies, “I really hope that’s true.” As we have seen, it seems that Bob’s hope is not that Frisco’s victory is necessary. One obvious candidate for what he does hope for is the following: What Bob hopes is that Frisco will actually win, namely, that the possible future that will become reality is a future in which Frisco wins. Now, suppose that Frisco really wins and that Bob says to Rob: “You were right! It was true!” As we have seen, it seems correct to say that the sentence uttered by Rob was true, even though it was possible that Frisco would not win. If the truth of that sentence does not amount to its truth in all possible futures, it is unclear what it amounts to. Again, one obvious answer is that it amounts to the fact that Frisco actually won. Thus, a sentence can be true without being determinately true, if it is true in the actual future but false in some other future.

The theory that we will call Ochkamism is inspired by Ockham in that it defines truth in terms of the actual future. Ockhamism, just like the theories considered in section 2.b, adopts a relative notion of truth: A future contingent “p,” uttered at a moment m, can be evaluated as true or false in a set of accessible histories. Truth in the non-relative sense—truth simpliciter—is defined in terms of this notion: “p” is true at m if and only if “p” is true at m in the actual history. Similarly, “p” is false at m if and only if “p” is false at m in the actual history (Øhrstrøm 2009; Rosenkranz 2012; Iacona 2013, 2014; Wawer 2014; Malpass and Wawer 2018).

If truth is defined in terms of the actual history, then truth does not entail determinate truth. This is why Ockhamism rejects (A1) and (A2). Suppose that “p” is true at m in the actual history. In this case, the antecedent of (A1) is true at m, while its consequent is false at m. Similarly, suppose that “p” is false at m in the actual history. In this case, the antecedent of (A2) is true at m, while its consequent is false at m.

This prompts the question of whether it makes sense to say that one of the possible futures is the actual future. The very idea of a unique actual future may easily raise doubts and misgivings. If one among the many possible futures is the actual future, it is unclear how the other futures can be equally possible, given that they will not become real. In other words, it seems impossible that what will happen is not predetermined. In order to adequately justify the distinction between truth and determinate truth, some convincing responses to these questions must be provided.

In sum, option 3 rescues bivalence and excluded middle, in accordance with classical logic. Moreover, it does not run into the assertion problem, because it implies that some future contingents are true, so it can explain the apparent correctness of some assertions about the future. The most problematic aspect of this option is the very idea of the actual future.

d. Further Considerations

The three logical options considered so far define the main positions within the debate on future contingents. Since these options do not exhaust the logical space of possibilities, this section dwells briefly on the only combination this article has not considered, namely, bivalence without excluded middle.

One way to give substance to this option, which comes from Pierce as interpreted by Prior, is the following: Future contingents are all false, because they describe future events as inevitable. For example, (1) and (2) are both false, because (1) says that there will necessarily be a sea battle tomorrow, while (2) says that there cannot be a sea battle tomorrow. Therefore, excluded middle does not hold: (3) is false, for both its disjuncts are false. Yet bivalence holds, because every sentence, including future contingents, is either true or false (Øhrstrøm and Hasle 1995; Prior 1967; Todd 2016).

The same problems that affect option 1 affect this position. First, the rejection of excluded middle is difficult to accept. (3) seems true, not false. Second, the assertion problem is still there. If all future contingents are false, then “The sun will rise tomorrow” cannot be true, in spite of the fact that it seems correct to assert it.

Independently of these two problems, the idea that all future contingents are false gives rise to further troubles. Consider (1) and (2). On the assumption that (2) is the negation of (1), as its syntactic structure suggests, it is unreasonable to think that (1) and (2) are both false. So, the most plausible way to claim that (1) and (2) are both false is to say that (2)—contrary to what its syntactic structure suggests—is not the negation of (1). The negation of (1) would rather be “It is not the case that there will be a sea battle tomorrow.” On the hypothesis that (2) and “It is not the case that there will be a sea battle tomorrow” express different contents, it is consistent to say that the former is false while the latter is true. Note, however, that this way, “Either there will be a sea battle tomorrow or it is not the case that there will be a sea battle tomorrow” turns out true. Thus, there is a clear sense in which excluded middle holds: If “It is not the case that there will be a sea battle tomorrow” is the negation of (1), the sentence that instantiates (E) is “Either there will be a sea battle tomorrow or it is not the case that there will be a sea battle tomorrow,” not (3). Moreover, we still need an explanation of why (2) and “It is not the case that there will be a sea battle tomorrow” express different contents, given that they seem to say exactly the same thing.

These troubles explain the scarce popularity of the option just considered. The debate on future contingents almost never sees the acceptance of bivalence combined with the rejection of excluded middle, because most thinkers take it for granted that bivalence is at least as controversial as excluded middle.

3. Three Metaphysical Views

a. Past, Present, and Future Entities

So far, we have considered three logical options that differ with respect to bivalence and excluded middle. Now we will address the key metaphysical issue that underlies the problem of future contingents: what there is in front of us.

Let us first introduce four basic ontological conceptions of time, that is, four conceptions of the existence of past, present, and future entities. Past entities and future entities resemble present entities in some respects but not in others. On the one hand, there is a sense in which Caesar is like us and unlike the Abominable Snowman: Ceasar was a real person, while the Abominable Snowman has never existed. The same goes for future children, who will be real persons just like us. On the other hand, there is a sense in which Caesar is not like us: We are here, while he is no longer here. Similarly, future children are not here yet. The four conceptions considered in this article weigh these similarities and differences in different ways.

Presentism is the conception according to which only present entities exist. We exist, but Ceasar and future children do not exist. Existing and being present are the same thing. Imagine an incredibly big and incredibly thin slice of salami. The slice is the present, and we are in it. Behind us there is nothing, because the past does not exist, and ahead of us there is nothing, because the future does not exist. This conception—which is defended by Prior (1970), Bigelow (1996), and Bourne (2006), among others—is represented in figure 1.Figure 1

Figure 1: Presentism

The growing block theory, alternatively, is the conception according to which past and present entities exist, but future entities do not exist. Ceasar exists, we exist, but future children do not exist. This conception—defended by Broad (1923), Tooley (1997), and Correia and Rosenkranz (2018), among others—describes reality as a totality that constantly increases as time passes. In figure 2, the slice of salami that represents the present is attached to the portion of salami that precedes it, the past.Figure 2

Figure 2: Growing block

A third conception that is purportedly opposite to the growing block theory is the shrinking block theory. According to this theory, which is not widely accepted (though see, for example, Casati and Torrengo 2011), present and future entities exist, but past entities do not exist. We exist, future children exist, but Ceasar does not exist. Reality is what is left, so to say, and the future is constantly eroded as time passes. In figure 3, the slice of salami that represents the present is attached to the portion of salami that follows it, the future.Figure 3

Figure 3: Shrinking block

Finally, eternalism is the view according to which past, present, and future entities exist. We exist, and the same goes for Ceasar and future children. This conception is defended by Williams (1951), Taylor (1955), Smart (1963), Putnam (1967), Mellor (1998), and Sider (2001), among others. In figure 4, the slice of salami that represents the present is part of a whole salami, a history, which may be conceived of as a sequence of moments.

Figure 4

Figure 4: Eternalism

While the first three conceptions are essentially dynamic, in that they imply that the passage of time is metaphysically real, eternalism may be understood either dynamically, assuming that the present really moves along the line of time, or statically, assuming that the experience of the passage of time is merely illusory. On both interpretations, the idea that underlies eternalism is that temporal relations are somehow similar to spatial relations. For example, Turin, Milan and Venice are located on three points ordered along the west-east axis. Although each of these three cities offers a distinct perspective on the other two, the spatial relations among them—the order in which they are located along the west-east axis—do not vary with the point of observation. According to eternalism, the same goes for temporal relations. Being present is like being in Milan. There is no ontological difference between Caesar, us, and future children, just as there is no ontological difference between Turin, Milan, and Venice (see the time).

The classification just presented will help with understanding the three metaphysical views considered in the next three sections. As these sections show, these three views can be associated with options 1-3, although there is no necessary connection between them. Each view provides a distinct answer to the question of what is there ahead of us.

b. No Future

The first view—the no-future view—says that there is absolutely nothing ahead of us: The future does not exist. Certainly, many things will happen, and it makes perfect sense to talk about such things. However, what will happen will exist only when it will happen; it does not exist now. When it will happen, it will no longer be future.

Presentism and the growing block theory entail the no-future view. Although these two conceptions differ with respect to the question of whether the past exists, they agree on the non-existence of the future. By contrast, the shrinking block theory and eternalism contradict the no-future view. Although these two conceptions differ with respect to the question of whether the past exists, they agree on the existence of the future. Therefore, the no-future view can be maintained either in a presentist perspective or in a growing-block perspective.

Of the three logical options considered in section 2, the one that best suits the no-future view is option 1. If the future does not exist, there is nothing that can make future-tense sentences true or false. For example, there is nothing that can make (1) and (2) true or false. It is thus sensible to claim that future-tense sentences violate bivalence. This is probably what Lukasiewicz had in mind, although he did not explicitly address the distinction between presentism and growing block theory.

Perhaps it is also sensible to claim that future-tense sentences violate excluded middle. If nothing can make true (1) or (2), the same goes for (3). The “perhaps” is due to the fact that the inference from the absence of truth of (1) and (2) to the absence of truth of (3) requires a further constraint that plays a crucial role in three-valued logic, namely, truth-functionality. Assuming that a disjunction is true only if one of its disjuncts is true, from the absence of truth of (1) and (2) we can infer the absence of truth of (3). Without that assumption, instead, the inference is not legitimate. As we have seen in section 2.2, supervaluationism differs from three-valued logic precisely in that it gives up truth-functionality to save excluded middle.

The no-future view—especially in the growing block version—provides a metaphysical substratum for the idea that future-tense sentences are sui generis from the logical point of view. The difference at the logical level can be explained by a difference at the metaphysical level: The past and the present exist, whereas the future does not exist. This is not to say that, strictly speaking, the no-future view entails that idea. For example, Correia and Rosenkranz (2018) argue that the growing block theory is consistent with bivalence.

c. Many Futures

The second and the third view differ from the first in that they entail the existence of future entities. Although this makes them compatible both with the shrinking block theory and with eternalism, they are usually framed in an eternalist perspective. In such a perspective, the contingency of a future event cannot be conceived of in terms of absence, as in the no-future view, because an event cannot be future without existing. Rather, it will be conceived of in terms of presence in some but not in all possible futures. This is why the second and the third view contemplate a plurality of histories. A history is a possible world, that is, a totality of past, present, and future entities that is completely defined in its spatial and temporal properties.

The second view—the many-futures view—says that there are many futures ahead of us, that is, many possible continuations of the present. These continuations are like branches that depart from the same trunk, and they are metaphysically on a par, that is, they all exist and they are all actual (or none of them is). Figure 5 illustrates the many-futures view by recalling the salami analogy. The slice is the present, as in the previous figures, but there are two portions of salami on the right, that is, two possible continuations of the present. Each of these two portions, together with the left portion, forms a whole salami. Therefore, the slice belongs to two distinct salami.

Figure 5

Figure 5: Branching

The idea illustrated in figure 5 can be represented in a more abstract way by using simple lines. In figure 6, h1 and h2 are histories, while m0, m1 and m2 are moments. m0 belongs both to h1 and to h2. Instead, m1 belongs only to h1, and m2 belongs only to h2. While m0 precedes both m1 and m2, m1 and m2 are unrelated, in that neither of them precedes the other. Diagrams of this kind, introduced by Kripke and Prior, are often employed in temporal logic to represent the set of future possibilities (Prior 1967).

Figure 6

Figure 6: One past, one present, two futures

The case of the sea battle can be described in terms of this figure. Suppose that m0 is today, that is, the moment at which (1) and (2) are uttered. h1 and h2 are histories that lead to different tomorrows: m1 is a peaceful tomorrow, while m2 is a tomorrow in which there is a sea battle. h1 and h2 have a part in common, that is, our past until today. The two portions of h1 and h2 that follow m0 are distinct possible futures. The contingency of the sea battle consists precisely in the existence of these futures.

Note that figure 6 shows two distinct tomorrows instead of one. Each of these two tomorrows belongs only to one history. However, this does not mean that it makes no sense to describe m1 and m2 as simultaneous. On the contrary, assuming that there is an absolute temporal axis, that is, that time can be measured from a point of view that is external to the histories, we can say that m1 and m2 are located at the same point along that axis. If we call instant an absolute temporal unit, definable as a set of equivalent moments, we can say that two moments that belong to different histories are in the same instant. In figure 7, i0 is the present instant, that is, the instant that includes m0, and i1 is the instant that includes m1 and m2.

Figure 7

Figure 7: The sea battle

The many-futures view is clearly in line with option 2. In the framework just sketched, future contingents can be evaluated as true or false at moments relative to histories. For example, (1) is true at m0 in h2 but false at m0 in h1. Similarly, (2) is true at m0 in h1 but false at m0 in h2. According to the supervaluationist definition of truth, this entails that (1) and (2) are neither true nor false at m0, so that bivalence does not hold. Instead, excluded middle holds. (3) is true at m0, for it is true at m0 both in h1, given that (2) is true at m0 in h1, and in h2, given that

(1) is true at m0 in h2. The two further theories considered in section 2.b fit the many-futures view equally well, in that they employ the same notion of truth relative to histories.

d. One Future

The third view—the one-future view—says that there is one future ahead of us, our future. This view has two versions. According to one of them—the thin red line—many possible futures depart from our present, but these futures are not metaphysically on a par because only one of them is actual. According to the other—divergence—we have a single future because we belong to a single history, the actual history, although there are other histories that are exactly like our history up to the present but have a different future. The key difference between the two versions concerns the possibility of overlap. To endorse the thin red line is to think that two histories can overlap, that is, that they can have some part in common. To endorse divergence, instead, is to conceive histories as entirely disconnected totalities. Here we will focus on divergence, although what will be said applies, mutatis mutandis, to the thin red line.

Figure 8 illustrates divergence. Imagine that we are in the salami below, and that the left portion of the salami above—the portion that precedes the slice—is identical to the left portion of our salami, but that the right portion of the salami above—the portion that follows the slice—differs from the right portion of our salami. In this case the two salami are divergent histories.

Note that figure 8 shows two presents, each of which belongs to a single history. This is not to say that it makes no sense to describe such moments as simultaneous. As in the many-futures view, simultaneity can be defined in terms of instants. Figure 9 represents the two histories considered above as horizontal lines, h1 and h2, and represents the instant that the two presents have in common as a vertical line that intersects h1 and h2. Our present, m0, is in h1 and differs from m1, which is in h2. However, m0 and m1 are simultaneous in the sense that they belong to the same instant i0.

Figure 8

Figure 8: Divergence

 

Figure 9

Figure 9: Two pasts, two presents, two futures.

The question is who the individuals in the other history, who are exactly like us up to now, are. Lewis, who defends divergence, calls such individuals counterparts. If we are in h1, then in h2 there are other individuals who are our counterparts. Just as we have a future, the right portion of h1, our counterparts have their own future, the right portion of h2 (Lewis 1986).

Now let us go back to the sea battle. Figure 10 represents two histories h1 and h2 that are exactly alike up to i0 but then differ. m0 and m1 are two distinct but qualitatively identical todays, each of which has its own tomorrow: m2 is a peaceful tomorrow, while m3 is a tomorrow in which there is a sea battle. Therefore, (1) is true at m1, while it is false at m0. Since m1 and m0 belong respectively to h2 and h1, this is to say that (1) is true in h2, while it is false in h1. Whether (1) is true or false simpliciter depends on which of the two histories is the actual history. If we are in m0 we will have peace, whereas if we are in m1 we will find ourselves in the middle of a sea battle.

Figure 10

Figure 10: The sea battle

It is important to note that being in a given history does not mean being in a position to discern that history from other histories. Suppose that we are in h1. Since m0 is qualitatively identical to m1, and the same goes for any moment that precedes m0, for us h1 is indistinguishable from h2. So at i0 we are not in a position to know whether we are in h1 or in h2. Consequently, we are not in a position to know whether our future includes m2 or m3. In a way, we do not know what will happen tomorrow because we do not know where we are.

The one-future view suits option 3. The framework just sketched preserves bivalence. Suppose, as before, that (1) is true at m1 and false at m0. Then, no matter which of the two histories is the actual history, (1) is either true or false. This is not to say that (1) is determinately true or determinately false. Assuming that determinate truth at a moment amounts to truth at all moments in the same instant, and that determinate falsity at a moment amounts to falsity at all moments in the same instant, (1) is neither determinately true at m1 nor determinately false at m0. Excluded middle is preserved as well. (3) is true both at m0 and at m1. Therefore, it is determinately true.

4. The Open Future

a. Alternative Possibilities

Most discussions on future contingents take for granted that fatalism is wrong. Despite this, it is not obvious what the right view is. The thought that underlies the rejection of fatalism is often expressed by saying that the future is open. The contemporary literature on future contingents, widely employs the metaphor of openness to characterize the view that the future is unsettled. Yet it is possible to understand openness in more than one way. This last section provides some clarifications about the claim that the future is open.

A simple and straightforward way to interpret the claim that the future is open is to define openness in terms of the existence of alternative possibilities: To say that the future is open is to say that, for some “p,” it is possible that p and it is possible that not-p. This interpretation is simple and straightforward because it equates the claim that the future is open with the pure negation of fatalism. As it turns out from section 1.c, fatalism is the claim that, for every “p,” either it is necessary that p or it is impossible that p. Consequently, its negation is the claim that, for some “p,” it is neither necessary nor impossible that p, that is, it is possible that p and it is possible that not-p.

If the openness of the future is understood in terms of the existence of alternative possibilities, then it is consistent with the three metaphysical views outlined in section 3. If one endorses the no-future view, one can say that, although there is presently nothing ahead of us, it is possible that what will exist is such that p and it is possible that what will exist is such that not-p. If one endorses the many-futures view, one can say that there are possible futures in which p and possible futures in which not-p. The same goes for the one-future view, even though in the case of divergence the possible futures have distinct pasts and distinct presents.

b. Indetermination

Another way to interpret the claim that the future is open is to define openness in terms of indetermination, understood as absence of determination: To say that the future is open is to say that nothing determines the future. This can mean two things: either that the future is not determined by some divine entity, or that the future is not determined by the laws of nature. Here we focus on the second reading, which became widespread by the early 21st century, although these considerations apply to the first as well.

The idea that every event is determined by the laws of nature goes back to antiquity and has been widely discussed in modern and contemporary philosophy. According to this idea, every event follows as an effect from some cause in accordance with the laws of nature. Determination may be defined as a relation between states, understood as global conditions in which the universe can be at an instant. Given a state S that obtains at i0 and given a state S0 that obtains at i1, S determines S0 if and only if the obtaining of S at i0, together with the laws of nature, entails that S0 obtains at i1. Determinism is the view that, for every instant, the state that obtains at that instant is determined by the states that obtained at previous instants (Hoefer, 2003).

None of the three metaphysical views outlined in section 3 entails determinism. Suppose that i0 is the present instant and that S is the state of the universe at i0. According to the no-future view, given an instant i1 later than i0, nothing exists in i1, even though when we will be in i1, another state S0 will obtain. The no-future view says nothing about the relation between S and S0, so it is consistent with the hypothesis that S does not determine S0. Now consider the many-futures view. Suppose, as in figure 7, that m0 is the present moment and that m1 and m2 are future moments that belong to i1. If S is the state that obtains at m0, while S0 and S00 are the states that obtain respectively at m1 and m2, then S determines neither S0 or S00, for it is compatible both with S0 and with S00. Finally, consider the one-future view. Suppose, as in figure 10, that m0 and m1 are in i0, and that m2 and m3 are in i1. If S is the state that obtains at m0 and m1—in that h1 and h2 are identical up to i0 while S0 and S00 are the states that obtain respectively at m2 and m3—then S determines neither S0 or S00, for it is compatible both with S0 and with S00.

It is important to note that indetermination is not the same thing as indeterminateness, understood as absence of determinateness. If determinateness is the property that a possible future has when it is completely defined in its spatial and temporal properties, then indetermination does not entail indeterminateness. It is consistent to claim, as in the case of branching or divergence, that indetermination holds because there are many possible futures, each of which is completely defined in its spatial and temporal properties. Indetermination and indeterminateness are independent properties.

c. Causal Power

A third way to interpret the claim that the future is open is to define openness in terms of causal power: To say that the future is open is to say that we can affect the future, in that our present actions have future effects. For example, if tonight we set the alarm on our phone to 7 a.m., the sound that the phone will emit tomorrow at 7 a.m. is an effect of the movements that we perform tonight.

The idea that our present actions have future effects is obviously consistent with the three metaphysical views outlined in section 3. In each of the three cases, it makes perfect sense to say that an event which occurs at a given time causes another event that occurs at a later time.

Note that the past does not depend on us in the same sense, because our present actions do not have past effects. This asymmetry can be described in terms of counterfactual dependence, as Lewis has suggested. The future counterfactually depends on the present, because it would be different if the present were different. Suppose that tonight we set the alarm on our phone to 7 a.m. It is correct to say that, if the alarm were not set, the phone would not emit any sound tomorrow at 7 a.m. Instead, the past does not counterfactually depend on the present, because it would not be different if the present were different. If the alarm were not set, what happened yesterday would remain exactly the same (Lewis 1979).

The claim that we can affect the future must not be confused with the claim that we can change the future, that is, that we can replace the future with another future. It is one thing is to say that a future event, such as the sound that the phone will emit tomorrow at 7 am, is caused by a present event; it is quite another thing is to say that a future event can be replaced by a different future event. The claim that we can change the future is hardly intelligible, or so it appears to most philosophers (an exception is Todd 2016). In any case, this claim seems incompatible with the three metaphysical views outlined in section 3. If the no-future view is true, then the future does not exist, so nothing can be changed. If the many-futures view is true, then there are many possible futures, so it makes no sense to say that we can change “the” future. And in any case, each of the possible futures is essentially identical to itself. Finally, if the one-future view is true, then there is a unique future, which cannot be changed.

d. Other Definitions

As it turns out from sections 4.a-4.c, there are three plausible interpretations of the claim that the future is open: The first is that, for some “p,” it is possible that p and it is possible that not-p; the second is that the future is not determined; and the third is that we can affect the future. Each of these interpretations is consistent with the three metaphysical views outlined in section 3: No matter whether one endorses the no-future view, the many-futures view, or the one-future view, one can coherently claim that the future is open. Since options 1-3 accord, respectively, with the no-future view, the many-futures view, and the one-future view, this suggests that the claim that the future is open, on the three interpretations considered, is compatible with any solution to the problem of future contingents.

Of course, the three interpretations considered are not the only admissible interpretations. Other interpretations are possible. Nothing prevents us from defining openness in terms of some specific logical option or metaphysical view. The question then arises of whether the future is really open in the sense defined. Merely stipulating that openness amounts to this or that condition does not provide any reason to think that the stipulation captures some pre-theoretical intuition.

Some philosophers have suggested that the openness of the future amounts to the failure of bivalence for future-tense sentences (as in Markosian 1995). On this interpretation, the claim that the future is open yields substantive consequences, for it licenses options 1 and 2 while it rules out option 3. However, as some have observed (Barnes and Cameron 2009; Besson and Hattiangadi 2014), it is controversial whether the future is open in this sense. Aristotle needed an argument to show that bivalence does not hold for future contingents.

Other philosophers have suggested that the openness of the future amounts to the many-futures view: To say that the future is open is to say that there are multiple branching futures which are metaphysically on a par (as in MacFarlane 2003). On this interpretation, again, the claim that the future is open yields substantive consequences, for it rules out both the no-future view and the one-future view. However, it is controversial whether the future is open in this sense.

The controversy emerges clearly in the dialectic between branching and divergence. According to the advocates of the many-futures view, divergence does not preserve openness. Suppose that Betty wonders whether she can become an internationally acclaimed photographer. As far as divergence is concerned, the answer is affirmative if Betty will become a door-to-door cosmetics seller, but there is a history in which another individual very similar to Betty—call her Betty*—will become an internationally acclaimed photographer. The fact, however, is that what Betty wonders—what concerns her—is whether she, Betty, can become an internationally acclaimed photographer, not whether another person has that opportunity. It does not seem that Betty’s future be open if it only includes the sale of cosmetics. The openness of the future seems to imply that the alternative possibilities not only exist, but that they exist for the same individuals.

To this objection it might be replied that divergence does not deny that one and the same individual has alternative possibilities. Let us assume that “Betty can become an internationally acclaimed photographer” is true. Insofar as divergence explains the truth of this sentence in terms of the existence of a history in which Betty* becomes an internationally acclaimed photographer, the individual to whom it is correct to attribute the modal property of possibly becoming an internationally acclaimed photographer is Betty, not Betty*. Certainly, this explanation cannot be understood as a description of what Betty has in mind when she wonders whether she can become an internationally acclaimed photographer. However, the same holds for any other explanation of the same fact. Just as Betty does not think about Betty*, she does not think that she inhabits two histories that share a common segment and branch towards the future.

It is difficult to judge who is right. The objection against divergence stems from a line of thought that goes back to Kripke and that is antithetical to the theory of counterparts defended by Lewis. According to this line of thought, the truth or falsity of a sentence that attributes a modal property to an individual depends on what happens to the same individual in possible worlds other than the actual world. For example, Kripke claims that the sentence, “It might have been the case that Aristotle was not a philosopher,” is true because there are possible worlds in which Aristotle, the same Aristotle, was not a philosopher. The question of which of these two positions is preferable concerns possible worlds in general, and cannot be settled simply by appealing to intuitions.

5. References and Further Reading

  • Barnes, E. and Cameron, R. 2009. The Open Future: Bivalence, Determinism and Ontology. Philosophical Studies, 146:291–309.
  • Besson, C. and Hattiangadi, A. 2014. The Open Future, Bivalence and Assertion. Philosophical Studies, 162:251–271.
  • Bigelow, J. 1996. Presentism and Properties. Philosophical Perspectives, 10:35–52.
  • Bourne, C. 2006. A Future for Presentism. Oxford: Oxford University Press.
  • Broad, C. D. 1923. Scientific Thought. London: Routledge.
  • Casati, R. and Torrengo, G. 2011. The Not So Incredible Shrinking Future. Analysis, 71:240–244.
  • Correia, F. and Rosenkranz, S. 2018. Nothing To Come: A Defence of the Growing Block Theory of Time. Cham, Switzerland: Springer.
  • Dowden, B. 2018. Time. Internet Encyclopedia of Philosophy. https://www.iep.utm.edu/time/.
  • Hoefer, C. 2003. Causal Determinism. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/determinism-causal/
  • Horwich, P. 1987. Asymmetries in Time. Cambridge (MA): MIT Press.
  • Iacona, A. 2013. Timeless Truth. In Around the Tree: Semantic and Metaphysical Issues Concerning Branching and the Open Future, edited by F. Correia and A. Iacona, 29–45. Cham, Switzerland: Springer.
  • Iacona, A. 2014. Ockhamism without Thin Red Lines. Synthese, 191:2633–2652.
  • Lewis, D. 1979. Counterfactual Dependence and Time’s Arrow. Noûs, 13:455–476.
  • Lewis, D. 1986. On the Plurality of Worlds. Oxford: Blackwell.
  • Lukasiewicz, J. 1970. On Three-Valued Logic. In Selected Works, edited by L. Borkowski, 87–88. Amsterdam: North-Holland.
  • MacFarlane, J. 2003. Future Contingents and Relative Truth. Philosophical Quarterly, 53:321–336.
  • MacFarlane, J. 2008. Relative Truth. In Truth in the Garden of Forking Paths, edited by M. Garcia-Carpintero and M. Kölbel, 81–102. Oxford: Oxford University Press.
  • Malpass, A. and Wawer, J. 2018. Back to the Actual Future. Synthese.
  • Markosian, N. 1995. The open past. Philosophical Studies, 79:95–105.
  • Mellor, H. 1998. Real Time II. London: Routledge.
  • Ockham, W. 1978. Tractatus de praedestinatione et de praecientia dei respectu futurorum contingentibus. In Opera philosophica et theologica, volume II. St. Bonaventure, New York: The Franciscan Institute.
  • Øhrstrøm. P. 2009. In Defence of the Thin Red Line: A Case for Ockhamism. Humana Mente, 8:17–32.
  • Øhrstrøm, P. and Hasle, P. F. V. 1995. Temporal Logic. From Ancient Ideas to Artificial Intelligence. Dordrecht: Kluwer.
  • Perloff, M., Belnap, N., and Xu, M. 2001. Facing the Future. Oxford: Oxford University Press.
  • Prior, A. N. 1967. Past, Present and Future. Oxford: Clarendon Press.
  • Prior, A. N. 1970. The Notion of the Present. Studium Generale, 23:245–248.
  • Putnam, H. 1967. Time and Physical Geometry. Journal of Philosophy, 64:240–247.
  • Rosenkranz, S. 2012. In Defence of Ockhamism. Philosophia, 40:617–31.
  • Sider, T. 2001. Four Dimensionalism. Oxford: Oxford University Press.
  • Smart, J. J. C. 1963. Philosophy and Scientific Realism. Humanities Press, 1963.
  • Taylor, R. 1955. Spatial and Temporal Analogies and the Concept of Identity. Journal of Philosophy, 52:599–612.
  • Thomason, R. H. 1984. Combinations of Tense and Modality. In Handbook of Philosophical Logic, volume 2, edited by D. Gabbay and G. Guenthner, 135–165. Dordrecht: Reidel.
  • Todd, P. 2016. On Behalf of a Mutable Future. Synthese, 193:2077–2095.
  • Tooley, M. 1997. Time, Tense, and Causation. Oxford: Oxford University Press.
  • van Fraassen, B. 1966. Singular Terms, Truth-Value Gaps, and Free Logic. Journal of Philosophy, 63:481–495.
  • von Wright, G. H. 1984. Determinism and Future Truth. In Truth, Knowledge, and Modality, 1–13. Oxford: Blackwell.
  • Wawer, J. 2014. The Truth about the Future. Erkenntnis, 79:365–401.
  • Williams, D. C. 1951. The Myth of the Passage. Journal of Philosophy, 48:457–472.

Author Information

Andrea Iacona
Email: andrea.iacona@unito.it
University of Turin
Italy

Metaphysics of Science

Metaphysics of Science is the philosophical study of key concepts that figure prominently in science and that, prima facie, stand in need of clarification. It is also concerned with the phenomena that correspond to these concepts. Exemplary topics within Metaphysics of Science include laws of nature, causation, dispositions, natural kinds, possibility and necessity, explanation, reduction, emergence, grounding, and space and time.

Metaphysics of Science is a subfield of both metaphysics and the philosophy of science—that is, it can be allocated to either, but it exhausts neither. Unlike metaphysics simpliciter, Metaphysics of Science is not primarily concerned with metaphysical questions that may already arise from everyday phenomena such as what makes a thing (a chair, a desk) the very thing it is, what its identity criteria are, out of which parts is it composed, whether it remains the same if we exchange a couple of its parts, and so forth. Nor is it concerned with the concrete entities (superstrings, molecules, genes, and so forth) postulated by specific sciences; these issues are the subject matter of the special philosophies of science (for example, of physics, of chemistry, of biology).

Metaphysics of Science is concerned with more abstract and general concepts that inform all of these sciences. Many of these concepts are interwoven with each other. For example, metaphysicians of science inquire whether dispositionality, lawhood, and causation can be accounted for in nonmodal terms; whether laws of nature presuppose the existence of natural kinds; and whether the properties of macrolevel objects supervene on dispositional or nondispositional properties.

This article surveys the scope (section 1), historical origin (section 2), exemplary subject matters (section 4), and methodology (section 5) of Metaphysics of Science, as well as the motivation that drives it (section 3).

Table of Contents

  1. What Is Metaphysics of Science?
    1. Metaphysics and Metaphysics of Science
    2. Philosophy of Science and Metaphysics of Science
    3. Explication
  2. Metaphysics of Science in the 20th (and Early 21st) Century
    1. The Logical Empiricist Critique of Metaphysics
    2. The Return to Metaphysics
    3. Naturalized Metaphysics and Inductive Metaphysics
  3. Why Do We Need Metaphysics of Science?
  4. Sample Topics in Metaphysics of Science
    1. Dispositions
    2. Counterfactuals and Necessities
    3. Laws of Nature
    4. Causation
    5. Natural Kinds
    6. Reduction, Emergence, Supervenience, and Grounding
    7. Space and Time
  5. The Methodology of Metaphysics of Science
    1. Theoretical Virtues
    2. Inference to the Best Explanation
    3. Indispensability and Serviceability Arguments
    4. Extensional Adequacy and the Canberra Plan
  6. References and Further Reading

1. What Is Metaphysics of Science?

Metaphysics of Science is a subdiscipline of philosophy concerned with philosophical questions that arise at the intersection of science, metaphysics, and the philosophy of science. The term “Metaphysics of Science,” which combines the names of these disciplines, is of 20th century coinage. In order to fully understand what Metaphysics of Science is, it is helpful to clarify how it differs from both metaphysics simpliciter and philosophy of science.

a. Metaphysics and Metaphysics of Science

Metaphysics simpliciter seeks to answer questions about the existence, nature, and interrelations of different kinds of entities—that is, of existents or things in the broadest sense of the term. It enquires into the fundamental structure of the world. For example, it asks what properties are, how they are connected to the entities which have them, and how the similarity of objects can be explained in terms of their properties. The subject matter of metaphysics is somewhat heterogeneous: topics include the composition of complex entities (such as tables, turtles, and angry mobs), the identity and persistence of objects, problematic kinds of entities (that is, entities about which it is unclear whether or in what sense they exist at all, like numbers and fictional objects such as unicorns), and many more. Metaphysics is usually understood as working at an abstract and general level: it is not concerned with concrete individual things or particular relations but rather with kinds of things and kinds of relations.

Metaphysics of Science is not completely disjoint from metaphysics simpliciter. Not only does it draw on the pool of methodological tools employed in metaphysics, but there is also substantial overlap regarding subject matter. Metaphysicians have their own reasons, independently of science, to investigate causation, modality, and dispositional properties, for example. Like space and time, these concepts pertain also to everyday phenomena. Although Metaphysics of Science, too, is usually attentive to our everyday intuitions and opinions about such phenomena, it engages in a specific investigation of the roles these concepts play in scientific contexts.

Metaphysicians of science often take scientific realism for granted—that is, they hold the philosophical stance that the sciences are apt to find out what the world is really like, that they track the truth, and that the entities they postulate exist. Antirealism about science, on the other hand, often coincides with a skeptical or agnostic attitude towards metaphysics. In the context of some broader metaphysical inquiries, scientific endeavors might well be seen as but one way to the truth. A mainly science-guided metaphysics might even be seen as mistaken (as, for example, in phenomenological approaches (compare Husserl 1936; 1970)).

Moreover, metaphysicians of science demand of themselves that they pay attention to discourses within the sciences. For example, some physicists like Richard Feynman (1967) speak of fundamental symmetry principles and conservation laws as being constraints on other, less fundamental laws of nature (they are the laws of laws, so to speak), rather than being laws about what is going on in the world. Metaphysicians working to develop a philosophical theory of nomicity (lawhood), therefore, should allow for the possibility of there being laws of nature as well as laws of laws.

In short, Metaphysics of Science is that part of metaphysics that enquires into the existence, nature, and interrelations of general kinds of phenomena that figure most prominently in science. Also, Metaphysics of Science grants the sciences authority in their categorization of the world and in their empirical findings.

In terms of content, the transition between Metaphysics of Science and science might well be smooth with no clear border, so the distinction might be one that can only be made sociologically, regarding the departmental structure of universities or focusing on the practitioners and their methods of inquiry. Whereas many physicists (although perhaps not all: see theoretical physics) engage in experimental work, metaphysicians are happy merely to consult the findings of their empirically working colleagues from the science departments.

b. Philosophy of Science and Metaphysics of Science

On the other hand, Metaphysics of Science may just as well be called a part of the philosophy of science. Philosophy of science consists of the philosophical reflection on the preconditions, practices, and results of science in general and of the particular sciences (such as physics, biology, mathematics, sociology, and so forth). Many philosophers of science are engaged in debates surrounding science as a (putative) source of knowledge: what makes scientific results especially reliable? That is, what distinguishes science from non- or pseudoscience, everyday knowledge, and philosophy? Which kinds of methods do and should scientists employ? What is scientific progress? Are scientific theories true (despite being fallible)? Are we ever justified in advocating a particular scientific theory, given that most scientific theories of the past have been replaced by others (like, for example, Newtonian mechanics was replaced with relativistic mechanics)? Can the sciences be unified into one big Theory of Everything? Together, these questions constitute the epistemology of science, that part of the philosophy of science which studies scientific knowledge.

Metaphysics of Science complements the epistemology of science. Whereas the latter asks questions of the sort, “How do we know of x?” Metaphysics of Science enquires, “What is the nature of x?” where “x” is a placeholder for some (kind of) entity, state of affairs, or fact discovered or postulated by science.

The task of Metaphysics of Science is not simply to list these entities or facts. Rather, it operates at a higher level of abstraction. For example, whereas the particular sciences inquire into specific causal relations—or, differently put, into some particular relation that holds between two particular measurable quantities, like the concentration of a drug and the soothing effect it has on headaches—Metaphysics of Science attempts to say what causation is in general. That is, it asks exactly which features a relation must have in order to count as a causal relation (like regular occurrence or modal force), and what the respective relata are. In short, Metaphysics of Science enquires into the key concepts of science not at the empirical but at a more abstract and general level.

c. Explication

Philosophers disagree about which key concepts constitute the subject matter of Metaphysics of Science. Some (like Mumford and Tugby 2013, 6) argue for a narrow interpretation of the term and claim that Metaphysics of Science is primarily concerned with concepts which are relevant to all branches of science, because without these central concepts, science would not be possible. For example, they suggest (16) that kindhood, lawhood, and causation are concepts of this kind. Others, for example the Society for the Metaphysics of Science, are more permissive: they also include in the domain of Metaphysics of Science issues that arise in only some branches of science, such as problems regarding species (biology), intentionality and consciousness (psychology), and social kinds (social science). Probably due to the emphasis that 20th century philosophy of science placed on physics, the larger part of debates within Metaphysics of Science revolves around topics that occur most prominently within the realm of physics, but which figure or bear connections to the other sciences as well:

  • laws of nature, causation, and dispositions
  • necessity, possibility, and probability
  • (natural) kinds and essences
  • reduction, emergence, and grounding
  • space and time.

Regardless of whether philosophers defend a narrow or a more permissive notion of Metaphysics of Science, they agree that the concepts in question are in need of explanation. At the very least, such an explanation must show how the concepts cohere. Some metaphysicians take one or more of the concepts they discuss (alongside their related phenomena) to be primitive, meaning that these concepts cannot be analyzed in terms of other concepts and their related phenomena cannot be subsumed under other phenomena. Typically, they then proceed to show that other concepts (alongside their related phenomena) can be explicated in terms of these primitive concepts. (For an exemplary account of some potentially primitive concepts and how they cohere, see parts a through d in section 4.)

As a discipline in its own right, Metaphysics of Science is still relatively young, especially when compared to other areas of philosophy (such as epistemology and ethics). Its topics, however, are not. For as long as science has existed, there has been metaphysical reflection on central scientific concepts. Metaphysics of Science of the 21st century differs from natural philosophy of the past in that the aspiration of natural philosophy was to speculatively describe the world as it is, whereas Metaphysics of Science is more concerned with what the world would be like if our best scientific theories were to turn out true (compare Carrier 2007, 42).

2. Metaphysics of Science in the 20th (and Early 21st) Century

a. The Logical Empiricist Critique of Metaphysics

Of the many historical roots of modern philosophy of science, Logical Empiricism (often interchangeably called “Logical Positivism”) stands out. The Logical Empiricists and their sympathizers (especially Rudolf Carnap, Moritz Schlick, Otto Neurath, Hans Reichenbach, Alfred Ayer, and Carl Gustav Hempel) were the progenitors of a new kind of philosophy (that directly relates to the philosophical work of Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein, which later came to be known as “analytic philosophy”). They influenced many of the most prominent philosophers of the late 20th century (among them Karl Popper and Willard Van Orman Quine). In a sense, it is with them and their themes (laws of nature, causation, counterfactuals) that modern Metaphysics of Science begins, although they would have rejected much that currently goes by that name. Their ideas sparked many of the debates central to Metaphysics of Science.

In the 1930s, the Logical Empiricists proposed an empiricist, positivist program. They held that experience is our only source of nondefinitional knowledge (hence Logical Empiricism) and that the task of philosophy is logical analysis; that is, analysis of the logical features of and relations between sentences (hence Logical Empiricism). According to the Logical Empiricists, all the empirical propositions we believe can be reduced to so-called protocol sentences, which are direct renderings of our perceptual experience, or “the given.” Only if we know how a sentence could in principle be verified—that is, which possible observations would result in our accepting it as true—can we say that the sentence is meaningful. This so-called verifiability criterion of meaning has one purpose in particular, namely, to exclude metaphysical speculation from the realm of meaningful discourse. For example, the metaphysical sentence “every thing has an immaterial substance” cannot be empirically verified; hence, according to the verifiability criterion of meaning, it is meaningless. A radical antimetaphysical stance was one of the key tenets of Logical Empiricism. Note that verificationism recasts the Empiricists’ epistemic doctrine that all factual knowledge comes from sense perception as a semantic doctrine. Indeed, if we believe that what we know is expressed (or at least expressible) in meaningful sentences, then the transition from Empiricist epistemology to semantics is straightforward: all factual knowledge is expressed in meaningful sentences and only those sentences for which we are able to give a method of verification in observation are meaningful.

It soon became apparent, however, that Logical Empiricism, and especially the verifiability criterion of meaning, houses some serious flaws. Two major blows came from Willard Van Orman Quine’s seminal paper, Two Dogmas of Empiricism (1951), which argued that two assumptions the principle of verification has to presuppose are untenable: the first is that there is a clear distinction between analytically true and synthetically true sentences. The second is that each meaningful sentence faces the tribunal of sense experience on its own for its verification or falsification (rather than holistically in concert with other sentences).

Logical Empiricism faces further problems. Clearly, the Logical Empiricists held the sciences in high esteem. Usually, it is taken for granted that the sciences aim to discover natural laws and that they research properties such as electro-conductivity of different materials, reactiveness of chemical compounds, and fertility of organisms. Prima facie, it seems that many laws of nature can be expressed as general statements, that is, as statements of the form “any particular thing x which has property F also has property G” (in logical notation: ∀x(Fx → Gx)). For example, we say that all samples of metal expand when heated. But universal generalisations of this kind cannot ever be proven true by actual empirical observations (because they have far more instances, maybe infinitely many, than could ever be observed and confirmed), so the verifiability criterion rules out (at least some) laws of nature as meaningless. Even if this consequence could be avoided, what the laws of nature say is often taken to not be merely accidentally true, but to ensue with modal force. Empirically, we cannot account for modality: we can only observe what is actually the case, not what else is possibly or necessarily true.

Similarly, Logical Empiricism runs into problems regarding dispositional properties. Everyday properties such as solubility and scientific properties like conductivity cannot easily be reduced to the observable qualities of soluble or conductive objects. For example, a sugar cube is a somewhat solid object, much like a matchstick, but if we were to place the sugar cube in water, it would dissolve, whereas the matchstick would not. Its manifest properties such as solidity, color, and taste provide no clue as to what will happen to the sugar cube if placed in water. What is more, even if a particular sugar cube (or even all the sugar cubes in the world) were never placed in water at all (or if it were placed in water but the water was already supersaturated with sugar so that the sugar cube would not dissolve in that particular situation), it would nevertheless retain its dispositional property of being soluble, although there is nothing about it that we observe which hints at its solubility. An analogous case can be made regarding dispositional properties discussed in the sciences, like conductivity or chemical bonding propensity, and similarly, regarding science’s theoretically postulated, not directly observable, entities like quarks or superstrings. Because dispositional properties, theoretical entities, and universally generalized laws of nature appear to belong to the conceptual inventory of the sciences, Logical Empiricism, which fails to adequately account for them, quickly became an unattractive option. (For more on laws of nature and dispositions, see section 4c and 4a.)

b. The Return to Metaphysics

The failure of Logical Empiricism to cope with some of the key concepts of science eventually led to the development of Metaphysics of Science. Philosophers realized that if concepts such as law of nature and necessity could not be eliminated by reduction to observation terms, it must then be legitimate to examine them thoroughly, by whatever means seem fit. The most likely candidate to fulfill this task is metaphysics. (For an overview of methods commonly applied in Metaphysics of Science, see section 5.)

The development of Metaphysics of Science occurred simultaneously with the revival of metaphysics in the analytic tradition of philosophy, a tradition that was rooted in Logical Empiricism (as well as in the linguistic turn, manifested by the ideal and ordinary language philosophies of the late 19th and mid-20th centuries). Analytic philosophers were initially hostile towards metaphysical questions. They rejected questions which transcended empirical observation or fell outside of the scope of the sciences. However, philosophers like Willard Van Orman Quine (most famously in his essay “On What There Is” (1948)) and Peter Strawson (especially in his monograph Individuals (1959)) soon realized that there is a supposedly innocent way of practicing metaphysics by describing human conceptual schemes rather than by speculatively conjuring up grand metaphysical edifices. Instead of laying claims to knowledge of the unobservable, they focused on finding out how humans in fact conceptualize reality—in their everyday language (Strawson) or their scientific theories (Quine) where, if stronger authority is given to the sciences, the latter may revise the commitments of the former. Quineans favor the revision and are, hence, closer to the attitude of Metaphysics of Science, where Strawsonians give much credibility also to folk’s general metaphysical background assumptions.

Encouraged by the failure of Logical Empiricism and the fact that metaphysical questions were once again beginning to be the subject of philosophical discussion, philosophers developed a renewed interest in metaphysics. They gradually grew confident in talking not merely about observations, semantics, and language, but also about reality.

Another significant step towards the return to metaphysics was the development of modal logic. Begun by Carnap—for example, in his Meaning and Necessity (1947)—the logic of necessity, possibility, and counterfactuality was refined considerably by Ruth Barcan Marcus (1947), Saul Kripke (1963), and David Lewis (1973a). Later, with Kripke’s Naming and Necessity (1980) and Hilary Putnam’s “The Meaning of ‘Meaning’” (1975), the formalisms were given ontological interpretations and the belief in necessity in nature gained new justifications. Building on these developments further still, even (Aristotelian) essences saw their revival: see Kit Fine’s work (1994) and its application within Metaphysics of Science by, for example, Brian Ellis (2001) and Alexander Bird (2007).

The return to metaphysics in the 20th century was not merely a trailblazing event for the development of modern Metaphysics of Science; rather, the two evolved alongside each other. For example, when it became acceptable for metaphysicians to speak of necessities in nature and discuss statements like “Water is necessarily H2O,” this paved the way for a realistic reading of other modalities, like nomological necessity or counterfactuality. These are, as we will see (in section 4b and 4c), central notions in debates on the nature and status of laws of nature in Metaphysics of Science.

c. Naturalized Metaphysics and Inductive Metaphysics

In the early 21st century, some philosophers argued for a naturalization of metaphysics. Their argument typically rests on the fact that the sciences appear to surpass metaphysics in many respects. The sciences, they claim, have a shared stock of accepted theories, a pool of respected methods and institutionalized standards, and they have predictive and technological successes to show for themselves. In contrast, there is long lasting dissent over positions and methods in metaphysics that rarely ever gets dissolved, and it is unclear what would even count as criteria for metaphysical success. As some metaphysical questions—such as “What is the world ultimately made of?” and “What is life?”—also belong to the domain of the sciences (physics and biology, respectively), naturalists insist that we must draw upon scientific findings to properly answer them.

Naturalistic metaphysicians come in all shapes and sizes. Some naturalists wish to prohibit any metaphysics that is not scientifically evaluable (compare Ladyman and Ross 2007). Some suggest that we should take our clues from scientific practice. For example, Tim Maudlin (2007) argues that lawhood is primitive, as working scientists see no need to analyze the concept. (For more on Maudlin’s position, see section 4c.) Others still allow for the possibility of relevant questions which may not have straightforwardly scientific answers. For example, consider the question “What is it for a thing to persist through time?” Imagine we take a ship out to sea and, little by little, replace every single part of it until none of the original parts remain. Certainly, science can describe how the ship changes, but it will not tell us whether the ship we sail home is still the same as the ship that put out to sea. The latter becomes a pressing, genuinely metaphysical problem, especially when we ask an analogous question about a person’s change and persistence through time.

What is important to remember is that although a naturalized metaphysics may, in a sense, also be called a “Metaphysics of Science,” its proponents may have a very different sort of metaphysics in mind than that presented in section 4.

In the 21st century, some philosophers have stressed that Metaphysics of Science could well be an inductive/abductive enterprise that, just as the sciences do, generalizes empirical data and builds explanatory models on that basis (Paul 2012; Williamson 2016; Schurz 2016; the research group Inductive Metaphysics). (Interestingly, precursors of the idea of an inductive/abductive metaphysics developed simultaneously with Logical Empiricism (Scholz 2018).) If so, metaphysical hypotheses might turn out to be fallible, only approximately true, and contingent.

3. Why Do We Need Metaphysics of Science?

In section 1 it was said that Metaphysics of Science examines the key concepts of science. But why do philosophers even bother to argue over issues in Metaphysics of Science? Is it not relatively clear what the basic concepts in science are and what they mean? Surely scientists know very well what they mean to say when they talk about the solubility of sugar, the second law of thermodynamics, and the relativity of space-time?

What inspires Metaphysics of Science is, of course, the idea that there is more to know about these phenomena and the concepts involved than science can say. Think of causation, for example. The concept of causation is commonsensical: we encounter causal processes in everyday life, like when we hit a golf ball with a putter and the ball begins to move, or when we drop a glass and it shatters. We intuitively distinguish these causal processes from noncausal processes. For example, if somebody in the next room sneezes as you raise your arm, you just know that raising your arm was not the cause of the other person’s sneezing. Still, it is quite complicated to say what establishes a causal connection between two events and what exactly distinguishes the putter-and-golf-ball scenario from the raise-arm-and-sneeze incident. Science records measurements and reveals statistical correlations between phenomena. It also has apt intuitions about whether two events are indeed causally connected or whether they merely co-occur accidentally, albeit regularly. Yet science is rarely interested in a general overall theory (detached from particular, concrete cause-effect relations) of what exactly distinguishes causes from accidents. Concepts such as causation or laws of nature, although relevant for science, are rarely the subject matter of science itself.

Science and Metaphysics of Science have different but complementary approaches to reality: the scientist’s work in this respect is predominantly empirical and consists in finding instantiations—describing particular causal interactions, listing things which are disposed in certain ways, pinning down particular laws of nature, and so on—while the metaphysician’s focus is on understanding and clarifying general concepts or the corresponding phenomena (like causation, disposition, and law of nature).

Still, the critic may object that even if the metaphysician’s and the scientist’s approaches to reality are indeed complementary, we can do perfectly well without Metaphysics of Science. For example, if science manages to find out the different variables and constants that determine how things in the world hang together, why do we also need to know what the general characteristics of a law of nature are or how that notion can be analyzed in terms of other notions? Isn’t this superfluous information? Clearly, scientists do not need metaphysicians to tell them about causation or dispositions in order to perform their research. Nevertheless, metaphysicians of science believe that questions regarding the existence and nature of causation, natural kinds, and necessity are valuable in their own right. At the very least, they are pressing questions that cannot be ignored by those who yearn to thoroughly understand the world we live in. By way of example, consider the dispute between defenders of Humean supervenience and antiHumeans, which revolves around the question of whether there are necessities in nature or not. (See 4a for a brief account of the debate.) Clearly, this is not a question that can be answered by purely scientific methods, but it is one that metaphysicians will nevertheless take to be meaningful and profound.

Some of the issues discussed in Metaphysics of Science are also relevant for practical contexts. For example, failure to render assistance (in case of an accident, a medical emergency, or the like) can lead to prosecution or social repercussions due to immoral behavior. However, you can only be held legally and morally responsible for events you are also causally responsible for. Accordingly, both ethics and law require a concept of causality that accounts not just for positive but also for negative causation, that is, causation by the absence of an event or act. If you pass an unconscious person lying on train tracks and fail to alert the authorities or pull him off the tracks, then you are (partly) causally responsible for his death if he is later killed by a train. Thus, although many questions within Metaphysics of Science are primarily aimed at complementing science, its debates may have far-reaching consequences in other fields as well.

To more fully understand the difference between the scientific and the metaphysical approach to the key scientific concepts that constitute the subject matter of Metaphysics of Science, it is helpful to consider samples of actual work in Metaphysics of Science (section 4) and to take a closer look at the methodology employed (section 5).

4. Sample Topics in Metaphysics of Science

As Metaphysics of Science is the study of the key concepts of science, its subject matter depends directly on what the sciences study and which concepts they employ. Because there are many different branches of science, there are also many potential topics for metaphysicians to discuss. It is impossible to name them all in a survey article, much less discuss them in detail. However, it is practically impossible to fully grasp what Metaphysics of Science is from general definitions only. (The same is true of metaphysics in general. No layperson will understand what metaphysicians do from hearing that metaphysics is the study of the fundamental structure of reality.)

In order to give the reader an idea of both the scope of Metaphysics of Science and its practice, this section briefly and tentatively introduces seven debates which have preoccupied metaphysicians of science in the past: counterfactuals and necessities, dispositions, laws of nature, causation, natural kinds, reduction and related concepts, and space and time. (See the respective articles for more information on modal logic and modality, laws of nature, reductionism, emergence, and time.)

a. Dispositions

Some objects have dispositional properties. For example, sugar is soluble, matchsticks are inflammable, and porcelain vases are fragile. Properties like solubility or fragility are often conceived of as becoming manifest only under so-called “triggers” or “stimulus conditions,” which set off the manifestation of the dispositional property. For example, for a sugar cube to manifest its solubility by dissolving, it must be placed in water.

Not all properties are like that. So-called categorical properties need no stimulus; they are always manifest. Just think of the properties of being solid, having a certain molecular structure (for example, being H2O), being rectangular, and so on. The distinction between categorical and dispositional properties is often drawn with the following three features in mind:

(i) Untriggered dispositions are not directly observable, whereas many categorical properties are. For example, from looking at some sort of powder, we cannot tell whether it is soluble or not. Looking at a football, we immediately see that it is round.

(ii) Because dispositional properties bestow objects with possibilities (of behaving in certain ways under certain circumstances), they are said to be modal properties: they imply, by their very nature, what can, might, or (given certain circumstances) must be the case. Categorical properties are not usually conceived of in this way.

(iii) Dispositional properties are often identified with productive powers. For example, scratching a match is not enough for it to light up; the match’s inflammability, too, is causally responsible for the flame. Usually, no such productive, causal force is directly associated with categorical properties.

Dispositional properties are not just a phenomenon we encounter in everyday contexts, but in science as well. For example, the property of being charged appears to fit this profile: it is not directly observable, it determines how objects would behave under certain conditions, and an object’s charge can be a vital factor in causal processes. Dispositionality has hence been of interest to Metaphysics of Science since its very beginning. In fact, the failure of Logical Empiricism to properly account for dispositional properties played a seminal role in the emergence of the discipline (see section 2a).

Because of their shared belief that all of our knowledge ultimately reduces to observational experience, Logical Empiricists like Rudolf Carnap (1936) attempted to account for dispositional properties in terms of observational properties using a simple conditional to connect the trigger to the manifestation: to say that a sugar cube is soluble just means that if we put it in water, it will dissolve. This and similar attempts at reduction fail, however, as they do not account for the modal behavior of disposed objects. For example, they do not supply a basis on which to ascribe (or not to ascribe) solubility to objects which have never been placed in water. This strikes us as odd, as it does not correspond to our everyday practice.

In order to adequately capture the modal nature of dispositions, philosophers soon suggested that we employ a counterfactual connective instead of the simple conditional. To say that some object has a disposition, they argued, means just that if the object were exposed to the trigger conditions, the disposition would manifest. This approach faces at least two problems. First, it requires a theory that specifies truth conditions for counterfactual conditionals (see section 4b). Second, there are some interesting counterexamples to the effect that under certain conditions we would intuitively ascribe dispositions to objects for which the proposed analysis fails (as in Charles Martin’s 1994 electro-fink example).

Although early attempts at reducing dispositions to categorical properties have failed, problems like the above have convinced some philosophers that we should strive for a reductive analysis after all. The philosophical position that holds that all properties are categorical and that supposedly dispositional properties can somehow be reduced to categorical properties is called “categoricalism.” For many categoricalists, a large part of their motivation comes not from Logical Empiricism but a fundamental insight of classical empiricism. David Hume famously observed that necessary connections, like those between causes and their effects, cannot be detected empirically. Hence, Hume concludes, we have no reason to assume that any sort of productive, necessary, or modal connection of events in nature exists. (This has come to be known as Hume’s Dictum.) Twenty-first century Humeans, too, claim that there are no necessary connections in nature. Consequently, they deny that there are irreducible, metaphysically fundamental dispositional properties that seem to imply some sort of necessary or modal connection between the trigger and the manifestation.

However, as reduction proves to be notoriously complicated, other philosophers opt for dispositionalism instead, which is, in its most radical form (pan-dispositionalism), the view that all properties are of a dispositional nature. Both categoricalism and pan-dispositionalism are monistic theories, as both claim that there is, at the fundamental level, only one type of property. It is also possible for philosophers to hold a neutral or dualistic view, according to which there are both categorical and dispositional properties at the fundamental level of reality.

The debate over dispositions has had substantial impact on other debates within Metaphysics of Science and vice versa. For example, some philosophers argue that laws of nature and causation are grounded in dispositional properties: a law of nature like “Like-charged objects repel each other” could well be true because of the dispositional nature of charge, and causal successions of events could be determined by the dispositional properties of objects involved (for example, wood paneling can be a partial cause of a house fire because it is inflammable). Other philosophers see the direction of dependence exactly the other way around: dispositions depend on laws of nature, because if the laws of nature were different, objects might have different dispositions. For example, if the laws of ionic bonding were different, salt might not dissolve in water. Similarly for causation: maybe salt has its disposition to dissolve because its ionic structure is a potential cause of dissolving. Hence, the debate over dispositions should not be viewed in isolation.

b. Counterfactuals and Necessities

We learned above that a central feature of dispositions is that they establish a modal relationship between the disposed object’s being in the trigger condition(s) and the disposition’s manifestation. A plausible candidate for understanding the nature of this modal relationship is counterfactual dependence. The standard notation for counterfactual dependence reads □→ q: if p were the case, then it would be the case that q. If a sugar cube is soluble, then that means, at least in part, that if it were placed in water, it would dissolve.

The sentential connective □→ is an intensional connective, which means that the truth value of the entire conditional cannot simply be read off the truth values of the antecedent and the consequent. The reason is easily understood: counterfactual conditionals describe counterfactual situations, which means that both the antecedent and the consequent are usually not currently true. Yet some such counterfactuals with a (currently) false antecedent and a (currently) false consequent are true (the above one capturing solubility, for example) and some such counterfactuals are false (such as “If I were to say ‘abracadabra’ a rabbit would appear”). How then can we evaluate the truth of counterfactual conditionals, given that the truth or falsity of its components is not decisive?

An idea proposed by Nelson Goodman (1947, 1955) and Roderick Chisholm (1946) is to have the truth of a counterfactual conditional depend on both the laws of nature and the background conditions on which they operate. On this account, a counterfactual conditional □→ q is true if and only if there are true laws of nature L and background conditions C which hold, such that p, L, and C communally imply q. (Some further conditions must be met, like that the background conditions must be logically compatible with p.) Obviously, if the laws of nature or the background conditions were different, □→ q might turn out not to be the case.

An alternative way of thinking about counterfactuals called “possible world semantics” was introduced by David K. Lewis (1973a). Lewis’s most important tool is the concept of a possible world. According to Lewis, our actual world is only one among a multitude of possible worlds. A possible world is best thought of as one way (of many) the actual world could have been: all other things being equal, the word “multitude” in the last sentence could have been misspelled, Lewis could never have been born, or atoms could have been made of chocolate. Robert Stalnaker (1968) proposed a similar account but without defending modal realism (that is, realism regarding possible worlds). To him, possible worlds are tools, and as such no more than descriptions of worlds that do not exist.

Some possible worlds are more similar to ours than others. For example, a world which is like ours in every respect except that “multitude” is misspelled in the preceding paragraph is more similar to the actual world than a world with chocolate atoms. In evaluating a counterfactual’s truth value, this fact plays a seminal role. Consider, for example, the sentence “If David had not overslept, he would not have been late for work.” In a world where all vehicles miraculously disappeared that morning, where the floor of David’s bedroom was covered in super strong instant glue, or where the laws of nature suddenly changed so that movement is no longer possible, he would not have made it into work in time, even if he had gotten up early. But these worlds do not interest us; this is clearly not what we mean by saying that had David not overslept, he would have made it in time. To judge whether the counterfactual conditional is true regarding our world, we need to consider only worlds where the laws of nature remain the same and everything else is rather normal—that is, similar to what actually did happen—except for the fact that David did not oversleep (and maybe some minor differences).

Lewis and Stalnaker suggest that an ordering of worlds with respect to similarity to our world is possible. Naturally, worlds where many facts are different from the facts of our world, and worlds with different laws of nature, count as particularly dissimilar. Counterfactual truth can then be determined as follows: of all the possible worlds where p is the case (for short, the p-worlds), some will be q-worlds and others non-q-worlds (that is, worlds where q is true or not true, respectively). To determine whether the counterfactual conditional □→ q is true for our world, we need to check whether the p-worlds that are also q-worlds are more similar to our world than the p-worlds that are non-q-worlds. So to find out whether it is true that David would have gotten to work in time had he not overslept, we look at possible worlds where David did not oversleep and check whether the worlds where he makes it into work are more similar to the actual world than worlds where he does not (because, say, all buses disappear or the floor is sticky).

According to this analysis, the consequent need not be true in all possible worlds (but only in similar p-worlds) in order for a counterfactual to be true. For example, had David overslept in a world where objects can be transported via beaming, he might still have made it to work in time. But as it is doubtful whether this technology will ever be available in our world (as it is not clear whether it is compatible with our laws of nature), the world where beaming has been invented is not relevant for the evaluation of the counterfactual conditional.

Related to what has just been said, we can point out a welcome feature of counterfactual conditionals: it can be true both that if David had not overslept, he would not have been late for work; and that if David had not overslept, yet the bus had had an accident, he would (still) have been late for work. This is a feature that necessary conditionals and mere material implications cannot well accommodate (or only with the undesirable implications that it is impossible for David to oversleep together with the bus having been involved in an accident).

In addition to providing a way of understanding counterfactual conditionals, possible world semantics allows us to spell out the modal notions of necessity and possibility in terms of quantification over possible worlds. Thus, a sentence p is necessarily true (in logical notation: □p) if and only if it is true in all possible worlds. If p is necessarily true, there is no way that p could be false; that is, there is no possible world where p is false. Similarly, p is possibly true (in logical notation: ◊p) if and only if it is true in at least one possible world.

Necessity is thus expressed in terms of universal quantification over (all) possible worlds, whereas possibility is existential quantification over (all) possible worlds. Like the general and existential quantifiers, necessity and possibility, too, are interdefinable: if p is necessary, then it is impossible that non-p, and if p is possible, then it is not necessarily the case that non-p.

Note that there are different sorts of necessity which can be easily accounted for if we conceive of necessity and possibility in terms of quantification over possible worlds: Logical, metaphysical, and nomological necessity can be defined by restricting the scope of worlds over which we quantify. For nomological necessity, for example, we restrict quantification to all and only worlds where our laws of nature hold.

Possible world semantics faces several problems, however. For example, it is unclear just how we can know about what is or is not the case in other possible worlds. How do we gain access to possible worlds that are not our own? However, possible world semantics is a valuable tool for understanding some of the most central issues in Metaphysics of Science, such as dispositions and causation. In addition, necessity is a crucial element in theories of laws of nature, essences, and properties. The modalities of necessity, possibility, and counterfactuality are also important in their own right: after all, knowing what would happen if something else were the case or what can or must happen is key to scientific understanding.

c. Laws of Nature

Here are some intuitions philosophers have about laws of nature: laws are true or idealized, objective, universal statements. Laws of nature support counterfactuals, are confirmable by induction, and are explanatorily valuable as well as essential for predictions and retrodictions. Laws have modal power in that they force certain events to happen or forbid them from occurring. Any analysis of the concept will attempt to account for at least some of these features. Roughly, there are five types of theories of laws of nature: regularity accounts, necessitation accounts, counterfactual accounts, dispositional essentialist accounts, and accounts which take laws to be ontological primitives.

The basic idea of early regularity accounts is that a law of nature is a true, lawlike universal generalization (usually of the form “All F are G,” or in formal notation: ∀x (Fx → Gx)). Whether a given generalization is true is, of course, an empirical matter and must be determined by the sciences, but what it means for a statement to be lawlike is left for metaphysics to define. Not all general statements are lawlike. For example, some general statements state logical truths which clearly are not laws of nature (like “All ravens are ravens”). The main challenge for regularity theories is figuring out what makes a universal statement lawlike without appealing to any sort of connection between events other than regularity.

The Best Systems Account (Lewis 1973a) is an example of a sophisticated regularity theory. It asks us to imagine that all facts about the world are known, such that you know of every space-time point what natural properties are instantiated at it. There are many different ways of systematizing this knowledge by using different sets of generalizations. These generalizations make up competing deductive systems. Defenders of the Best Systems Account hold that a (contingent) generalization is a law of nature if and only if it is a theorem within the best such system. Which system is the best is determined by appeal to certain criteria: simplicity, strength (or informational content), and fit.

The Best Systems Account has been criticized for not taking seriously the intuitions that laws of nature are objective, have explanatory value, and hold with modal force. The Best Systems Account yields regularities, but it does not explain why they obtain. Opponents of regularity theories stress that laws do not merely state what is the case, but enforce or produce what happens.

Necessitation accounts are alternatives to the Best Systems Account that endorse this idea. Such accounts have been proposed by David Armstrong (1983), Fred Dretske (1977), and Michael Tooley (1977). For Armstrong, a law of nature is a necessitation relation N between natural properties. (Armstrong speaks of universals.) For two natural properties to be related by necessitation means that one of them gives rise to and must be accompanied by the other (hence necessitation). To give a coarse-grained example: Coulomb’s law (which states, very roughly, that charges exert forces onto other charges), is a true law statement if and only if necessitation holds between the properties of having a certain charge (C) and exerting a certain force (F): N(C, F).

Necessitation accounts have some advantages over regularity theories. For example, they can more easily allow for uninstantiated laws. But how exactly do we know which properties are related by the necessitation relation, and why should we even assume that it exists? Armstrong argues that necessitation can be experienced insofar as it manifests in causal processes. However, not all laws are causal laws. Defenders of necessitation accounts must work out these issues.

The counterfactuals account focuses on a feature related to necessity, namely, the fact that laws of nature are stable under counterfactual perturbations. For example, that nothing can be accelerated beyond the speed of light is a law of nature because it is a fact that no matter what fantastical interventions we were to devise, we still couldn’t travel faster than the speed of light. Versions of the counterfactuals account of laws of nature have been proposed by James Woodward (1992), John Roberts (2008), and Marc Lange (2009).

A bullet that counterfactual accounts have to bite is that the intuitive order of explanation regarding laws and counterfactuals is upside down: whereas the counterfactual theory of laws says that it is a law that all bodies fall down to earth because it is fundamentally true that “were some arbitrary massive body dropped it would fall,” we intuitively believe that “were we to drop this body it would fall” is true because the law of gravitation holds. In other words, it is more intuitive to hold that the laws of nature support counterfactuals rather than that counterfactuals support the laws.

Another prominent way to account for laws of nature is to appeal to dispositional essentialism. Dispositionalists, like Brian Ellis (2001), Alexander Bird (2007), or Mumford and Anjum (2011), believe that some or even all properties are essentially dispositional. For example, if an object has the property of being electrically charged, that just means that it has the dispositional property of being attracted or repelled by other charged objects nearby. In this sense, the property of being electrically charged is essentially dispositional, because no object is electrically charged unless it is disposed to be attracted or repelled in this way.

Now, if natural properties bestow on their bearers dispositions, then that means it is always true that if something has a given natural property (Px), it also has a certain disposition (Dx) and thus it will manifest in a certain way (Mx), given that the disposition’s corresponding trigger occurs (Sx). (In formal notation: ☐∀x((Px ∧ Sx) → Mx)). This is precisely what many metaphysicians ask of laws: that they bring about or make necessary what happens when something else is the case. Dispositional essentialists thus claim that dispositions ground nomological facts: laws arise from the dispositions things have.

Obviously, the dispositional essentialist account of lawhood hinges on non-trivial premises, which must be evaluated in their own right—for example, the premise that dispositions are basic.

If analyzing lawhood is so complicated an affair that it requires elaborate theories and intricate tools, why not assume that lawhood is conceptually and ontologically primitive—that is, that the concept of lawhood cannot be defined in terms of other concepts, and that it cannot be reduced to underlying phenomena? Tim Maudlin (2007) argues that scientists do not seek to analyze laws, but rather accept their existence for a brute fact in their daily practice, and that philosophers should do likewise.

To Maudlin, a law of nature is that which governs a system’s evolution through time and determines what future states can be produced from the current state of the system. As lawhood is a primitive concept for Maudlin, he attempts to utilize it in defining other notions, like causation and counterfactual truth. Whether Maudlin’s approach is viable or not depends to a large part on whether these definitions of causation and counterfactual dependence by means of laws of nature work out or not.

d. Causation

Causation is obviously intimately connected to the laws of nature, as we would expect at least some laws to govern some causal relationships. Causation, however, is not a straightforward notion. For example, philosophers disagree over which kinds of entities are the proper relata in causal relationships, some potential candidates being substances, properties, facts, or events. There are several approaches to understanding causation: regularity theories, counterfactual theories, transfer theories, and interventionist theories.

Regularity theories follow in the footsteps of David Hume’s treatment of causation. According to regularity theories, all that can be said about causation comes down to stating a regularity in the sequence of events. The motivation for regularity theories stems from the fact that instances of a regularity can be observed, unlike the production of one event by another or a necessary relation between events.

One of the most widely known regularity theories is John Mackie’s INUS account of causation (1965). According to Mackie, an event is a cause if it is an Insufficient but Necessary part of an Unnecessary yet Sufficient condition for the effect to occur. For example, a short circuit (C) alone is not sufficient for a house to burn down (E); there must also be inflammable materials nearby (A) and there must not be sprinklers which extinguish the fire (B). Call this a complex condition (ABC). As the absence of sprinklers and the presence of inflammable materials is not enough to cause a fire, the short circuit is necessary within this complex condition, which is then sufficient for the fire. But there may be other complex events (DFG, HIJ, and so on) which could also bring about the same effect. For example, a lit candle in a dried-up Christmas tree may also cause the house to burn down. As the short-circuit scenario (ABC) is only one of many potential causes of a fire, it is not necessary for the effect to occur, but if it occurs, it is sufficient to bring about the fire.

Like other regularity theories, Mackie’s INUS theory has the disadvantage of classifying as causal some regularly co-occurring coincidences that are, for all we know, not causally related. For illustration, consider a simpler type of regularity theory according to which causation is just regular succession. The problem is that if causation were nothing but regular succession, then we would be forced to say that the rise of consumer goods prices in the late 20th century causes the oceans’ water levels to rise. Obviously, these events coincided but are not causally related.

To forgo this problem, philosophers devised counterfactual theories of causation. The initial idea presented by David K. Lewis (1973b) is to equate causal dependence with counterfactual dependence. The idea seems plausible: had the cause not occurred, there would (all else being equal) not have been the effect. More precisely, for event e to (causally) depend on event c, whether e occurs or not must depend (counterfactually) on whether c occurs or not (that is, on whether both c □→ e and ¬c □→ ¬e are true, where ¬ is the negation operator). For example, if the short circuit is the cause of the fire, then the house would have burned down if the short circuit had occurred, and it would not have burned down if the short circuit had not occurred.

Lewis saw that this initial account is flawed as it yields intuitively incorrect results in so-called pre-emption scenarios. Imagine two people, Suzy and Billy, throwing stones at a bottle. Now picture a situation where if Suzy does not throw her rock, Billy will. Suppose Suzy throws her rock, hits, and the bottle shatters. The effect, namely the shattering of the bottle, is evidently caused by Suzy’s throwing the rock. However, the effect would have occurred even if Suzy had not thrown, because in that case Billy would have thrown his rock and shattered the bottle. In this scenario, we recognize Suzy’s throw as the cause of the shattering, but the latter does not counterfactually depend on the former (because it is incorrect that had Suzy not thrown, the bottle would not have been shattered).

Although more sophisticated counterfactual theories are more successful in dealing with pre-emption and other problems, some philosophers choose to take a different approach. Proponents of transfer or conserved quantity theories like Salmon (1984, 1994), Phil Dowe (1992), and Max Kistler (2006) claim that causation is best understood as a transfer of a physical quantity from one event to another. For example, Suzy is causally responsible for shattering the bottle (and Billy is not) if it was her energy that set the stone in motion to physically interact with the bottle on impact and shatter it. Transferable quantities include energy, momentum, and charge, for example. These quantities are subject to conservation laws, which means that in any isolated system, the sum total of the remaining and the transferred amount of the quantity will always equal the initial amount.

Transfer theories face difficulties in accounting for negative causation. For instance, omitting to water plants may cause them to wither, but there is no transfer of a conserved quantity from anything to the withering. Other problems derive from examples where the supposed causal relationship is not obviously of a physical nature. For example, we may say that wild speculations at the stock market caused the economy to break down or that Suzy’s throwing Billy a kiss causes him to blush.

Of the fourth group of theories of causation, interventionist theories, James Woodward’s approach (2003) is a prime example. Woodward suggests that causation is best characterized by appeal to intervention. Consider the following example: Testing a drug for efficiency consists in finding out whether a group of people who are administered the drug are cured while a group who does not receive the drug remains uncured. In other words, drug testers intervene by giving the drug to some patients and a placebo to others. If the drug intervention leads to recovery while the placebo intervention does not, the drug is said to be causally relevant for the recovery.

Woodward places further constraints on interventions, one of which is that the intervention (of administering the drug or the placebo, respectively) must be performed in such a way that other potential influences are absent. For example, if the drug were given to healthy and young patients while only the elderly and frail receive the placebo, the test might falsely attribute causal efficacy to the drug.

Even when these precautions are taken, Woodward’s theory is at risk of being circular: the analysis presupposes that we understand beforehand what it means to intervene on a system. Intervention, however, is itself a causal notion. Woodward has clarified that his theory is meant to explicate and enlighten our concept of causation, not to reduce causation to other phenomena.

It seems that all theories of causation face difficulties (either in the form of recalcitrant exemplary cases or in that they do not capture certain features of causation). One possible conclusion to draw from this is that causation is not one unified phenomenon but at least two and potentially many more. For example, Ned Hall (2004) argues that our intuitions characterize causation both as production and counterfactual dependence, and that the problems of analyses of causation can be traced back to the attempt of squeezing these into one unified concept.

The debates over the nature of dispositions, modality, laws of nature, and causation are still ongoing. Many promising approaches have been proposed in their course and will continue to be explored in the future. (For a detailed account of the relation between the debates surrounding dispositions, counterfactuals, laws of nature, and causation in Metaphysics of Science, see Schrenk (2017).)

e. Natural Kinds

In everyday contexts we habitually classify objects or group them together. Some of these groupings seem more natural to us than others. Philosophers who believe that nature comes with her very own classifications speak of “natural kinds.” For example, samples of gold closely resemble each other, differ clearly from other chemical elements, and share a common microstructure, whereas sea life comprises organisms of very different sorts (including crustaceans, fish, and mammals). Terms like “sea life” and “tile-cleaning fluid” are convenient for human purposes such as thinking and talking about groups of things, but we do not expect them to reflect the structure of the natural world (which does not mean that the classifications they introduce are entirely arbitrary). Natural kinds, on the other hand, supposedly “carve nature at the joints” (Plato’s Phaedro 265d–266a). They are also highly projectible: we can inductively infer from the behavior of one object to that of all objects of the same natural kind.

If natural kinds exist and contribute to the structuring of the world, then ideally we want the sciences to discover what natural kinds there are. A natural kind enthusiast may claim that physics tells us that electrons and quarks exist, chemistry says that there are chemical elements like gold (Au) and compounds like water (H2O), and biology seems to suggest that organisms are ordered hierarchically along the lines of family, genus, and species. However, there are also conventionalists who believe that so-called natural kinds are not independent of the minds, theories, and ambitions of human beings, or that no way of dividing up the world is inherently better than any other. To illustrate their claims, they remind us that the concept of biological species used to be regarded a prime example for natural kinds, but that, in the meantime, various paradigms (based on the morphology, interbreeding capacities, or shared ancestry of organisms) have been proposed, each leading to a different system of classifications.

If natural kinds exist in nature, then what are they? What makes a natural kind the kind it is? Different ideas have been proposed and have given rise to a multitude of questions: Do objects which belong to natural kinds share at least some properties? Are these special, “natural” properties? Are natural kinds determined by the roles they play in inductive inferences or laws of nature? Is there a hierarchy of natural kinds, such that some kinds are more fundamental than others?

A position that has been particularly influential in the 20th century is the view that natural kinds have essences. It supposedly follows from Hilary Putnam’s Twin Earth thought experiment (1975). Suppose there is a planet just like Earth in every way, but there is a liquid that the inhabitants of Twin Earth call “water” and which resembles water in every respect except for its microstructure, which is not H2O, but XYZ. Intuitively, Putnam claims, XYZ is not water, which leads him to assume that, unlike the superficial properties of being wet, potable, and so on, being H2O is a necessary condition for being water. Similar conclusions can be drawn from Saul Kripke’s argument that if we were to find out that the color we have up to now associated with elementary gold is actually an illusion, we would all agree that gold remains gold so long as it has atomic number 79, no matter what color it is (1980). (Kripke and Putnam’s primary aim is to show that the meaning of the terms “water” and “gold” comes not from our concepts but is determined by the structure of the world. We must, hence, acquire it a posteriori.)

Linked to but distinct from the question of what natural kinds are is the question of whether natural kinds form an ontological category in their own right, or if they can be reduced to other existents like properties. Realists regarding natural kinds believe that talk of natural kinds and successful inferences presupposes the existence of natural kinds in nature. Reductionists, on the other hand, may argue that membership in natural kinds is not only determined by a number of shared properties, but also that it consists in nothing over and above having these properties.

Unsurprisingly, metaphysicians of science are especially interested in finding out which, if any, natural kinds are postulated or discovered by the various branches of science and whether they really identify as natural kinds by the standards of contemporary metaphysical theories, or whether the theories of natural kinds need to be revised.

f. Reduction, Emergence, Supervenience, and Grounding

The world consists of many different things. Philosophers have always dreamed of rendering it more orderly by systematizing it in just the right way. An important step towards doing so seems to entail an analysis of the relationships and dependencies between things which belong to different strata or levels of reality. The world apparently comes structured in levels, with things on higher levels somehow depending on the things on lower levels. For example, a factory consists of machines, conveyor belts, and so forth; machines are made of various interacting cogs, levers, and wires (which, if left to themselves, cannot fulfill the functions they fulfill within the machine); the cogs are made out of molecules, the molecules are made of atoms, and the atoms are made of protons, neutrons, electrons, and so on. Dependencies like these are studied by the various special sciences. (Note that the idea that science suggests that the world comes structured in levels has been contested by some philosophers (Ladyman et al. 2007, 178).) It is clear, however, that a factory is not composed of machines, conveyor belts, and so on in the same way that an atom consists of particles. Surveying the whole of science, Metaphysics of Science strives to account for the various ways higher level objects depend on lower level entities. The aim is not just to establish what depends on what, but to also clarify and explicate the nature of the dependencies. The kinds of relations most fervently discussed in Metaphysics of Science include reduction, emergence, supervenience, and grounding.

Reduction is often conceived of as a two-place, asymmetrical relationship to the effect that one thing is somehow made of, accounted for, or explained in terms of another thing. Typically, the reduced thing is conceived of as somehow less fundamental or less real, or even considered to be eliminated. Two types of reduction are relevant to Metaphysics of Science. First, there is reduction of one theory to another. For example, is it possible to express some theories of chemistry in terms of physical theories? If so, can all chemical theories be thus reduced? What about biological, psychological, and sociological theories? Second, reduction is sought between different sorts of entities or ontological categories such as phenomena, events, processes, and so on. Potential candidates include reduction of macro-level objects to molecules, atoms, and subatomic particles, reduction of properties to sets of objects which resemble one another, reduction of states of affairs to entities and properties (including relations), and reduction of the mental to the physical. The latter especially has been widely discussed in metaphysics. (Note that the first and second kind of reduction cohere: if reduction of one theory to another succeeds, then ontological reduction of the entities postulated by the former to the entities mentioned in the latter may thereby also be achieved.) For Metaphysics of Science, claims of reduction pertaining to entities postulated by the sciences are of great interest, as are claims regarding reductive relationships between theories and their key concepts.

In a way, then, an armchair is reducible to its constituent parts: the fabric, upholstery, wood, and metal springs. However, an armchair is obviously not the same as a random pile of these materials. Unsurprisingly, philosophers disagree over whether, for particular cases, complete reduction can be achieved or not. For example, how could Bach’s Brandenburg Concerto No. 6 be reduced to its physical properties? Sure, a particular performance depends on the physical movements of the musicians and on how the created soundwaves causally impact on the hearers’ eardrums, but the Concerto is not identical to these physical properties apparent in any given performance of it, as it exists independently of them.

Those who argue that such reductions do not succeed often speak of the irreducible as emergent from the underlying basis. They want point out that although there is a dependence of the higher on the lower level, the higher level adds something novel and can thus not be completely reduced to the lower level. An emergent property or phenomenon cannot be accounted for by reduction, because it is believed not to be a property of any of the component parts, and it is not obviously caused solely by their interplay. For example, whether or not you find abortion morally reprehensible does not seem to depend on the physical facts. Given the same situation, somebody else might pass the opposite moral judgment. Whereas such moral considerations are of no great professional import to the metaphysician of science, emergent properties in the sciences are. For example, biology still struggles to explain why higher forms of life have certain properties like consciousness, aspirations, and phenomenal experiences, which are not obviously properties of the underlying matter.

Reduction and emergence are interlevel relations. The most innocent, weakest dependence relation that is compatible with both reduction and emergence is called supervenience. Some thing A (the so-called supervenience set) is said to supervene on some other thing B (the so-called supervenience base) if and only if there can be no difference in A without there also being a difference in B—or, for short, if there is no A-difference without a B-difference. For example, an oil painting’s macro-properties (A)—what it depicts and how it looks to us—supervene on its microphysical properties (B): unless the location, intensity, or color of the paint blotches are changed, the painting will always look the same to us. To better understand the world, metaphysicians of science research supposed supervenience relations in the sciences.

In the early 21st century, metaphysicians turned their attention to another sort of interlevel relation: grounding relations. Grounding relations are metaphysical relations which establish a special sort of (noncausal) priority of one over the other. Of two propositions or facts which are related by a grounding relation, one is taken to ground, or account for, the other. Grounding is stronger than supervenience, as it amounts not just to the claim that some A-facts only vary when B-facts vary—which may occur coincidentally—but that A-facts vary because B-facts vary. Unlike some forms of reduction, grounding does not seek to eliminate the grounded fact; attributing full existence to both of them, it merely ascribes a more fundamental status to the grounding fact.

Debates over grounding revolve around a number of pivotal questions, such as whether instances of grounding are all of the same kind or whether they embody a number of different relations (which fall under the larger category of grounding relations), whether the grounding relation is primitive or can be analyzed in terms of other relations, and whether it is an irreflexive, asymmetric, and transitive relation or if other properties should be ascribed to it. The answers to these questions may also have an effect on how we should conceive of interlevel relations in the sciences, and the latter are of great interest to metaphysicians of science.

g. Space and Time

To most philosophers interested in the field, Metaphysics of Science is not confined to discussing concepts that pervade the whole of science (as, arguably, law of nature and causation do). It is also concerned with metaphysical questions that arise with respect to the particular sciences, like “What is life?” (biology) or “What is the ontological status of cultures, governments, and money?” (sociology). The philosophy of physics, too, gives rise to many interesting metaphysical questions. Among them are questions regarding the nature of space and time, which have been debated since the early dawn of western philosophy and, in the light of modern-day physics, are still at issue in philosophical debates.

As humans, we perceive space and time as different phenomena with differing properties. Space, as we perceive it, extends in three dimensions, and we can (almost) freely move in any direction. Through the physical forces which act upon our bodies, we are capable of detecting some sorts of motion through space (like when we run or jump) but not others (like Earth’s rotation). Time, on the other hand, has a sort of directedness to it (commonly referred to as “the flow of time”). We cannot linger at a particular moment in time, and we cannot go back to previous times. Entities somehow change yet persist through time.

Metaphysicians of science are interested in these phenomena especially in the light of Albert Einstein’s theories of Special and General Relativity. These theories were proposed in order to make sense of the fact that the speed of light was measured to remain constant regardless of the motion of the light source, whereas the velocities of objects depend on the motion of the object relative to an observer. For example, the speed of a train measured by a stationary observer on the platform is greater than its relative speed with respect to another, slower train that moves in the same direction. The speed of light emitted by a lamp on the train, however, will be the same regardless of whether it is measured by a passenger or a bystander. In popular interpretations, Einstein’s theory of Special Relativity suggests that the problem can be solved by postulating that the three spatial and the one temporal dimension form a continuum by the name of space-time. An astonishing consequence could be this: Different observers are at motion with respect to different objects. Their perception of the present is determined by which information is accessible to them, which in turn is a matter of which light signals reach them at a given moment. Therefore, their individual present, past, and future differ according to their state of motion with respect to other objects. Thus, an objective, observer-independent order of points in time does not exist. This view is often referred to as the block universe view, because everything seems to simply exist conjointly, with no objective past or future. Some philosophers also suggest that, on this view, familiar material things are three-dimensional slices of four-dimensional objects (sometimes called “space-time worms”).

Some philosophers claim that the block universe view is incompatible with presentism (the philosophical position that holds that only what is present exists) and supports eternalism (the view that all events past, present, and future exist). Unfortunately, the latter seems not to correspond to our subjective experiences of time. This poses a genuine dilemma for metaphysicians: should we accept Einstein’s theories and dismiss our subjective experiences, or do we need to reinterpret the remarkably well corroborated theories to accommodate our everyday conceptions of space and time?

More such fascinating questions remain. How is the (perceived) directedness of time and its irreversibility (which manifests as increase of entropy) best explained? Are space and time finite or infinite? Do they exist fundamentally and independently of the objects in them, or does their existence hinge on the existence of those objects? Quite obviously, these are questions on which scientific theories have a bearing, and Metaphysics of Science works towards solutions that are both philosophically rewarding and scientifically tenable.

5. The Methodology of Metaphysics of Science

Although Metaphysics of Science is concerned with the key concepts that figure prominently in science, its methods are not predominately those of the sciences. Apart from referencing scientific results and practices, Metaphysics of Science has a number of argumentative tools at its disposal that do not usually play an explicit role in scientific methodology but are not entirely unscientific either. In science these forms of arguments are implicitly employed to establish hypotheses when the empirical evidence is insufficient (for example, because two theories are equally well supported by the available evidence). Unlike many scientific theories, metaphysical claims often cannot be tested experimentally at all—not because we lack the technological means to do so, but because the very nature of these claims defies empirical confirmation or falsification. Think, for example, of the claim that laws of nature hold across all possible worlds. This is why reference to theoretical virtues, Inferences to the Best Explanation, arguments from indispensability and serviceability, extensional adequacy, and the Canberra Plan method are of great argumentative importance in Metaphysics of Science.

Note that some philosophers—for example, proponents of naturalized metaphysics (as mentioned in section 2b)—may reject all or some of these methodological tools as transcendental or indefensibly a priori. However, the issue is not currently settled among philosophers, and the tools described below remain widely used in contemporary Metaphysics of Science.

a. Theoretical Virtues

In both science and metaphysics, we strive for internally consistent, comprehensive, unambiguous theories which cohere with our accepted beliefs, have an adequately large scope, and so on. Among the various desiderata, explanatory power and simplicity are often accorded a central role. To strive for an explanatorily powerful theory is to demand that a theory must explain a certain number of phenomena which stand in need of explanation, that it does so thoroughly and systematically, and that it is not ad hoc. The value of explanatory power is obvious: explanation (or at the very least, systematization) is the very purpose of any hypothesis. Not so with simplicity. There are many ways a theory can be simpler than its competitors; for example, it may contain fewer variables than another. Usually, the call for simplicity is understood in terms of parsimony. Occam’s Razor, a principle frequently appealed to in this context, says that entities must not be multiplied beyond necessity—that is, if faced with otherwise equally good theories (in terms of their explanatory power, for example), we are to prefer the one that postulates fewer (kinds of) entities. However, it is unclear whether simplicity and the other explanatory virtues are truth conducive or whether they are primarily pragmatic or aesthetic theoretical virtues (which means, for example, that simplicity is preferable because it is easier to work with simple theories or because they are somehow more agreeable).

Although theory choice criteria are certainly at work in everyday reasoning, philosophy, and science—remember that nobody wants a complicated, inconsistent, unclear, shallow, or incomprehensive theory—the application of such criteria is not straightforward: they must be measured and traded off against each other. Unfortunately, there are no shared standards or guidelines on how this should be done. How do we find out which of two theories is simpler or more consistent with the body of already accepted beliefs? How do we know which criterion trumps another? What is more, whereas in science theory choice criteria are interim solutions until a theory can be empirically proven, there is usually no such post hoc test in Metaphysics of Science. For all these reasons, justifying our appeal to theoretical virtues is not a trivial or easy task.

b. Inference to the Best Explanation

Once it has been determined through careful assessment of the theoretical virtues which available theory is the best explanation for a given phenomenon, we tend to infer that it must also be the correct explanation. In most cases, we will then also say that the entities (objects, fields, structures) postulated in the explanatory theory really exist. That is, we apply a so-called Inference to the Best Explanation (often referred to as “IBE”). For example, astronomers found that the best explanation for a divergence in the orbit of Uranus is the existence of another planet, Neptune, whose gravity interferes with Uranus’ trajectory. Thus, they inferred that Neptune must exist. This hypothesis was confirmed when Neptune was later discovered through telescopes. Similarly, many metaphysicians of science believe that IBE can be applied to metaphysical theories. For example, Nancy Cartwright believes that the best explanation for the fact that laboratory results produced in controlled, sterile settings can be applied to the messy circumstances of the outside world is the existence of underlying dispositions that are examined in the laboratory but also pervade the rest of the world, and she therefore accepts this view as true (Cartwright 1992, 47–8).

Quite obviously, IBEs are not deductively valid, and even the best explanations we have at our disposal can later turn out to be incorrect. For example, when astronomers sought to explain anomalies in the orbit of Mercury, they failed to find Vulcan, a planet postulated explicitly for this purpose, and the anomalies were later explained with the help of the General Theory of Relativity.

Note also that Occam’s Razor and IBEs sometimes pull in opposite directions: whereas IBEs often enrich, rather than reduce, our ontology, Occam’s Razor is set on eliminating as many entities as possible from our ontology. On the other hand, one of the marks of a good explanation is that it does not postulate more than is necessary; that is, it is parsimonious in the sense of Occam’s Razor. Either way, even if metaphysicians can agree on using theoretical virtues and IBEs as argumentative tools, there is still room for debate.

c. Indispensability and Serviceability Arguments

In addition to IBEs, metaphysicians appeal to further inferential arguments to the effect that we should accept certain hypotheses as true. More specifically, indispensability and serviceability arguments basically consist in claiming that if X plays a crucial role with respect to Y, and if Y is either uncontroversial or relates to some postulate that we are unwilling to let go, then the existence of X can (or must) be asserted—that is, we should believe that X exists for the sake of Y.

One reason for accepting the existence of an entity X may be that its existence is indispensable for the existence of Y; that is, Y cannot be the case unless X exists. For example, some metaphysicians argue that the existence of mathematical entities is indispensable for science, and as science is important and probably at least approximately true, we have every reason to believe in the existence of numbers (as Platonic objects, say). Very roughly put, indispensability arguments infer from the premise that X is indispensable for Y and the premise that Y is the case to the conclusion that X exists.

(An older variant of the argument from indispensability is the so-called transcendental argument, which usually runs like this: if X is a necessary condition for the possibility of Y, and if we believe that Y is the case, we should also hold that X exists.)

Serviceability arguments are weaker than indispensability arguments. They advise us to accept the existence of a (kind of) entity X if X is serviceable towards end Y. For example, David K. Lewis argues that the assumption that possible worlds are concrete objects (just as our actual world) is highly serviceable (1986, 3): among other things, it provides us with the means to spell out the semantics of counterfactual conditionals. However, there may be other ways of accounting for the truth conditions of counterfactuals (for example, by referring to complete descriptions of fictitious possible worlds instead). Whereas indispensability offers a strong argument for the existence of some sort of entity, serviceability allows for contenders. Different kinds of entities may serve equally well to implement a goal, and serviceability arguments alone may not suffice to determine which of these entities we should believe in.

The evaluation of indispensability and serviceability arguments depends on what you already believe and what goals you pursue (as represented by variable Y). At best, they yield conditional existence claims: if you believe that science is successful and that science would not be successful if it were not for the existence of mathematical entities, then you had better believe in the existence of mathematical entities. If you do not believe that science is successful, then the argument is moot. Awareness of the occurrences of these kinds of arguments within debates in Metaphysics of Science will certainly help you understand your opponent, but it will seldom suffice to settle the issue.

d. Extensional Adequacy and the Canberra Plan

One particularly useful tool in evaluating metaphysical hypotheses is the test for extensional adequacy. To test a theory for extensional adequacy means to examine cases that, according to pretheoretical, intuitive judgment, fall under a concept the theory aims to explicate and to check whether the theory indeed subsumes these cases as instances of the concept. In addition, the theory may be tested with regard to scenarios in which its concepts should intuitively not apply; if the theory (wrongly) applies, it may have to be corrected. For example, suppose someone proposes a metaphysical theory as to what a law of nature is in claiming that a law of nature is nothing but a general statement of the form “All things which have property F also have property G.” This theory will quickly be challenged: “All pigs can fly” is a general statement, but, intuitively, it is not a law of nature, because it is clearly false. Whereas the sentence matches the alleged criterion for lawhood, it is intuitively not a law and thus a counterexample to the proposed analysis of lawhood.

Tests from extensional adequacy presuppose judgments regarding the extension of the concept in question; that is, it presupposes having a strong intuition about which entities or phenomena fall under it or are denoted by it. Preconceptions and intuitions as to what a concept denotes can diverge, however. They may be products of the culture we live in or the way we speak, and professional philosophers’ intuitions may well differ from the preconceptions of the folk.

Understanding a concept is not merely a matter of knowing what it denotes. Usually, concepts also carry meanings, or intensions. The so-called Canberra Plan is a complex two-step method for clarifying both the correct extension and intension of concepts. In other words, the Canberra Plan first seeks to fix the meaning of concepts (intension) by describing the role that instances of a given concept have to fulfill then, second, strives to identify its actual fulfillers (extension). It was proposed by philosophers associated with the Research School of Social Sciences in Canberra (most notably Frank Jackson and David K. Lewis). First, a concept’s use in everyday, scientific, and philosophical contexts is analyzed by collecting all sorts of platitudes about it. A platitude can be anything we say or believe about the concept. For example, regarding causation, we might believe that causes always precede their effects, that nothing causes itself, and so on. By systematizing the platitudes, the Canberra Planners determine which roles the referents of the concept are usually expected to fulfill. In the second step, they then search for referents, that is, entities or phenomena in the world that match these roles. For our example of causation, the transfer of energy could be proposed as such a role player. Because scientific theories are elaborate attempts at describing the world and because Canberra Planners are generally inclined to believe that scientific theories are at least approximately true (that is, they are scientific realists), particular attention is given to the postulates of the sciences. Depending on whether the second step is successful, we may find out the real extension of the concept in question—or we may have to concede that it has no basis in reality and should be discarded. However, note that there are multiple ways of systematizing platitudes and evaluating scientific theories, and hence the outcome may vary.

Apparently, whichever method(s) we employ, there will always be ways to question our claims in Metaphysics of Science (and in philosophy generally). Apart from the proponents of a radical naturalization of metaphysics, philosophers tend to see this not as a fatal flaw but simply as a characteristic feature which is grounded in the very nature of the discipline. The fact that Metaphysics of Science knows no ultimately decisive method but draws on many different tools that may result in different outcomes is not necessarily a bad thing: these tools may just be the best we have to answer questions that we cannot avoid asking, and there may nonetheless be progress in the form of ever more precise, extensionally adequate theories. At the very least, they allow us to map the field of possible views within Metaphysics of Science.

6. References and Further Reading

    • Armstrong, D. M. 1983. What Is a Law of Nature? Cambridge: Cambridge University Press.
      • Argues that laws of nature are necessitation relations between universals.
    • Barcan Marcus, R. 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic 11: 1-16.
    • Barcan Marcus, R. 1967. “Essentialism in Modal Logic.” Noûs 1: 91-96.
      • Both seminal texts by Barcan Marcus lay the groundwork for formal modal logic and afford later developments like Kripke’s and Putnam’s ideas on direct designation, rigid designation, and essence.
    • Bird, Alexander. 2007. Nature’s Metaphysics. Oxford: Oxford University Press.
      • Develops a dispositional essentialist account of laws of nature according to which laws are grounded in dispositions and turn out to be metaphysically necessary.
    • Carnap, R. 1936. “Testability and Meaning.” Philosophy of Science 3: 419–471 and 4: 1–40.
      • Discusses the simple conditional analysis and proposes the reduction sentences analysis of dispositionality.
    • Carnap, R. 1947. Meaning and Necessity. Chicago: University of Chicago Press.
      • Historically relevant work on the semantics of natural and formal languages which lays the foundations for modal logic.
    • Carrier, M. 2007. “Wege der Wissenschaftsphilosophie im 20. Jahrhundert.” In Wissenschaftstheorie: Ein Studienbuch, edited by A. Bartels and M. Stöckler, 15–44. Paderborn: Mentis.
      • Brief historical introduction to 20th century philosophy of science (in German).
    • Cartwright, N. 1992. “Aristotelian Natures and the Modern Experimental Method.” In Inference, Explanation, and other Frustrations, edited by J. Earman, 44–70. Berkeley: University of California Press.
      • Argues that one cannot make sense of modern experimental method unless one assumes that laws are basically about capacities/dispositions.
    • Chisholm, R. 1946. “The Contrary-to-Fact Conditional.” Mind 55: 289–307.
      • An early attempt at analyzing counterfactual conditionals.
    • Cooper, J. M., ed. 1997. Plato: Complete Works. Indianapolis: Hackett.
      • Collection of English translations of works ascribed to Plato with helpful footnotes and introductory information.
    • Dowe, P. 1992. “Wesley Salmon’s Process Theory of Causality and the Conserved Quantity Theory.” Philosophy of Science 59: 195-216.
      • Criticizes Salmon’s process theory of causality and suggests that a causal theory based on conserved physical quantities should replace it.
    • Dretske, F. 1977. “Laws of Nature.” Philosophy of Science 44: 248–268.
      • Argues that laws of nature are relations between universals.
    • Ellis, Brian. 2001. Scientific Essentialism. Cambridge: Cambridge University Press.
      • Defends the view that the fundamental laws of nature depend on the essential properties of the things on which they are said to operate and that they are metaphysically necessary.
    • Feynman, R. 1967. The Character of Physical Law. Cambridge: MIT Press.
      • A series of lectures discussing several physical laws and analysing their common features, with a focus on mathematical features.
    • Fine, K. 1994. “Essence and Modality.” Philosophical Perspectives 8: 1-16.
      • Criticizes the idea that essence is a special case of metaphysical necessity (and argues that it actually is the other way around) and discusses the relationship between essence and definition.
    • Göhner, J.F., K. Engelhard, and M. Schrenk. 2018. Special Issue: Metaphysics: New Perspectives on Analytic and Naturalised Metaphysics of Science. Journal for General Philosophy of Science 49: 159-241.
      • Addresses various aspects regarding the relationship between metaphysics and science, with a focus on the questions which metaphysical lessons we should learn from linguistics and the social sciences and whether mainstream metaphysical research programmes can have any positive impact on science.
    • Goodman, N. 1947. “The Problem of Counterfactual Conditionals.” Journal of Philosophy 44: 113–128.
      • Examines the problems that face analyses of counterfactual conditionals and attempts a partial definition of counterfactual truth.
    • Goodman, N. 1955. Fact, Fiction, and Forecast. Cambridge: Harvard University Press.
      • Introduces the “new riddle of induction” (grue-problem) and explores the concepts of counterfactual truth and lawhood in order to develop a theory of projection which resolves it.
    • Hall, N. 2004. “Two Concepts of Causation.” In Causation and Counterfactuals, edited by J. Collins, N. Hall, and L. A. Paul, 225–276. Cambridge: MIT Press.
      • Argues that there are two distinct concepts of causation, one of which is best analyzed in terms of dependence, the other in terms of production.
    • Husserl, E. 1970. The Crisis of European Sciences and Transcendental Phenomenology. Evanston: Northwestern University Press.
      • Unfinished classical text in phenomenology originally published in German in 1936, which bemoans the fact that modern science is oblivious to the life-world of humans.
    • Kistler, M. 2006. Causation and Laws of Nature. Oxford: Routledge.
      • Develops and applies a transfer theory of causation.
    • Kripke, S. 1963. “Semantical Considerations on Modal Logic.” Acta Philosophica Fennica 16: 83-94.
      • Gives an exposition of some features of a semantical theory of modal logics.
    • Kripke, S. 1980. Naming and Necessity. Oxford: Blackwell.
      • Argues that the meaning of names is not determined by descriptions and that natural kind terms rigidly designate (that is, that they designate the same natural kind across all possible worlds), thus allowing for a posteriori necessities.
    • Ladyman, J. and D. Ross, D. Spurrett, and J. Collier. 2007. Every Thing Must Go: Metaphysics Naturalized. Oxford: Oxford University Press.
      • Argues for a naturalization of metaphysics by criticizing contemporary analytic metaphysics and develops a scientifically informed structuralist realist metaphysics.
    • Lange, M. 2009. Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature. Oxford: Oxford University Press.
      • Instead of saying that laws support counterfactuals, Lange proposes to reverse the order and say that laws are those generalities that are stable or invariant under counterfactual perturbations.
    • Lewis, D. K. 1973a. Counterfactuals. Oxford: Blackwell.
      • An account of counterfactual conditionals in terms of modal realism. Introduces the Best Systems Account of laws of nature.
    • Lewis, D. K. 1973b. “Causation.” Journal of Philosophy 70: 556–567.
      • Proposes and modifies the counterfactual account of causation in terms of counterfactual dependence.
    • Lewis, D. K. 1986. On the Plurality of Worlds. Oxford: Blackwell.
      • Defends modal realism, which is the view that the actual world is only one of many possible worlds all of which exist, on the basis that it is highly serviceable in solving longstanding philosophical problems.
    • Mackie, J. L. 1965. “Causes and Conditions.” American Philosophical Quarterly 2: 245–264.
      • Proposes the INUS account of causation.
    • Martin, C. B. 1994. “Dispositions and Conditionals.” The Philosophical Quarterly 44: 1–8.
      • Introduces finkish dispositions as a problem for counterfactual analyses of dispositions.
    • Maudlin, T. 2007. The Metaphysics within Physics. Oxford: Oxford University Press.
      • Argues that lawhood is irreducible but can account for causation, counterfactuals, and dispositionality.
    • Mumford, S. and R. L. Anjum. 2011. Getting Causes from Powers. Oxford: Oxford University Press.
      • The authors develop not only a theory of causation based on powers, but also offer a detailed analysis of causal powers themselves.
    • Mumford, S. and M. Tugby. 2013. “What is the Metaphysics of Science?” Metaphysics and Science, Edited by S. Mumford and M. Tugby, 3–26. Oxford: Oxford University Press.
      • Introduction to a collection of state-of-the-art papers on core issues in Metaphysics of Science.
    • Paul, L. A. 2012. “Metaphysics as Modeling: The Handmaiden’s Tale.” Philosophical Studies 160: 1–29.
      • Claims that science and metaphysics of science differ with respect to their respective subject matter, but that there is no categorical difference in method, as both construct theories by building models.
    • Putnam, H. 1975. “The Meaning of ‘Meaning.’” Minnesota Studies in the Philosophy of Science 7: 131–193.
      • Argues for semantic externalism (the claim that the meaning of a term does not determine its extension, which means that the meanings of a word are not determined by the psychological state the speaker is in, but by external factors) using the Twin Earth thought experiment.
    • Quine, W. V. O. 1948. “On What There Is.” In From A Logical Point of View, 1953, 1–19. Cambridge: Harvard University Press.
      • Proposes that ontological commitments can be read off statements or scientific theories by formalizing them in predicate logic and identifying bound variables.
    • Quine, W. V. O. 1951. “Two Dogmas of Empiricism.” In From A Logical Point of View, 1953, 20–46. Cambridge: Harvard University Press.
      • The two dogmas Quine argues against are: (i) that there is a clear distinction between analytically true and synthetically true sentences, and, (ii), that each meaningful sentence faces the tribunal of sense experience on its own for its verification or falsification (rather than holistically in concert with other sentences).
    • Roberts, J. 2008. The Law-Governed Universe. Oxford: Oxford University Press.
      • Introduces the measurability account of laws of nature, which states that lawhood is a role that propositions play rather than a property of facts and that laws guarantee the reliability of methods of measuring natural quantities.
    • Salmon, W. 1984. Scientific Explanation and the Causal Structure of the World. Princeton: Princeton University Press.
      • Develops a causal/mechanical account of explanation which incorporates the idea that causation is best considered a process.
    • Salmon, W. 1994. “Causality without Counterfactuals.” Philosophy of Science 61: 297–312.
      • Agrees with Dowe’s improvement of Salmon’s 1984 theory and also proposes a transfer or conserved quantity theory of causation.
    • Scholz, Oliver R. 2018. “Induktive Metaphysik – Ein vergessenes Kapitel der Metaphysikgeschichte.” In Philosophische Sprache zwischen Tradition und Innovation, edited by D. Hommen and D. Sölch. Frankfurt am Main: Peter Lang.
      • Describes and analyses the historical programme of inductive metaphysics which developed simultaneously with Logical Empiricism.
    • Schrenk, M. 2017. Metaphysics of Science: A Systematic and Historical Introduction. London: Routledge.
      • Comprehensive, easily accessible systematic and historical introduction to Metaphysics of Science including the topics of dispositions, counterfactuals, laws of nature, causation, and dispositional essentialism, as well as information on the origins and methodology of Metaphysics of Science.
    • Schurz. G. 2016. “Patterns of Abductive Inference.” In Springer Handbook of Model-Based Science, edited by L. Magnani. and T. Bertoletti, 151–174. New York: Springer.
      • Analyses the structure of abductive inferences and recommends that metaphysics should make use of such inferences.
    • Stalnaker, R. 1968. “A Theory of Conditionals.” American Philosophical Quarterly 2: 98–112.
      • Uses possible worlds semantics to analyze counterfactual conditionals without a commitment to possible worlds realism.
    • Strawson, P.F. 1959. Individuals: An Essay in Descriptive Metaphysics. New York: Routledge.
      • Distinguishes between descriptive and revisionary metaphysics and examines the relationship between our language and our habit of conceiving of the world in terms of individuals (particulars and persons).
    • Tahko, T.E. 2015. An Introduction to Metametaphysics. Cambridge: Cambridge University Press.
      • Comprehensive and easily accessible introduction to 20th century and current debates about the methodology and epistemology of metaphysics.
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      • Argues that the relations between universals are truth-makers for laws of nature.
    • Williamson, Timothy. 2016. “Abductive Philosophy.” Philosophical Forum, 47 3–4: 263–280.
      • Recommends both ampliative inferences such as abductions (or, nearly synonymous, inferences to the best explanation) and model-building as valuable methodologies not only for the sciences but also for philosophy and metaphysics.
    • Woodward, J. 1992. “Realism about Laws.” Erkenntnis 36: 181–218.
      • Defends the view that the notion of lawfulness is linked to the notion of invariance rather than the notion of necessary connection.
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Author Information

Julia F. Göhner
Heinrich Heine University
Dusseldorf, Germany

and

Markus Schrenk
Email: markus.schrenk@phil.uni-duesseldorf.de
Heinrich Heine University
Dusseldorf, Germany

Language in Classical Chinese Philosophy

At first glance, early Chinese thought as expressed in Warring States period (475-221 BCE) texts does not seem to focus on the kinds of questions about language that one might expect from philosophers working on “the philosophy of language.”  This does not mean, however, that language is philosophically insignificant to early Chinese thinkers.  But it does show that discussions of language in these texts are part of early Chinese authors’ engagement with a larger set of philosophical problems, particularly the problem of self-cultivation.  Here, “self-cultivation” means a set of generalized practices directed toward the goal of moral action, focusing on the development of a set of virtues and norms as they relate to the individual as well as progressively higher units of social organization.  Although positions on self-cultivation differ widely across strands of early Chinese thought, a common goal of all competing traditions is the rehabilitation of human conduct.  Discourse about appropriate “models” (fa 法) for such rehabilitation – whether they be concrete tools, exemplary individuals or abstract ideas – is found in all early Chinese philosophical texts.  This, then, raises the issue of language: how does the sage (shengren 聖), as one who has successfully mastered exercises of self-cultivation and thus furnishes us with the requisite fa, speak? Or, as some traditions ask, does the sage speak at all?  Do words promote or impede an individual’s development, and is the sage’s insight an ineffable experience or is it one that can, and should, be articulated for the benefit of others?  Thus, the problem of self-cultivation functions as a stage for various other intersecting concerns into human nature, the relation between human feelings and thought or judgment, the ideal social and political organization, and the relation between the human subject and the larger processes of nature and the cosmos, among other topics.  Discussions of the linguistic dimensions of sagehood then generate other questions about language:  How do words relate to psychological states? Is language a constitutive element of human nature, or is it a conventional practice that stands in a particular orientation to a naturally given state? Is language inherently tied to the incidence of social and political chaos, or is it a technology that can be used to institute order?   This entry offers a brief overview of how inquiries concerning language are developed in classical Confucian, Mohist, and Daoist writings.

Table of Contents

  1. Key Terms and Problems
  2. Speech (yan 言) as Virtuous Conduct (xing 行) in the Analects
  3. Language and Self-Cultivation in the Mencius
  4. Zhengming 正名 in the Xunzi
  5. The Mohist Canons
  6. ‘Not Speaking’ in the Daodejing
  7. ‘Goblet Words’ in the Zhuangzi
  8. Additional Trends
  9. References and Further Reading

1. Key Terms and Problems

Contemporary debates on language in Chinese philosophy, in the analytic tradition, have been determined to a large extent by the research of Graham (1989, 1978) and Hansen (1983) on the linguistic models displayed in the Mohist Canons. Harbsmeier (1989b, 1991), Mou (1999), Fraser (2007) and Robins (2000) represent a selection of scholars who have extended the inquiry into the grammatical and syntactical structures in the Canons by further developing some of the central theses put forward by Graham and Hansen, such as those concerning the use of word-types (like mass-nouns) and structures of predication. An enduring premise in this approach is the clear distinction between language (variously construed as speech/yan言 and names/ming名) and the reality (shi 實, literally, ‘objects’ or ‘solids’) with which it shares a formal, representational relationship.

Another trend in inquiries concerning language involves a less formal approach, replacing the focus on referential structures with an analysis that identifies language as part of an embodied, empirical model of experience. Geaney (2010, 2002), for instance, argues that conceptions of language in early China cannot be grasped without appreciating the larger perceptual index of sight and sound of which ‘names’ and ‘speech’ are a constitutive element. Wagner (2003) similarly underscores how conceptions of ming in early linguistic models (like that of Wang Bi) define speech in terms of aurality, with ‘names’ being understood as meaningful units of sound. Lewis (1999) calls for situating language somewhere between a purely oral, and thus aural, dimension and a written technology that serves as a more robust medium for recording and articulating judgments.

Alternate directions in the literature display a different set of concerns, foregrounding the socio-political applications of a theory of language. In this latter approach, conceptions of language are often perceived as being coextensive with a conception of culture. We find, as a result, numerous schools attempting to furnish an account of how culture is to be distinguished from a natural state, and how ‘names’ or ‘speech’ fit in relative to this distinction. Multiple accounts of this distinction—as either oppositional, as a continuum, as unconnected—lead to diverse possibilities for conceiving language as a spectrum that displays a naturalist bias at one extreme and a social normative agenda at the other.

Whether we choose to capture the discussions of language in classical Chinese philosophy with a referential model that focuses on predicate logic, a perception-based model of the senses, or a more expansive understanding of language as a socio-political technology, a basic vocabulary emerges across a wide selection of texts that ties the question of language to the larger problem of how one can know the world and provide an articulate judgment of one’s experience in it. Early Chinese accounts of language are intimately bound up with how one discriminates (bian 辨) one thing from another, categorizing the world accordingly in terms of what ‘is so’ (shi 是) and what is ‘not so’ (fei 非). This dialectical capacity for division separates things both on the descriptive as well as normative registers, and thus built into the ascription of something as ‘so’ is the clear sense that it ought to be so. Chris Fraser describes these dual senses of the distinction between shi and fei as follows:

They [shi and fei] apply both to the descriptive, empirical question of whether or not something is a certain kind of thing and the normative question of whether some action or practice is morally right or wrong. In effect, shi and fei refer to a very basic, general normative status that does not distinguish between the different flavors of correctness and error implicated in describing, commanding, recommending, permitting, or choosing . . . Because of their normative use, they are seen as inherently evaluative terms with action-guiding force. In ethical contexts, this feature is obvious, as shi-fei distinctions articulate values. Even in nonethical contexts, however, the attitude of deeming something shi or fei is regarded as action guiding.

A recurrent theme that we accordingly encounter in pre-Han texts concerns the relation of names (ming) to how one discriminates and orders one’s categories. What is a name (ming) in relation that which is so (shi)? Is the negation of a thing by pointing to what it is not (fei) the opposite of a given name in that context? And how does the normative dimension of the model of bian affect the use of names along distinctions between shi and fei? As we see later in the article, these are all problems concerning language and epistemology that emerge as points of contention between the various competing schools of classical China.

2. Speech (yan 言) as Virtuous Conduct (xing 行) in the Analects

Concerns with language in Confucius’ Analects come to rest squarely within the text’s overarching composition of a program of self-cultivation. Names (ming 名) and the activity of speaking (yan 言), broadly construed in both a nominal and verbal sense, therefore do not present the reader with the kind of problematic that requires establishing a logical relation between mental content (as determining the ‘meaning’ of a word) and the world as a given, objective correlate. Rather, the salient question the text repeatedly poses is how to use words and speak in general such that one’s linguistic comportment can coincide with one’s character as a virtuous person. A direct consequence of aligning the question of language along these lines is to be seen in frequent discussions in the Analects where both the style of a person’s speech (its elocutionary attributes, such as tempo and diction) as well as its content emerge as useful measures of moral development. The Master is thus concerned with whether one’s words are sincere (xin 信) and unequivocally identifies “clever or cunning speech” (qiao yan巧言) (Analects, 1.3) with the absence of ren or virtue, as it is broadly construed in this text.

There exists in the Analects, then, no sense of the inherent value of words as signifiers of an external reality. Rather, language is analyzed as a philosophical problem only in relation to the viability of a virtue-based ethics, and its efficacy is to be judged in its successful subordination to, and implementation of, a model of virtuous conduct (xing 行) (see Analects, 9.24). At one end of this spectrum, the Master invokes the rhetorically powerful example of the Ancients, who remain silent out of fear that their actions will not match their words (see 4.22). But of more use is the model of the ‘nobleperson’ or junzi 君子, who displays a flawless calibration of words to action. Scattered across the text, the majority of discussions regarding the nature and use of words comes to settle on the need to emulate the linguistic perspicuity exhibited by this ideal type. The junzi speak with sincerity (xin 信) (see 1.7) and their use of language is repeatedly described as careful (see 1.14), slow (12.3) and always bound by the larger concerns with virtuous conduct (2.13, 4.24).

The capacity to undermine the Confucian art of self-cultivation through a gross misuse of language emerges as a necessary corollary to the conceptual bind the text forges between one’s speech (yan 言) and conduct (xing 行). While all who are virtuous speak in accordance with their character, it is not the case that all who speak are necessarily virtuous (see 14.4). Language can then serve equally as a marker of both moral health as well as moral decrepitude. It is this basic observation that underlies a central Confucian conviction that the health of a society, and its apex political institutions, can be achieved through the practice of zhengming 正名, or ‘correcting names.’ While this is an overt concern and stated objective in the Xunzi, the Analects underscores the important role that zhengming plays in a famous passage that links socio-political disorder ultimately with a state of linguistic disorder (see 13.3). If names (ming ) in their specific designation refer not to discrete objective correlates (‘son,’ ‘father’ as neutral, discrete units) but rather to how one must act in relation to the roles associated with such names (to ‘be a son,’ to ‘be a father’), then a state of linguistic disorder is one in which the designation of behavioral norms implied in the use of names no longer works or implies a failure of these norms. Where the performative designations of our names are not properly understood, socio-political chaos must necessarily reign. The Analects thus points in the direction of a prescriptive theory of language in its brief formulation of a program of zhengming, which involves the rehabilitation of such a comprised language and its social and political ill-effects.

3. Language and Self-Cultivation in the Mencius

In the Mencius, the Confucian program of self-cultivation is given further conceptual depth to the extent that a more robust metaphysics of human nature (ren xing 人性) anchors the entire project. The text organizes its discussions of language with particular attention to its overriding concerns with the nature and development of the heart (xin 心) and the attainment of a kind of moral animation in the human subject, which it describes in Mencius 2A2 as having a “flood like qi” (hao ran zhi qi 浩然之氣). In other words, the imperative in the Mencius is not simply to secure a complementary organization of language (yan 言) and virtuous conduct (xing 行), as we have seen in the Analects. The text adds depth to this generalized formulation of language by integrating the question of how to use words with its more intricate moral psychology of the heart and human nature. One appreciates the implications of this move in the naturalized status that extends to language itself. For instance, Mencius 4A15 establishes a parity between certain basic physical attributes, like the pupils of a person’s eyes, and the kind of language they speak. Crucially, these attributes—one anatomical, another linguistic—function as potent markers of a more fundamental moral signature of human nature. Thus, if the inherently moral capacities of being human are to be realized, the text points to both one’s pupils as well as one’s words as the natural markers of moral development.

The position the Mencius takes on the status and role of language is, however, not so straightforward if we consider two basic paradigms in the text that bring everything into moral orientation. The first of these models is that of the ‘nobleperson’ or junzi 君子, who is able to grow the “four (moral) sprouts” (si duan 四端) of the heart and successfully master the virtuous conducts of benevolence (ren 仁), ritual propriety (li 禮), righteousness (yi 義) and knowledge (zhi 知). Such a perfected moral state, while it manifests in the junzi’s physical comportment, remains wordless (bu yan不言, Mencius 7A21). At the cosmological level, the text is emphatic about the silence of Heaven (tian 天), whose commandments, which remain unarticulated, can be gleaned only from the evidence of the King’s conduct and the people’s acceptance (see Mengzi 5A5).

However, it is between the poles of silence and grandiose speech that the Mencius affirms the efficacy and value of language. While it describes the junzi as effecting a wordless practice, the text simultaneously upholds speech that is simple and concise (compare Mencius 7B32, 4B15). The overarching framework of ren xing, furthermore, supplies the authors with a standard for truth or genuineness such that speech that complements the natural development of virtuous conduct is positively upheld as corresponding with the reality (shi 實) of things (Mengzi 4B17). A corollary to a genuine/natural language is the potentially false modality of speech, and the Mencius explicitly participates in this arbitration between truth and falsity by rejecting what it terms as “one-sided” and “perverse” speech (see Mencius 2A2, 3B9). Here we are presented with an important dimension to the linguistic philosophy of the Mencius in its thematization of the activity of disputation, or bian 辯, a dialectical framework of language characterized by the eristic exchanges between various parties to a debate. Words in this context admit either to being true or false, and the text explicitly stakes its claims by rendering the principles of competing schools, like those of Yang Zhu and Mo Di, as “one-sided” and “perverse.” Yet, measures of truth and falsity in the Mencius, it bears repeating, do not function in relation to an objective, neutral external world. Rather, the performative dimension of self-cultivation remains the basic conceptual frame. To speak truly and genuinely, in a way that corresponds to the reality of things, implies that such words are distinguished primarily by their virtuous quality. The perversity of the speech of adversaries, like Yang Zhu and Mo Di, is a problem precisely because of the potential of such misguided language to draw society down into a bestial condition, where the genuine principles of benevolence and righteousness are nowhere to be seen (Mencius 3B9).

4. Zhengming 正名 in the Xunzi

Xunzi’s philosophy revolves around the central premise that one’s humanity can be successfully shaped only through concerted effort within the institutional frameworks of education and ritual. A conceptual locus in the text is accordingly represented by the concept of wei偽, ‘deliberate effort,’ a model of virtuous conduct that involves the concerted implementation of institutionally mandated practices. Xunzi’s often cited constructivism is thus to be distinguished from the Mencian belief in the continuity between nature (xing 性) and institutions, the latter being mechanisms by means of which natural dispositions, as positive traits already present in an individual, can be fully actualized. Nature and nurture for Xunzi are not complementary as they are for Mencius, and the former’s claim that “human nature is evil” (xing e 性惡) implies that the work of nurture is a focused undoing or rectification of a naturally undesirable configuration of elements in an individual. The notion of wei偽 therefore implies a concerted level of intervention in natural processes and patterns, denoting an activity that is distinguished by its levels of artifice rather than spontaneity.

Xunzi’s concern with establishing right order, then, does not extend to achieving a harmonious state prescribed in nature, but instead refers to appropriately functioning conventions of society and politics. It is within this overall context of assumptions regarding nature and the institutions that are necessary for a society’s ordered existence that the question of language proves to be of pivotal importance in the text. Names (ming 名) in the Xunzi are a technology through which the undesirable traits of human nature can both be expressed as well as curtailed. As the text states, names have neither “innate appropriateness” (gu yi固宜), nor do they admit to any “intrinsic reality” (gu shi固實). Yet, there are those which are “intrinsically good” ([ming you] gu shan 名有固善). Xunzi thus frees language from any problematic tie with nature since words share no constitutive bond with xing 性, a state that, in turn, is described as “evil,” e 惡. At the same time, however, they are potential markers of virtuous conduct, and it is successfully utilizing this potential of language to rehabilitate society that constitutes a central aim of the text.

The chapter entitled Zheng Ming 正名, “Correcting Names,” details the Xunzi’s intricate treatment of language in both its calamitous as well as remedial versions. The text begins by attributing a significant source of disorder in society to a particular linguistic condition, which it associates with a series of flawed acts like “splitting names,” “making up new names,” and “throwing into disorder established names.” What comes in for censure here is, in essence, the relativism of standards provoked by the competing theories of the Mohists and other camps like the School of Names (Ming jia 名家). The text diagnoses as deplorable a situation in which each school articulates a ‘name’ for itself, evaluating and discriminating reality on the basis of a set of purely subjective observations. One’s ability to understand and negotiate reality (shi 實), according to the Xunzi, depends on the quality of our names or ming 名 (broadly construed to include categories and distinctions) made in language. Where numerous distinctions crowd around the same reality (be it an object, a relation, a character, a role, and so forth), the designation between ming 名 and shi 實 breaks down to result in chaos and confusion.

How, then, does one go about “correcting names”? The text upholds its Confucian commitment to tradition, adapting its conservatism, however, to the specific task of rehabilitating the linguistic standards perfected and fixed by the previous generations of kings. These are the “common names” (san ming 散名), which exhibit a clarity of designation between ‘names’ and ‘reality’ that must be modeled if the disorder that prevails in society is to be corrected. The Xunzi elaborates a nuanced framework to explain this positive linguistic model, explaining the origin of ‘correct’ names in relation to other aspects of an individual’s physical, psychological and epistemic experience, and, in this respect, arguably makes its most significant contribution regarding questions of language. What the sage, like the true kings of the past, is able to successfully identify is the evolution of a given experience through its various stages of development: starting with the elemental origins in the senses; the psychological shaping of such sensory stimuli in feelings/dispositions or qing 情; and the overall understanding or knowledge (zhi 知) of the heart that is able to make sense of and correctly judge the entire process as it unfolds. Sages display a mastery over this entire psycho-physical complex, and their acute zhi 知 enables them to identify which things involve a similar sensory experience and evoke corresponding, similar dispositions, and which things must be accordingly distinguished as generating divergent stimuli and responses. This perspicacity leads to the correct designations in language, where each set of names exhibits a careful sorting of accumulated sensory and psychological data with the constant inflow of new experiences. It is this sorting activity at the level of names that constitutes, in the most rudimentary sense, the deliberate effort (wei 偽) that the Xunzi praises in the work of sages and the larger institutional frameworks of education and ritual. The implementation of zheng ming obviates the proliferation of multiple standards and classes of things by which people can judge their reality. To ‘correct names,’ then, is, first and foremost, to safeguard a society from the scourge of relativism. The text accordingly recommends the king to regulate definitions of names in order that his citizens clearly understand the meanings and referents of words that are in use. Ming 名and shi 實 are thereby harmonized, such that the relations between words and their referents are made plainly manifest and are agreed upon in the social and political conventions through which language is put to use. Zhengming is thus primarily about the social and political benefits to be gained from using language in a particular mode. As the text affirms in its advice to kings, correcting names equips the people with a unified intention and enables them, ultimately, to follow the law. This is the only path to good and successful governance.

5. The Mohist Canons

The short tracts of text that comprise the Mohist Canons as well as the longer work of the Mozi offer a series of dense statements on the nature of language. The Canons in particular put forward a theoretical framework that establishes standards for making true statements and engaging in clear and effective communication. As scholars have often suggested, the Canons are remarkable for the technical nature of their discussions on names (ming), on the relation between names and the reality of objects (shi), and on the epistemic status of our language. Yet, there is an unmistakable sense that the text remains bound to the narrow objective of establishing a sound theory of language for the purposes of defining the basic tenets of Mohist doctrine. A general frame for these inquiries into the nature and the proper use of names is therefore the model of ‘debate’ or bian, which is explicitly thematized in the Canons as the guiding activity through which the proper dao (as envisioned by the Mohists) can be codified and defended. The text defines bian as “contending over claims which are the converse of each other” and continues to state that “winning in disputation is fitting the fact.” Claims which are, in a bian-type exchange, the “converse” of each other are, as we have already seen, the dichotomy of claiming one thing to be so (shi) and another to be not-so (fei). The Mohist is emphatic on the factual nature of this distinction, explicitly marking out the categories of shi and fei as either fitting with reality or not, and the Canons equip the practitioner with the requisite tools and knowledge with which to master this art of discrimination and to articulate the true and correct picture of Mohist doctrine.

We should thus read the Canons as, first and foremost, a text that expounds a dialectical model equipping a speaker to clearly distinguish what is so or right (shi) from what is not so or wrong (fei). As a manual of argumentation or debate (bian), it accordingly inquires into the fundamental laws governing names (ming 名) and their referencing of objects/reality (shi), and discusses more complex problems surrounding the nature of evidence in arguments, the relation between sentences and a speaker’s thoughts, the uses of analogy, and the methods of illustrating, matching, adducing, and inferring (to name but a few of the themes covered).

At the heart of the diverse discussions on language in the Canons lies what Angus Graham has called a “radically nominalist approach to naming.” Such a model does not admit a premise of essences at work in language, whereby a name for a thing might be understood as referencing a core, defining idea that transcends all particular instantiations. To categorize something as ‘this’ or as ‘so’ (shi), and to extend that category to a ming or ‘name,’ is to simply pick out one thing among others and identify it as what it is called. “[T]here is no ‘essence’,” as Graham suggests, “merely the existence (you 有) of the thing with all its properties.”

The nominalism of the Canons does not, however, commit the Mohist to a relativistic view on truth or to a skepticism regarding the epistemic status of names. A central objective of the text in this respect is the identification of the correct procedures for relating names to objects so that language can be used consistently and correctly. The Canons thus articulate a larger epistemological framework by presenting specific sources of knowledge and identifying specific objects of knowledge that allow for a more structured and nuanced discussion of how names are engendered and the various orders of meaning they convey. Knowledge (zhi 知) can be obtained “by hearsay [report], by explanation, and by personal experience [observation]” and its specific objects are “names (ming), objects (shi), how to relate [an object to a name], and how to act.” We find here a basic set of premises shared by the Confucians—namely, that distinguishing between objects using names, and being able to successfully apply the correct names (that is, relate names to objects) produces knowledge and has the effect of guiding one’s actions. Yet, while the Confucian paradigm, as we have seen it on display in Analects 13.3 and in the Xunzi, sets about rectifying the reality of behavior and conduct so as to rehabilitate the correct norms codified in language, the Mohist Canons are emphatic on the need to grasp the act of naming itself. The name (ming), in other words, functions as a definition of the thing (shi), and in doing so denotes its reality.

At the heart of the Canons, then, lies a basic set of premises regarding how to discriminate between the names for various things based on more subtle distinctions between the various kinds or classes of names and referents. Thus, for example, Canon A78 identifies three classes of ming that align with the kinds of referents they point to:

Names. Unrestricted; Classifying; Private.

‘Thing’ (wu 物) is ‘unrestricted’; any object necessarily requires this name. Naming something ‘horse’ is ‘classifying’; for ‘like the object’ we necessarily use this name. Naming someone ‘Jack’ is ‘private’; this name stays confined in this object.

Unrestricted (da 達) names, covering the largest class or kind, have a general scope of designation (like the name, thing/wu 物); then there are class (lei 類) names, which refer to particular kinds/classes of things and are thus limited in scope (like horse/ma 馬); finally, there are personal or private (si 私) names, which are singular in reference (like a proper noun, Jack). That this typology functions on the basis of an underlying ontology of sameness and difference is evident in the logic which drives us from using one type of name to another. Between the word ‘thing’ and ‘horse,’ we have separated out members and distinguished one kind of ‘thing’ from others with which it does not share defining traits. A horse is not a hammer, and thus can be distinguished by a name that marks both its difference from other things (hammers) and its sameness with others (other horses). The Canons appear to take for granted the idea that the reality of objects (shi 實) is divided along such natural classes of sameness and difference, and names, as definitions of this reality, correspond to and express these divisions of classes as given facts that are observable in one’s experience.

The act of speaking (yan 言), then, is a dynamic composite of naming, where a directed intention on the part of the speaker to convey some idea or thought (yi 意) leads to an explicit choice of naming in relation to reality. This act of referring (ju 舉) is an integral moment of the speech act, which the Canons define as “picking out an object from among others by means of its name.” To refer, furthermore, “is to present the analogue for the object” and every reference therefore is an act of setting up an “archetype” (ni 擬) which the chosen name evokes as a meaningful standard (fa 法). Speaking (yan 言) is described as an “emergence of references” (chu ju出舉), a linking up of various names that evoke models or archetypes that all speakers are in possession of. Thus, in addition to the premise that there are different kinds of names (based upon sameness and difference, for example), the Canons also appear to assume the role that convention plays through mutually agreed upon standards or archetypical referents for the names shared among a linguistic community.

6. ‘Not Speaking’ in the Daodejing

The canonical texts of early Daoism also question the role and status of language in relation to an ideal of self-cultivation that is set up as a prime objective to be achieved. However, in sharp contrast to the constructivist tendencies of Confucian discourses, texts like the Daodejing and Zhuangzi explicitly reject the idea that language can be optimally regulated in and through institutional frameworks and conventional practices. There is, moreover, a thoroughgoing suspicion that pervades these texts regarding the value of language in general, and we repeatedly encounter the claim that linguistic expression, in its very constitution, is ridden with epistemic poverty (insofar as words do not attain any true standards for knowledge). This leads to a more extreme position, often cited by scholars in both the Daodejing and Zhuangzi, that rejects language, as such, as a medium of expression. Harmonization with dao, the focus of self-cultivation, is thus understood to be a distinctly extra-linguistic experience.

The Daodejing makes its case for the ineffable quality of a practice of self-cultivation by describing the sage repeatedly as one who does not speak. Daodejing 56 emphasizes in this regard the inversely proportional relation between knowledge and speaking, where “one who understands [dao] does not speak” and one who has no understanding whatsoever has much to say (zhi zhe bu yan, yan zhe bu zhi 知者不言,言者不知). As a categorical rebuke of the Confucian faith in institutional practice and of the conceptual locus established by the notion of deliberate effort (wei偽) in texts like the Xunzi, the Daodejing extols the model of “non (or non-coerced) action” (wu wei 無為). Sages, in other words, must abandon the strictures that come down by way of conventional standards, habits, cultures of education, and other institutionalized patterns of behavior and conduct. Acting without acting, then, is to divest oneself of the social mores that, in a Confucian practice, are pivotal to the successful implementation of a program of self-cultivation. The text appears to suggest that such sagacity entails a termination of speech, as we learn in Daodejing 2, which describes how sages who excel in the affairs of non-action “practice the teaching that is without words” (xing buy an zhi jiao行不言之教).

And yet, the irony, if not the outright contradiction, of an argument that claims the inadequacy of language that is itself put in words is not lost on the authors of the Daodejing. To use language to extol a condition that appears, on the face of it, to be extra-linguistic therefore suggests a more nuanced perspective that these authors hold. We find, for instance, an additional set of claims in the text that uphold a certain kind of speech, and which positively describe words of the sage that mirror the spontaneous patterns of the dao. The ontology captured by the character ziran 自然, the ‘self-so-ing’ essence of dao that manifests in diverse cycles of change and natural progression, finds expression in a particular modality of speech in which words match the fluidity of nature. Rather than a state of complete and total aphasia (the speechlessness that, for example, defines the Pyrrhonian skeptic), the art of wuwei involves a perspicuous and measured operation of language. The Daodejing does in fact describe positive linguistic traits to be modeled, like words that are “trustworthy” (信, Daodejing 8) and that are “lacking in that which can be blamed” ([善言]無瑕讁, Daodejing 27). The text even identifies certain standards by which the reliability of speech can be judged, stating in Daodejing 81, for instance, that “trustworthy words are not beautiful” (信言不美). The sage who acts without acting, then, also speaks without speaking. As a linguistic complement to its model of wuwei, the Daoejing, rather than eliding language completely from its agenda, recommends a certain modulation of speech whereby the errors in how we utilize language might be removed and its potential to express the patterns of dao might be affirmed.

7. ‘Goblet Words’ in the Zhuangzi

While it retains the core themes of the Daodejing, the Zhuangzi elevates its criticism of Confucian and Mohist discourse and dismantles, in a spectacular fashion, the fundamental structures of dialectical speech that underlie both philosophical positions. The authors of the Inner Chapters (Neipian 內篇) build, in this respect, an elaborate critique of argumentation [or disputation] (bian 辯) —a genre of thinking and speaking that is defined by eristic speech, which, as we have seen, pivots on the choice of arguing for one alternative over another. The Qiwulun, the second of the Inner Chapters, evaluates the tenability of such a basic kind of dialectical exchange it associates with the debates of the Confucians and Mohists, where each party argues for its set of claims as true and as constituting a body of knowledge, and correspondingly associates the opposing party’s claims with falsity. The linguistic structure underpinning all such eristic speech is represented by the clear distinction between a positive ascription of what is the case (conveyed by the character shi 是) and a negative attribution using the character fei 非 to reference all that is not. In sharp disagreement with the linguistic models of texts like the Mozi and the Mohist Canons, the Zhuangzi associates this dichotomy of shi-fei claims—of what is and is not so, of what is right and wrong—with a vocabulary of artifice and inflexibility.

夫道未始有封,言未始有常,為是而有畛也。

The way has never had borders; speech has never had any regularity. Make claims about what is so, or what is right, and there are boundaries.

The method of defining what is so, as we read here, consists literally in a making of a definition (conveyed by the characters wei shì為是), where the artifice of a fixed category stands in direct contrast to the processual nature of experience that is dao. Furthermore, dividing language in terms of strict labels, standards or categories continually eludes the reality of dao and only serves to delude an individual with false standards for knowledge. Bian 辯, owing to the very nature of sophistical speech, therefore endlessly carries on and, as per the diagnosis of the Zhuangzi, serves only to wear out the heart-mind (xin 心).

Yet, in analogous fashion to the Daodejing, the Zhuangzi does not recommend an indiscriminate abandoning of all speech. The exemplary model of the sage not only speaks, but does so in a language that, in fact, occasionally spills into the genre of dialectics.

物無非彼,物無非是。自彼則不見,自知則知之。故曰:彼出於是,是亦因彼。

Of things, there are none that are not ‘that’ (bi 彼); of things there are none that are not ‘this’ (shi 是); One cannot see a thing if one approaches it as ‘that,’ one knows it as ‘this’ only as it is known to oneself. Thus it is said: ‘That’ emerges from ‘this,’ ‘this’ follows from ‘that.’

. . . 為是不用而寓諸庸…因是已。已而不知其然,謂之道。

[The sage] does not use a [fixed] definition of what is the case (wei shi為是) but instead lodges it in the usual . . . This is to judge what is so on a given basis (yin shi因是) and stop. Stopping without knowing (bu zhi不知) it to be so, this is called dao.

Unlike the rhetorical ploys and logic-chopping inherent to the activity of bian 辯, the generation of categories in the sage’s dialectic is fluid and perpetually under revision. A key insight in the Zhuangzi thus relates to the inescapability of linguistic expression and the corresponding need to constantly modulate our categories so they can adapt to shifting perspectives and contexts.

The text articulates this positively appraised framework of language using the metaphor of “goblet words” (zhiyan 卮言), a class of speech that is set apart from the ordinary use of language. While the latter functions through a stable matrix of ascriptions and designations between words and reality, the image of the goblet serves the purpose here of emphasizing a thorough dynamism in the way that words can be deployed. Like a goblet that continually overflows only to be filled again with water, the Zhuangzi perceives of a transformative speech that similarly ‘overflows’ each act of categorization or definition. Language, in such a figuration, enables a speaker to express multiple possibilities of experience, and it takes on a varied and rich descriptive quality that, as the text states, “harmonizes with the natural” (he yi tian ni 和以天倪). In sharp contrast to the Confucian agenda of zhengming, which strives toward instituting a catalog of names deemed to be singular and fixed in their denotations, the goblet language of the Zhuangzi is forever under revision, accumulating ever more shades and textures to our names so they may correspond to the self-so-ing (ziran 自然) ontology of dao.

8. Additional Trends

There are of course additional texts and trends, both in pre-Han Chinese literature and in later literary traditions, that further illuminate the line of inquiry that has been introduced here. One body of work that offers ample opportunity for further research is the corpus of excavated materials that has yet to receive an in-depth treatment focusing on the themes and problems of language. Two texts, the Tai Yi Sheng Shui 《太一生水名》and Heng Xian《恆先》, for example, identify a set of positions on names (ming) as part of larger cosmogonic models. In the case of the Tai Yi Sheng Shui text, the problem of naming is specifically related to a cosmogonic account in which an underlying structure of binary pairings governs the nature and use of names. The text articulates the question of language, in other words, in relation to an account of genesis, and the potential of names (ming 名) is rendered in their ability to either maintain or upset a generative structure that is understood to subtend all things. This imbrication of cosmogony and language, moreover, points explicitly to the role of cultivation that we have identified as deeply connected to the question of language in classical Chinese accounts. The regenerative logic of the cosmogonic account, when it is replicated at the level of language, endows the speaker with the ability to bring harmony to the realm of human endeavors and to aid in the cultivation of one’s person. The Tai Yi Sheng Shui resorts to the familiar model of sages, and presents them as figures who utilize cosmogonic principles of regeneration and rebirth by appropriately wielding the ‘name’ of dao. In doing so, the text explicitly praises them for achieving the completion of affairs (shi 事) and the cultivation of their persons (shen身).

The Heng Xian seems to offer an alternative account in which the organizing conceptual frame is the ontological division between being or presence (you 有) and non-being or absence (wu 無). ‘Names,’ in this binary account, are endowed with a mediating role between a conscious, coercive activity and a complete absence of the same. The text articulates this middle ground through the creative notion of names and accompanying “endeavors” (shi 事) that “become (or happen) of themselves” (zi wei自為).

This article has offered but one perspective on the treatment of language in classical Chinese texts, foregrounding the intersection of concepts of language and the larger concern with cultivation practices. Numerous possibilities for thinking about the nature of language emerge along a spectrum where speech is rendered, at one end, as a natural disposition, or, at the other, as an artificial construct that must be calibrated to achieve a desired state at the individual as well as communal levels. Irrespective of a bias toward naturalism or constructivism, a recurring theme emerges in the figure of the sage or shengren who supplies each of the schools with a model or fa 法for how language should ideally be deployed. The excavated literature adds additional diversity to this conversation, offering another iteration of the sage who appears to borrow from both the Confucian as well as Daoist theories of language and their corresponding models of sagacity.

9. References and Further Reading

  • Allan, Sarah. 2003. “The Great One, Water, and the Laozi: New Light from Guodian.” T’oung Pao 89 (4/5):237–285.
  • Boltz, William. 1985. “Desultory Notes on Language and Semantics in Ancient China.” Journal of the American Oriental Society 105 (2):309–313.
  • Brindley, Erica F. 2013. “The Cosmos as Creative Mind: Spontaneous Arising, Generating, and Creating in the Heng Xian.” Dao 12 (2):189–206.
  • Fraser, Chris. 2007. “Language and ontology in early Chinese thought.” Philosophy East and West 57 (4):420–456.
  • Fraser, Chris. 2016. The Philosophy of the Mòzĭ: The First Consequentialists: Columbia University Press.
  • Geaney, Jane. 2002. On the Epistemology of the Senses in Early Chinese Thought: University of Hawaii Press.
  • Geaney, Jane. 2010. “Grounding “language” in the senses: What the eyes and ears reveal about Ming 名 (names) in early chinese texts.” Philosophy East and West 60 (2):251–293.
  • Graham, Angus C. 1978. Later Mohist Logic, Ethics, and Science: Chinese University Press.
  • Graham, Angus C. 1989. Disputers of the Tao: Philosophical argument in ancient China: Open Court La Salle, Ill.
  • Hall, David L., and Roger T. Ames. 1987. Thinking Through Confucius: State University of New York Press.
  • Hansen, Chad. 1983. Language and Logic in Ancient China: University of Michigan Press.
  • Harbsmeier, Christoph. 1989a. “The Classical Chinese Modal Particle Yi.” In Proceedings of the Second International Conference on Sinology, 471–503. Academia Sinica.
  • Harbsmeier, Christoph. 1989b. “Marginalia Sino-Logica.” In Understanding the Chinese Mind: The Philosophical Roots, edited by Robert E. Allinson, 59–83. Oxford.
  • Harbsmeier, Christoph. 1991. “The mass noun hypothesis and the part-whole analysis of the White Horse Dialogue.” In Chinese Texts and Philosophical Contexts: Essays Dedicated to Angus C. Graham, 49–66. Open Court.
  • Hutton, E.L. 2014. Xunzi: The Complete Text: Princeton University Press.
  • Kjellberg, Paul. 2007. “Dao and Skepticism.” Dao 6 (3):281–299.
  • Lewis, Mark E. 1999. Writing and Authority in Early China: State University of New York Press.
  • Loy, Hui-chieh. 2003. “Analects 13.3 and the Doctrine of “Correcting Names”.” Monumenta Serica 51:19–36.
  • Mou, Bo. 1999. “The structure of the Chinese language and ontological insights: a collective-noun hypothesis.” Philosophy East and West:45–62.
  • Perkins, F. 2014. Heaven and Earth Are Not Humane: The Problem of Evil in Classical Chinese Philosophy: Indiana University Press.
  • Robins, Dan. 2000. “Mass nouns and count nouns in classical Chinese.” Early China 25:147–184.
  • Wagner, R. G. 2003. Language, Ontology, and Political Philosophy in China: Wang Bi’s Scholarly Exploration of the Dark (Xuanxue): State University of New York Press.
  • Yearley, Lee H. 2005. “Daoist Presentation and Persuasion: Wandering among Zhuangzi’s Kinds of Language.” Journal of Religious Ethics 33 (3):503–535.
  • Zhuangzi. 1956. Zhuangzi Yinde (A Concordance to Chuang Tzu), Harvard-Yenching Institute Sinological Index Series. Cambridge MA: Harvard University Press.

Author Information

Rohan Sikri
Email: rsikri@uga.edu
University of Georgia
U. S. A.

Plato: Meno

PlatoPlato’s Meno introduces aspects of Socratic ethics and Platonic epistemology in a fictional dialogue that is set among important political events and cultural concerns in the last years of Socrates’ life. It begins as an abrupt, prepackaged debater’s challenge from Meno about whether virtue can be taught, and quickly becomes an open and inconclusive search for the essence of this elusive “virtue,” or human goodness in general. This inquiry exhibits typical features of the Socratic method of elenchus, or refutation by cross-examination, and it employs typical criteria for the notoriously difficult goal of Socratic definitions. But then a distinctive objection to the possibility of learning anything at all by such inquiry prompts the introduction of characteristically Platonic themes of immortality, mathematics, and a “recollection” of knowledge not learned by experience in this life. A model geometry lesson with an uneducated slave is supposed to illustrate the importance of being aware of our own ignorance, the nature of proper education, the difference between knowledge and true belief, and the possibility of learning things without being taught. When the conversation returns to Meno’s initial question of whether virtue can be taught, Socrates introduces another manner of investigation, a method of “hypotheses,” by which he argues that virtue must be some kind of knowledge, and so it must be something that’s taught. But then Socrates also argues to the contrary that since virtue is never actually taught, it seems not to be knowledge after all.

This dialogue portrays aspects of Socratic ignorance and Socratic irony while it enacts his twofold mission of exposing common arrogant pretensions and pursuing a philosophical knowledge of virtue that no one ever seems to have. It is pervaded with typical Socratic and Platonic criticisms of how, in spite of people’s constant talk of virtue, they value things like wealth and power more than wisdom and justice. And it includes a tense confrontation with one of the men who will bring Socrates to trial on charges of corrupting young minds with dangerous teachings about morality and religion. The dialogue closes with the surprising suggestion that virtue as practiced in our world both depends on true belief rather than knowledge and is received as some kind of divine gift.

Table of Contents

  1. Overview of the Dialogue
    1. Dramatic Setting
    2. Characters
      1. Socrates
      2. Meno
      3. Anytus
    3. Summary of Arguments, in Three Main Stages
  2. Major Themes of the Dialogue
    1. Virtue and Knowledge
    2. Recollection and Innate Ideas
    3. Teaching and Learning
    4. Theory and Practice
  3. Relations of the Meno to Other Platonic Dialogues
  4. References and Further Reading
    1. The Standard Greek Text
    2. Some English Translations
    3. Some Book-Length Studies
    4. Some Articles and Essays on the Major Themes
      1. Virtue and Knowledge
      2. Recollection and Innate Ideas
      3. Teaching and Learning
      4. Theory and Practice

1. Overview of the Dialogue

a. Dramatic Setting

The Meno is a philosophical fiction, based on real people who took part in important historical events. Plato wrote it probably about 385 B.C.E., and placed it dramatically in 402 B.C.E. Socrates was then about sixty-seven years old, and had long been famous for his difficult questions about virtue and knowledge. In just a few years, he would be convicted and executed for the crime of corrupting the youth of Athens. This dialogue probably takes place in one of Athens’ gymnasia, where men and boys of leisure gathered not just for exercise, but also for education and socializing. Socrates often conducted his distinctive philosophical conversations in places like that, and ambitious young men like Meno, who studied public speaking and the hot intellectual topics of the times, wanted to hear what Socrates had to say. Some wanted to try refuting him in public.

The larger setting is the political and social crisis at the end of the long Peloponnesian War. After finally being defeated by Sparta, Athens has narrowly escaped total destruction, and is now ruled by a Spartan-backed oligarchy. The questions in the Meno about teaching virtue are directly related to longstanding tensions between oligarchic and democratic factions. For generations, Athens had been an intellectual, economic, and military leader, especially after her crucial role—together with Sparta—in repelling the Persian invasions of Greece in 490 B.C.E. and 480 B.C.E. Athens’ radically democratic form of government was distinctive but influential in typically oligarchic Greece, and influential largely because she presided over the Delian League of nearly 200 city-states, which became an Athenian empire. After those Persian invasions, many independent cities had asked Athens to replace Sparta in leading a united defense and reprisal against the Persian empire. But eventually most were just supplying mandated funds to Athens, basically for the continuation of Athens’ war against Sparta’s Peloponnesian League. Through many reversals of fortune, Athens both suffered greatly and flourished culturally, using some of that tribute for her own development and adornment. Much of the best Greek art still familiar to us today—the sculpture and architecture, the tragedy and comedy—comes from the Athens of that time. Artists and intellectuals flocked to Athens, including the new kind of traveling teachers, called “sophists,” who are so disparaged in the last part of the Meno. These teachers were independent entrepreneurs, competing with each other and providing an early form of higher education. Much of their influence came through their expensive courses in public speaking, which in Athens prepared young men of old aristocratic families for success in democratic politics. But various sophists also taught various other subjects, from mathematics to anthropology to literary criticism.

Shortly before this dialogue takes place, some leading Spartans and allies considered killing all the Athenian men and enslaving the women and children. But they decided instead to support a takeover by a brutal, narrow oligarchy, led by thirty members of aristocratic Athenian families who were unhappy with the democracy. Their executions, expropriations, and expulsions earned them the hatred of most Athenians; later “the Thirty” became known as “the Thirty Tyrants.” The extremists among them first purged their more obvious enemies, then turned to the moderates who resisted their cruelty and wanted a broader oligarchy or restricted democracy that included the thousands in the middle class. Thousands of Athenians were killed or fled the city, and many who stayed acquiesced in fear for their lives. But supporters of a return to democracy soon rallied outside the city, defeating the Thirty’s army in May 403 B.C.E. The conversation in the Meno takes place in late January or early February 402 B.C.E. (after Anytus’ return from exile in 403 B.C.E., before Meno’s departure for Persia by early 401 B.C.E., and shortly before annual rites of initiation to the religious Mysteries, which are mentioned at Meno 76e). Democratic and oligarchic factions might then still have been negotiating terms of reconciliation in order to prevent further civil war. The resulting agreement included a general amnesty for crimes committed up to that time, excluding only the Thirty and a few other officials. But the last of the extreme oligarchs would soon massacre the nearby town of Eleusis and take power there, and then attempt another takeover at Athens in 401 B.C.E., before they are finally put down for good.

As Meno and Socrates discuss the nature of virtue and how it might be acquired, the Athenian success story is not over. The democracy would continue for most of the next century, and even a semblance of the empire would be revived. But for now, the recently restored democracy is anxious about continuing class conflict, and fearful of renewed civil war. Some democrats were suspicious of Socrates, and may have believed that he had sided with the extreme oligarchs, because of his prior relationships with some of them. The general amnesty did not allow prosecuting such allegations. But after the war, Socrates continued his uniquely nondemocratic yet anti-elitist, unconventional yet anti-sophistic interrogations. Many Athenians thought that he was undermining traditional morality and piety, and thereby corrupting the young minds of a vulnerable community. Those were the formal charges that led to Socrates’ execution in 399 B.C.E.

b. Characters

i. Socrates

About the historical Socrates, much of what we think we know is drawn from what Plato wrote about him. Socrates published nothing himself, but, probably soon after his death, the Socratic dialogue was born as a new genre of literature. He was portrayed with different emphases by different authors, including Xenophon, Aeschines, Antisthenes, Phaedo, Euclides, and others. But what interests most people about Socrates today comes from Plato’s philosophical portraits. Even these Platonic portraits vary somewhat across his many dialogues, but all are similar in one way or another to what we see in the Meno. Generally, Plato’s Socrates focuses his inquiries on moral subjects, and he will discuss them with anyone who is interested. He claims not to know the answers to his questions, and he interrogates others who do claim to know those answers. He seeks definitions of virtues like courage, moderation, justice, and piety, and often he suggests that each virtue, or virtue as a whole, is really some kind of knowledge.

As Plato depicts Socrates, it was not easy to understand his position in either the politics or the controversial new teachings of the time. Many of his contemporaries, like Meno and Anytus in this dialogue, probably could not distinguish his kinds of questions from other “arts of words” practiced by other intellectuals or “sophists.” But Plato often has Socrates criticizing sophists for claiming to teach more than they knew, and he emphasizes that, by contrast, Socrates never claimed to be a teacher, never accepted fees for his conversations, never sought wealth or political power, and always pursued subjects related to seeking the real nature of virtue.

To make matters more confusing, a few of the Thirty Tyrants or their extremist supporters, like Critias and Charmides, had earlier been associates of Socrates. But again, Socrates’ position in the conflict is not obvious. While he criticized democracy generally for putting power in the hands of an unwise and fickle majority, he never advocated rule by the wealthy either, and certainly not any of the Thirty’s cruel deeds. Plato emphasizes that Socrates respected common citizens more than the famous and powerful (Apology 21b-22e), and that he disobeyed direct orders from the Thirty, at risk to his own life (32cd). Socrates generally advocates humility and justice above all (for example, Apology 20cff, 29dff, Crito 49aff), and he specifically refutes and chastises Charmides and Critias in Plato’s Charmides.

ii. Meno

Meno is apparently visiting the newly restored Athenian government to request aid for his family, one of the ruling aristocracies in Thessaly, in northern Greece, that was currently facing new power struggles there. Meno’s family had previously been such help to Athens against Sparta that his grandfather (also named Meno) was granted Athenian citizenship. We do not know what resulted from Meno’s mission to Athens, but we do know that he soon left Greece to serve as a commander of mercenary troops for Cyrus of Persia—in what turned out to be Cyrus’ attempt to overthrow his brother, King Artaxerxes II.

Meno was young for such a position, about twenty years old, but he was a favorite of the powerful Aristippus, a fellow aristocrat who had borrowed thousands of troops from Cyrus for those power struggles in Thessaly, and was now returning many of them. The contemporary historian Xenophon (who also wrote Socratic dialogues) survived Cyrus’ failed campaign, and he wrote an account whose description of Meno resonates with Plato’s portrait here: ambitious yet lazy for the hard work of doing things properly, and motivated by desire for wealth and power while easily forgetting friendship and justice. But Xenophon paints Meno as a thoroughly selfish and unscrupulous schemer, while Plato sketches him as a potentially dangerous, overly confident young man who has begun to tread the path of arrogance. His natural talents and his privileged but unphilosophical education are not guided by wisdom or even patience, and he prefers “good things” like money over genuine understanding and moral virtue. In this dialogue, Plato imagines Meno encountering Socrates shortly before that disastrous Persian adventure, when he has not yet proved himself to be the “scoundrel” and “tyrant” that Socrates suspects and Xenophon later confirms. According to Xenophon, when Cyrus was killed and his other commanders were quickly beheaded by the King’s men, Meno was separated and tortured at length before being killed, because of his special treachery (see Xenophon’s Anabasis II, 6).

iii. Anytus

Anytus is a prominent Athenian politician and Meno’s host in Athens. He too was wealthy, not in Meno’s old aristocratic way, but as heir to the successful tannery of a self-made businessman. Anytus is passionately opposed to those sophists who thrived in Athens’ democracy and claimed to teach virtue along with so many other things. He prefers the more traditional assumption that good gentlemen learn goodness not from professional teachers but by association with the previous generation of good gentlemen. (That was a traditional aristocratic notion, but it has a democratic shape at Meno 92e, Apology 24d ff., and Protagoras 325c ff.) Although Plato was not a fan of most sophists either, he portrays Anytus’ attitude as clearly prejudicial. And though Socrates is no professional teacher, Anytus considers him just as bad, or worse. Anytus is one of three men who will bring Socrates to trial in 399 B.C.E.

Anytus had himself been prosecuted in 409 B.C.E., for failure as a general in the war against Sparta, and allegedly he escaped punishment by bribing the jury. Later, he supported the moderate faction among the Thirty Tyrants, and was banished by the extremists. Then he was a general for the democratic forces in the fight to overthrow the Thirty in 403 B.C.E., and he quickly became a leading politician in the restored democracy. In the Meno, Socrates presses Anytus about why so many of Athens’ leading statesmen have failed to teach even their own sons to be good, and Anytus could probably see that these questions apply to himself. Xenophon’s Apology of Socrates, which is rather different from Plato’s, suggests that Anytus had a personal grudge against Socrates, since Socrates had criticized Anytus’ education of his own son, and predicted that he would turn out to be no good. But Anytus may well have sincerely believed that Socrates corrupted young men like Critias and Charmides by teaching them to question good traditions. At any rate, Socrates’ questions about education in the Meno upset Anytus enough to warn Socrates to desist, or risk getting hurt—thus foreshadowing Anytus’ role in Socrates’ trial. (Compare Meno 94e f. and 99e f. with Apology 23a-24a and 30cd.)

c. Summary of Arguments, in Three Main Stages

There are three main parts to this dialogue, which are three main stages in the argumentation that leads to the tentative conclusion about how virtue is acquired.

The dialogue opens with Meno’s challenge to Socrates about how “virtue” (aretê) is achieved. Is it something that is taught, or acquired through training, or possessed by nature? Socrates quickly turns the discussion into an investigation of something more basic, namely, what such virtue is. Since Socrates denies knowing the nature of virtue, while Meno confidently claims to know all about it, Socrates gets Meno to try defining it. Most of this third of the dialogue is then an extended series of arguments against Meno’s three attempts to define virtue. We see the famous “Socratic Method,” in which Socrates refutes someone’s claim to knowledge by revealing that one of their claims is contradicted by others that they also believe to be true. For example, Meno’s initial claim that there are irreducibly different virtues for different kinds of people (71e) is incompatible with his implicit belief (elicited by Socrates) that virtues cannot be different insofar as they are virtues. And Meno’s definition of virtue as the ability to rule over others (73d) is incompatible with his agreements that a successful definition of virtue must apply to all cases of virtue (so including those of children and slaves) and only to cases of virtue (so excluding cases of unjust rule). In each case, since Meno accepts these claims that contradict his proposed definitions, he is shown not to know what he thought he knew about virtue. As Socrates three times exposes the inadequacies of Meno’s attempted definitions, giving examples and guidelines for further practice, Meno’s enthusiasm gives way to reluctance and frustration. Eventually, Meno blames Socrates for his trouble, and insults Socrates by comparing him with the ugly, numbing stingray. Then he makes a momentous objection to conducting such an inquiry at all.

The second stage of the dialogue begins with that momentous, twofold objection: if someone does not already know what virtue is, how could he even look for it, and how could he even recognize it if he were to happen upon it? Socrates replies by reformulating that objection as a paradoxical dilemma, then arguing that the dilemma is based on a false dichotomy. The dilemma is that we cannot learn either what we know or what we do not know, because there is no need to learn what we already know, and we cannot recognize what we do not yet know. Socrates tries to expose the false dichotomy by identifying states of cognition between complete knowledge and pure ignorance. First, he introduces a notion that the human soul has learned in previous lives, and suggests that learning is therefore possible by remembering what has been known but forgotten. (Forgotten-but-capable-of-being-remembered is a state of cognition between complete knowledge and pure ignorance.) Then he tries to illustrate this “theory of recollection” with the example of a geometry lesson, in which Socrates refutes a slave’s incorrect answers much as he had refuted Meno, and then leads him to recognize that the correct answer is implied by his own prior true beliefs. (Implicit true belief is another state of cognition between complete knowledge and pure ignorance.) After the geometry lesson, Socrates briefly reinterprets the alleged “recollection” in a way that can be taken as the discovery of some kind of innate knowledge, or innate ideas or beliefs. Meno finds Socrates’ explanation somehow compelling, but puzzling. Socrates says he will not vouch for the details, but recommends it as encouraging us to work hard at learning what we do not now know. He asks Meno to join him again in a search for the definition of virtue.

But in the third stage of the dialogue, Meno nonetheless resists, and asks Socrates instead to answer his initial question: is virtue something that is taught, or is it acquired in some other way? Socrates criticizes Meno for still wanting to know how virtue is acquired without first understanding what it is. But he agrees, reluctantly, to examine whether virtue is something that is taught by way of “hypotheses” about what sorts of things are taught, and about what sorts of things are good. Here Socrates leads Meno to two opposed conclusions. First, he argues, on the hypothesis that virtue is necessarily good, that it must be some kind of knowledge, and therefore must be something that is taught. But then he argues, from the fact that no one does seem to teach virtue, that virtue is not after all something that is taught, and therefore must not be knowledge. This is where Anytus arrives and enters the discussion: he too objects to the sophists who claim to teach virtue for pay, and asserts that any good gentleman can teach young men to be good in the normal course of life. But then Anytus cannot explain Socrates’ long list of counterexamples: famous Athenians who were widely considered virtuous, but who did not teach their virtue even to their own sons. When Anytus withdraws from the conversation in anger, Socrates reminds Meno that sometimes people’s actions are guided not by knowledge but by mere true belief, which has not been “tied down by working out the reason.” He provisionally concludes that when people act virtuously, it is not by knowledge but by true belief, which they receive not by teaching but by some kind of divine gift. But then Socrates warns again that they will not really learn how virtue is acquired until they first figure out what virtue itself is.

2. Major Themes of the Dialogue

a. Virtue and Knowledge

In this whole inconclusive conversation, the most important Socratic proposal is that “virtue” (aretê in Greek) must be some kind of knowledge. But a crucial fact about the dialogue is that this central subject matter, while obviously very important, remains elusive from beginning to end. When Meno asks how aretê is acquired, Socrates denies knowing what aretê really is. Meno thinks he knows what aretê is, but he is soon surprised to find that he cannot define it. As they work at the definition, alleged examples of aretê range from political power to good taste and from justice to getting lots of money. At first, Meno wants to deny that all aretai share some common nature, but he quickly becomes ambivalent about that. Eventually, Socrates seems to persuade him that the essence of aretê must be some kind of knowledge, but then this provisional conclusion gives way under the observation that what they are looking for is apparently never actually taught. In closing, Socrates reminds Meno that their confusion about whether aretê is taught is a result of their confusion about the nature of aretê itself.

So what sort of thing is this aretê that they are trying to understand? Much of ancient Greek literature shows that aretê was a central ideal and basic motivator throughout the culture. The stylized heroes of Homer’s legendary Trojan war and the real soldiers of their own contemporary campaigns, the athletes at the Olympic games and the orators in political debates—all of these, whether they fought for survival or retribution or the common good, were also seeking honor from their peers for aretê. Both the importance and the vagueness of the term is expressed in Socrates’ question to Anytus:

Meno has been telling me for some time, Anytus, that he desires the kind of wisdom and aretê by which people manage their households and cities well, and take care of their parents, and know how to receive and send off fellow-citizes and foreign guests as a good man should. To whom should we send him for this aretê? (91a)

The standard English translations of aretê are “excellence” and “virtue.” “Excellence” reminds us that the ancient concept applies to all of the above and even to some admirable qualities in nonhuman things, like the speed of a good horse, the sharpness of a good knife, and the fertility of good farmland. But “virtue” too is sometimes still used that way, when we speak of the virtues of the plan or the brand that we prefer. And “excellence” is rather weak and abstract for the focus of these Socratic dialogues, which is something people spent a lot of time thinking and worrying about. Intellectuals debated how it is acquired; politicians knew they had to speak persuasively about it; and Socrates himself considered it the most important thing in life. In our dialogue, Meno keeps thinking of aretê in terms of ruling others and acquiring honor or wealth, while Socrates keeps reminding him that aretê must also include things like justice and moderation (73a, d, 78d), industriousness (81d, 86b). and self-control: “rule yourself,” he says, “so that you may be free” (86d). In this connection, it is often said that Greek ethical thinking evolved from a focus on competitive virtues like courage and strength to a greater appreciation of cooperative virtues like justice and fairness. But this could be at most a shift of emphasis, since even Homer’s epics of war and adventure celebrate pity and humility, justice and self-control. So it may help to think of our dialogue as asking how we can acquire “virtue” in the very general sense of human goodness or human greatness. Like Meno, most of us think we already know what “being a good person” or “being a great person” is like, but we would be stumped if we had to define it. The whole range of examples used in this dialogue would be relevant. And Socrates’ basic suggestion, that “being good and great” requires some important kind of knowledge, would seem both attractive and puzzling.

A further reason for the inconclusiveness of the Meno is the inherent difficulty of providing the kind of definition that Socrates seeks. He was notorious for always seeking and always failing to identify the essences of things like justice, piety, courage, and moderation. A successful definition in Socrates’ sense does not just state how a given word is used, or identify examples, or stipulate a special meaning for a given context. A Socratic definition is supposed to reveal the essence of a unitary concept or a type of real thing. Such a definition would specify not just any qualities that are common to that kind of thing, but the qualities that make them be the kind of thing they are. Other characters in Plato’s dialogues usually have difficulty understanding what Socrates is asking for; in fact, the historical Socrates may have been the first person to be rigorous about such definitions. The task is more difficult than it first seems, even for things like shape and color (see 75b-76e); it is even harder to accomplish for something like virtue. The first third of our dialogue takes the time to show that Meno’s list of examples will not do, because it does not reveal what is common to them all and makes them be virtue while other things are not (72a ff.); and that this kind of explanation must apply to all relevant cases (73d) and only to relevant cases (78d-e); and that something cannot be so explained in terms of itself or related terms that are still matters of dispute (79a-e). At the beginning of the dialogue, Meno did not know even how to begin looking for the one essence of all virtue that would enable us to understand things like how it is achieved. Socrates shows him these guidelines, and tries to get him to practice. But while Socrates clearly knows more than Meno about how to investigate the essence of virtue, he has not been able to discover exactly what it is.

Socrates is drawn to the idea that the essence of all virtue is some kind of knowledge. In the last third of the dialogue, when Meno will not try again to define virtue, Socrates introduces and explores his own suspicion in terms of the following “hypothesis”: if virtue is taught then it is knowledge, and if it is knowledge then it is taught, but not otherwise. This line is pursued with the further “firm hypothesis” that virtue must always be a good thing. Socrates argues that only knowledge is necessarily good, and the goodness or badness of everything else depends on whether it is directed by knowledge. The conclusion of this hypothetical investigation would be that virtue is taught because it is some kind of knowledge—and the argument to that effect requires the rejection of Meno’s constant preference for “good things” like wealth and power (78c-d, 87e-89a). But what kind of knowledge? Or what kind of wisdom? In this discussion, Socrates uses a variety of Greek knowledge-terms, combining epistêmê, phronêsis, and nous as if they were interchangeable. The cumulative meaning ranges from knowledge and intelligence to understanding and wisdom. Clearly, what Socrates is looking for would be not just theoretical knowledge but some kind of practical wisdom, a knowledge that can properly direct our behavior and our use of material things. But this dialogue gets no further than arguing that virtue is some sort of wisdom, “in whole or in part” (89a). And then Socrates introduces a reason for reconsidering even that: it seems that such wisdom is never taught.

b. Recollection and Innate Ideas

A surprising interpretation of knowledge occurs in the middle third of the Meno, when Socrates suggests that real learning is a special kind of remembering. Meno’s frustration in trying to define virtue had led him to object:

But in what way will you look for it, Socrates, this thing that you don’t know at all what it is? What sort of thing, among the things you don’t know, will you propose to look for? Or even if you should meet right up against it, how will you know that this is the thing you didn’t know? (80d)

Is Meno here honestly identifying a practical difficulty with this particular kind of inquiry, where the participants now seem not to know even what they are looking for? Or is he just throwing up an abstract, defensive obstacle, so that he does not have to keep trying? Socrates interprets Meno’s objection in the obstructionist way, and reformulates it as a paradoxical theoretical dilemma:

Do you see what a contentious debater’s argument you’re bringing up—that it seems impossible for a person to seek either what he knows or what he doesn’t know? He couldn’t seek what he knows, because he knows it, and there’s no need for him to seek it. Nor could he seek what he doesn’t know, because he doesn’t know what to look for. (80e)

This reformulation of Meno’s objection has come to be known as “Meno’s Paradox.” It is Plato’s first occasion for introducing his notorious “theory of recollection,” which is an early example of what would later be called a theory of innate ideas.

The notion that learning is recollection is supposed to show that learning is possible in spite of Meno’s objection: we can learn by inquiry, because we can begin in a state of neither complete knowledge nor pure ignorance. To understand what Plato intends with his sketchy theory, we should compare the initial statement of the idea (81a-e), the alleged illustration of it (82a-85b), and the restatement of it after the illustration (85b-86b). According to the initial statement, all souls have already learned everything in many former lives, and learning in this life is therefore a matter of remembering what was once known but is now forgotten. But this is apparently an attention-grabber, dubiously citing unnamed priests and poets, who are just the kind of people Socrates later criticizes for having intermittent true beliefs rather than stable knowledge about their subjects (99c-d). Meno is in fact intrigued, and when he asks for a demonstration, Socrates illustrates by cleverly leading an uneducated slave to the correct answer to a geometrical problem—and doing so by “only asking questions” and eliciting the correct answer from the slave himself. Here, Socrates clearly asks “leading questions,” and eventually even shows the slave the answer in the form of a question (84e). But more important is the fact that he legitimately helps the slave to work out the reasoning, and thereby see the way in which the unexpected answer was implied by other true beliefs that he already had. So the geometry lesson successfully demonstrates some of the beauty of Socratic education, and the power of deductive reasoning in learning. That is enough to refute Meno’s Paradox, which inferred the impossibility of learning from a false dichotomy between complete knowledge and pure ignorance.

But the geometry lesson with the slave clearly does not demonstrate the reminding of something that was learned in a previous life. So it is important to notice that Socrates partly restates the “theory of recollection” after the geometry lesson. This time he concludes not that the slave has remembered some geometrical knowledge from what his mind had learned from experiences in previous lives, but instead that the slave has discovered the relevant true beliefs in his mind, which is somehow “always in a state of having learned” (86a). In the context, that “always” does seem to include many lifetimes, though it could in principle refer just to however long the mind has existed, perhaps since some point of development in the womb. In any case, the phrase “always in a state of having learned” is unusual and striking. If a mind could always be in a state of having learned something, then there would be no point at which it learned that thing. This paradoxical phrasing turns the initial statement of the theory of recollection, which stretched a common-sense notion of learning from experience over a number of successive lifetimes, into the beginnings of a theory of innate ideas, because the geometrical beliefs or concepts somehow belong to the mind at all times. Near this point in the dialogue, Socrates also states that after employing such ideas to elicit the relevant true beliefs, more work is still required for converting them to knowledge (85c-d). Later in the conversation, Socrates even seems to identify “recollection” with this latter part of the process (98a).

Some philosophers and experimental psychologists today agree that basic mathematical concepts, and the beliefs implicit in them (along with many others), are innate—not as an eternal possession of an immortal soul, but as a universal and specialized human capacity determined in part by biological evolution. So in a sense, Socrates’ conclusion that something of “the truth about reality” is “always in our minds” (86b) is even roughly compatible with modern science. The Meno does not end up specifying just what kind of innate resources enable genuine learning about geometry or virtue: Socrates infers from the geometry lesson both that the slave had innate knowledge (85d), and that he had innate beliefs that can be converted to knowledge (85c, 86a), but the dialogue ends with an agreement that “men have neither of these by nature, neither knowledge nor true belief” (98c-d). In fact, while Plato seems quite serious about the idea that genuine learning requires discovering knowledge for ourselves on the basis of our innate resources, he has Socrates disclaim confidence about any details of the theory in this dialogue (86b-c).

c. Teaching and Learning

According to Socrates, the practical purpose of the theory of recollection is to make Meno eager to learn without a teacher (81e-82a, 86b-c). It seems that Meno is used to thinking of learning as just hearing and remembering what others say, and he objects to continuing the inquiry into the nature of virtue with Socrates precisely because neither of them already knows what it is (80d). The geometry lesson shows that we can learn things we do not yet know (at least what we do not yet consciously and explicitly know) if they are entailed by other things that we know or correctly believe. And Socrates emphatically alleges that when the slave becomes aware of his own ignorance, he properly desires to overcome it by learning; this too is supposed to be an object lesson for Meno (84a-d). But Meno does not learn this lesson. Instead of desiring to inquire into the real nature of virtue, he asks instead to hear Socrates’ answer to his initial question about how virtue is acquired. He asks again whether virtue is something that is taught, and once again he wants to be taught about this just by being told (86c-d; compare 70a, 75b, 76a-b, 76d).

This time Socrates apparently relents, but he warns that the rest of their discussion will be compromised by a flawed approach. At least he gets Meno to follow him in a self-consciously “hypothetical” approach—a kind of method that he claims to borrow from mathematicians, who use it when they cannot prove more securely what they want to prove. He illustrates with a geometrical hypothesis that is notoriously obscure, but the corresponding hypothesis about virtue seems to be this: if virtue is something that is taught, then it is a kind of knowledge, and if it is a kind of knowledge, then it is something that is taught (87b-c). Next, Socrates offers an independent argument (based on a different hypothesis) that virtue must in fact be some kind of knowledge, because virtue is necessarily good and beneficial, and only knowledge could be necessarily good and beneficial. Together with the hypothesis that knowledge and only knowledge is taught, Socrates would have proved that virtue is something that is taught.

But there is something wrong with the hypothesis that all and only knowledge is taught. Surely much of what is taught is just opinion, and surely some knowledge is learned on one’s own, without a teacher. In fact, one main point of the theory of recollection and the geometry lesson was that real learning requires active inquiry and discovery from one’s own resources, which include some form of innate knowledge. Even if Socrates did “teach” the geometry lesson in a Socratic way, by leading the slave to the answer with the right questions, nonetheless he showed that while he could in some sense just show the slave the answer, he could not successfully give him knowledge or understanding. That requires working out the explanation for oneself (82d, 83d, 84b-c, 85c-d; compare 98a). This whole lesson was conducted in order to encourage Meno to try learning what virtue is, when he does not have a teacher to tell him what it is (81e-82a, 86c).

So why would Socrates use the faulty hypothesis that knowledge and only knowledge is taught, when it contradicts his notion of recollection and his model geometry lesson? Perhaps because, in effect, it is really Meno’s own hypothesis, as his opening questions and his behavior throughout the dialogue persistently imply. Meno’s opening set of questions substitutes “learned” for “taught” as if they were the same thing (Is virtue taught? Or is it trained? Or is it neither learned nor trained…). And then he just wants to hear Socrates’ answers, and keeps resisting the hard work of definition that Socrates keeps encouraging. When Meno resists yet again after the theory of recollection and the geometry lesson (86c), Socrates cleverly investigates this hypothesis, implicit in Meno’s behavior, to redirect Meno’s attention from his question about how virtue is acquired (Is it taught?) back to the unanswered question of what virtue is (Is it knowledge?). So Socrates could be quite serious in his lengthy argument that virtue must be some kind of knowledge (87c-89a), while reluctantly making use of the unsupported hypothesis that knowledge must be taught because, in effect, Meno insists upon it. Meno refuses to pursue knowledge of virtue the hard way, and he thinks that what he hears about virtue the easy way is knowledge.

After persuading Meno to take seriously his own favorite notion—that virtue is achieved through some kind of knowledge, rather than through wealth and political power—Socrates endeavors to convince Meno that learning just by hearing from others does not provide real knowledge or real virtue. Meno’s host Anytus now arrives at just the right moment, since Anytus is passionately opposed to the sophists who claim to teach wisdom and virtue with their traveling lectures and verbal displays. Anytus believes that virtue can be learned instead by spending time with any good gentleman of Athens, but Socrates shows that this view is superficial, too. He gathers well-known examples of allegedly virtuous men who did not teach their virtue even to their own children, which indicates that virtue is not something that is taught. Anytus departs in annoyance at Socrates’ seemingly dismissive treatment of Athens’ political heroes, so Socrates continues the issue with Meno. He reminds Meno that even professional teachers and good men themselves disagree about whether virtue can be taught. The closing pages argue that if their earlier hypothesis was true, and “people are taught nothing but knowledge,” then since virtue is not taught, virtue would not be knowledge. Socrates suggests that perhaps it could be correct belief instead. Correct belief can direct our behavior well, too, though not nearly as reliably as knowledge.

In this final portion of the dialogue, Socrates twice again asks Meno whether “if there are no teachers, there are no learners.” And Meno keeps affirming it, though no longer with full confidence: “I think … So it seems … if we have examined this correctly” (96c-d). Meno’s challenge to Socrates in the opening lines of the dialogue had used the terms “learned” and “taught” interchangeably. In the meantime, Socrates’ notion of learning as “recollection” indicates that knowledge requires much more than verbal instruction. As Socrates says to Anytus:

For some time we have been examining … whether virtue is something that’s taught. To that end we are asking whether good men past or present know how to bestow on another this virtue which makes them good, or whether it just isn’t something a man can give or receive from another. (93a-b)

Meno’s assumption that knowledge must be taught, and taught by mere verbal instruction, prevents a fuller investigation in this dialogue of Socrates’ hope that virtue is a kind of knowledge.

d. Theory and Practice

And what about Socrates: does he teach virtue in the Meno? He offers a theory that “there is no teaching but recollection” (82a). But what about his practice? Isn’t Socrates trying to teach Meno, by leading him to a correct definition of virtue, as he led Meno’s slave to the correct answer in the geometry lesson?

Rather, Socrates’ practice in the geometry lesson actually goes pretty well with his theory that there is no teaching, because his leading questions there require that the slave think through the deduction of the answer from what he already knew. And Socrates finishes by emphasizing that real knowledge of the answer requires working out the explanation for oneself. So even if a “teacher” can show the answer, he cannot give the understanding. The understanding requires active inquiry and discovery for oneself, based on innate mental resources and a genuine desire to learn. Whatever else might prove true or false about the notion that learning is a kind of recollection, these practical implications are what Socrates insists upon.

On behalf of the rest of the theory, I wouldn’t much insist. But we’ll be better men, braver and less lazy, if we believe that we must search for the things we don’t know, rather than if we believe that it’s not possible to find out what we don’t know, and that we must not search for it—this I would fight for very much, so long as I’m able, both in theory and in practice. (86b-c)

The practical side of learning as recollection applies no less in Socrates’ interactions with Meno. Socrates tries leading Meno to desire real knowledge of what virtue is rather than just collecting others’ opinions about how it is acquired, and tries to get him to practice active inquiry and discovery of the truth for himself, starting from his own basic and sincere beliefs about virtue. Meno’s moral education would call for all of that even if Socrates could tell him what the essence of virtue is, which he claims he cannot do.

Active Socratic inquiry requires humble hard work on the part of all learners: practice in the sense of the personal effort and training that properly develops natural ability. Socrates’ efforts to guide Meno throughout the dialogue indicate that achieving the wisdom that is virtue would require both the right kind of natural abilities and the right kind of training or practice—so that teaching can help if it is not mere verbal instruction but discussions that help a learner to discover the knowledge for himself. That could be the whole dialogue’s answer to Meno’s opening challenge, which specifies three options:

Tell me if you can, Socrates: Is virtue something that’s taught? Or is it not taught, but trained? Or is it neither trained nor learned, but people get it by nature, or in some other way? (70a)

Some have argued that Plato mentions training in the opening lines only because it was one of the traditional options debated in his day. It seems to be tacitly dropped from the rest of the dialogue, and when Meno later revisits his opening challenge, he omits the option about training (86c-d). But if Meno forgets or deliberately avoids it, Socrates does not. When Meno starts to recognize his difficulties, Socrates encourages him to practice with definitions about shape (75a) and gives him a series of paradigms or examples to practice with (73e-77a); later, he criticizes Meno for refusing to do so (79a). At a number of points, Socrates draws attention to the kind of training and habits Meno has already received (70b, 76d, 82a). The geometry lesson, which is supposed to exhibit successful persistent inquiry in the face of previous failures, concludes with advice about the need to work through problems “many times in many ways” (85c) and with a repeated warning about intellectual laziness (86b). While the theory that learning is recollection suggests that an essential basis for wisdom and virtue is innate, Socrates also reminds Meno that any such basis in nature would still require development through experience (89b). When Anytus enters the discussion, his father is praised as a man who, unlike Anytus himself, did not receive his prosperity as a gift from his father, but earned it “by his own skill and hard work” (90a). And the combination of quotations from Theognis near the end of the dialogue suggest that virtue is learned not through verbal teaching alone, but through some kind of character-apprenticeship under the guidance of others who are already accomplished in virtue (95d ff.)

Socrates’ persistence in encouraging Meno to practice active inquiry points in the same direction as the sketchy theory of recollection: while the kind of wisdom that could be real virtue would require understanding the nature of virtue itself, it would not be achieved by being told the definition. And it would not be a theoretical understanding divorced from the practice of virtue. In fact, our dialogue as a whole shows that Meno will not acquire the wisdom that is virtue until after he already practices some measure of virtue: at least the kind of humility, courage, and industriousness that are necessary for genuine learning.

3. Relations of the Meno to Other Platonic Dialogues

We cannot be precise or certain about much in Plato’s writing career. The Meno seems to be philosophically transitional between rough groupings of dialogues that are often associated in allegedly chronological terms, though these groupings have been qualified and questioned in various ways. It is commonly thought that in the Meno we see Plato transitioning from (a) a presumably earlier group of especially “Socratic” dialogues, which defend Socrates’ ways of refuting unwarranted claims to knowledge and promoting intellectual humility, and so are largely inconclusive concerning virtue and knowledge, to (b) a presumably “middle” group of more constructively theoretical dialogues, which involve Plato’s famous metaphysics and epistemology of transcendent “Forms,” such Justice itself, Equality itself, and Beauty or Goodness itself. (However, that second group of dialogues remains rather tentative and exploratory in its theories, and there is also (c) a presumably “late” group of dialogues that seems critical of the middle-period metaphysics, adopting somewhat different logical and linguistic methods in treating similar philosophical issues.) So the Meno begins with a typically unsuccessful Socratic search for a definition, providing some lessons about good definitions and exposing someone’s arrogance in thinking that he knows much more than he really knows. All of that resembles what we see in early dialogues like the Euthyphro, Laches, Charmides, and Lysis. But the style and substance of the Meno changes somewhat with the formulation of Meno’s Paradox about the possibility of learning anything with such inquiries, which prompts Socrates to introduce the notions that the human soul is immortal, that genuine learning requires some form of innate knowledge, and that progress can be made with a kind of hypothetical method that is related to mathematical sciences. This cluster of Platonic concerns is variously developed in the Phaedo, Symposium, Republic, and Phaedrus, but in those dialogues, these concerns are combined with arguments concerning imperceptible, immaterial Forms, which are never mentioned in the Meno. Accordingly, many scholars believe that the Meno was written between those groups of dialogues, and probably about 385 B.C.E. That would be about seventeen years after the dramatic date of the dialogue, about fourteen years after the trial and execution of Socrates, and about the time that Plato founded his own school at the gymnasium called the Academy.

More specifically, significant relations of the Meno to other Platonic dialogues include the following.

The Meno is related by its dramatic setting to the famous series of dialogues that center on the historical indictment, trial, imprisonment, and death of Socrates (Euthyphro, Apology, Crito, and Phaedo). Anytus in the Meno will be one of the three men who prosecute Socrates, which is specifically foreshadowed in the Meno at 94e.

The failed attempt to define virtue as a whole in the Meno is much like the failed attempts in other dialogues to define particular virtues: piety in the Euthyphro, courage in the Laches, moderation in the Charmides, and justice in the first book of the Republic. (And two other dialogues attempt and fail to define terms that are related to virtue: friendship in the Lysis and beautiful/good/fine (to kalon) in the Hippias Major.) Those dialogues emphasize some of the same criteria for successful definitions as the Meno, including that it must apply to all and only relevant cases, and that it must identify the nature or essence of what is being defined. The Meno adds another criterion: that something may not be defined in terms of itself, or in related terms that are still subject to dispute.

One of Socrates’ arguments late in the Meno, that virtue probably cannot be taught because men who are widely considered virtuous have not taught it even to their own sons, is also used near the beginning of Plato’s Protagoras. But there it is countered by a long explanation from the sophist Protagoras of how virtue is in fact taught to everyone by everyone, not with definitions or by mere verbal instruction, but in a life-long training of human nature through imitation, storytelling, and rewards and punishments of many kinds. Socrates does not object to this theory of moral education (instead he objects to other parts of Protagoras’ account), and elements of it are included in the system of education outlined by Socrates in Plato’s Republic. But while Plato’s treatment of Protagoras’ theory of education in the Protagoras is fairly sympathetic, the Meno’s general disparagement of sophistic teaching is explored at length in Socrates’ debates with individual sophists in Plato’s Euthydemus, Gorgias, Hippias Minor, and Hippias Major.

The Meno’s geometry lesson with the slave, where success in learning some geometry is supposed to encourage serious inquiry about virtue, is one indication of Plato’s interest in relations between mathematical and moral education. In the Gorgias (named after a sophist or orator who is mentioned early in the Meno as one of Meno’s teachers), Socrates debates an ambitious young orator-politician who is drawn to a crass hedonism, and claims that his soul lacks good order because he neglects geometry, and so does not appreciate the ratios or proportions exhibited in the good order of nature. Book VII of the Republic describes a system of higher education designed for ideal rulers, which uses a graduated series of mathematical studies to prepare such rulers for philosophical dialectic and for eventually understanding the Form of Goodness itself. In this connection, Socrates’ introduction of a “hypothetical” method of inquiry, adopted from mathematics, is developed somewhat in the Phaedo and in Republic Book VI.

The notion of learning as recollection is revisited most conspicuously in Plato’s Phaedo (72e-76e) and Phaedrus (246a ff.), both of which associate it closely with theories of human immortality and eternal, transcendent Forms. The passage about recollection in the Phaedo even begins by alluding to the one in the Meno, but then it discusses recollection not of specific beliefs or propositions (like the theorem about doubling the square in the Meno), but of basic general concepts like Equality and Beauty, which Socrates argues cannot be learned from our experiences in this life. In the Phaedrus, recollection of such Forms is not argued for but asserted, in a rather suggestive and playful manner, as part of a myth-based story about the human soul’s journeys with gods, which is meant to convey the power of love in philosophical learning. Plato also explores other models of innate knowledge elsewhere, such as an innate mental pregnancy in the Symposium (206c-212b; compare Phaedrus 251a ff.) and an innate intellectual vision in the Republic (507a-509c, 518b ff.).

4. References and Further Reading

a. The Standard Greek Text

  • Burnet, John. Platonis Opera, vol. III. Oxford: Clarendon Press, 1903.

b. Some English Translations

  • Plato: Meno. Translated by G. M. A. Grube. Second Edition. Hackett Publishing, 1980.
  • Plato: Meno and Phaedo. Translated by Alex Long and David Sedley. Cambridge Texts in the History of Philosophy. Cambridge University Press, 2011.
  • Plato: Protagoras and Meno. Translated by Adam Beresford and introduced by Lesley Brown. Penguin Classics, 2006.

c. Some Book-Length Studies

  • Bluck, R. S. Plato’s Meno, Edited with Introduction and Commentary. Cambridge University Press, 1961.
  • Klein, Jacob. A Commentary on Plato’s Meno. University of North Carolina Press, 1965.
  • Scott, Dominic. Plato’s Meno. Cambridge University Press, 2006.
  • Sharples, R. W. Plato’s Meno, Edited with Translation and Notes. Chicago: Bolchazy-Carducci, 1984.
  • Weiss, Roslyn. Virtue in the Cave: Moral Inquiry in Plato’s Meno. Oxford University Press, 2001.

d. Some Articles and Essays on the Major Themes

i. Virtue and Knowledge

  • Fine, Gail. “Inquiry in the Meno.” In The Cambridge Companion to Plato, edited by Richard Kraut, 200-226. Cambridge University Press, 1992.
  • Brickhouse, Thomas C., and Nicholas D. Smith. “Socrates and the Unity of the Virtues.” The Journal of Ethics 1 (1996): 311-324.
  • Santas, Gerasimos. “Socratic Definitions.” In Gerasimos Santas, Socrates: Philosophy in Plato’s Early Dialogues, 97-135. Routledge and Kegan Paul, 1979.
  • Vlastos, Gregory. “The Socratic Elenchus: Method Is All.” In Socratic Studies, edited by Gregory Vlastos, 1-37. Cambridge University Press, 1994.
  • Woodruff, Paul. “Plato’s Earlier Theory of Knowledge.” In Essays on the Philosophy of Socrates, edited by Hugh Benson, 86-106. Oxford University Press, 1992.

ii. Recollection and Innate Ideas

  • Moravcsik, Julius. “Learning as Recollection.” In Plato I: Metaphysics and Epistemology, edited by Gregory Vlastos, 53-69. Anchor Books, 1971.
  • Rawson, Glenn. “Platonic Recollection and Mental Pregnancy.” Journal of the History of Philosophy 44 (2006): 137-155.
  • Vlastos, Gregory. “Anamnesis in the Meno.” Dialogue IV (1965): 143-167.

iii. Teaching and Learning

  • Devereaux, Daniel T. “Nature and Teaching in Plato’s Meno.” Phronesis 32 (1978): 118-126.
  • Scolnicov, Samuel. “Three Aspects of Plato’s Philosophy of Learning and Instruction.” Paideia Special Plato Issue (1976): 50-62.
  • Woodruff, Paul. “Socratic Education.” In Philosophers on Education, edited by Amelie Rorty, 13-29. Routledge, 1998.

iv. Theory and Practice

  • Nehamas, Alexander. “Meno’s Paradox and Socrates as a Teacher.” In Essays on the Philosophy of Socrates, edited by Hugh Benson. Oxford University Press, 1992.
  • Rawson, Glenn. “Speculative Theory, Practical Theory, and Practice in Plato’s Meno.” Southwest Philosophy Review 17 (January 2001): 103-112.

Author Information

Glenn Rawson
Email: grawson@ric.edu
Rhode Island College
U. S. A.