Problems in metaphysics

The reality of the external world

The problem in early modern philosophy

Although sensations (i.e., the conscious experiences that result from stimulation of the sense organs) are mental events, they seem to most people to be a source of information—fallible, perhaps, but in the main reliable—about a nonmental world, the world of material or physical objects, which constitutes the environment of the perceiver. Regarding that “external world,” many philosophers have attempted to answer the following related questions: Is there an external world? If there is, do the senses provide reliable information about it? If they do, do human beings know—or can they come to know—what the external world is like? If they can, what exactly is the source or basis of that knowledge? To attempt to answer such questions is to address the problem of the reality of the external world.

That problem belongs entirely to modern (that is, postmedieval) philosophy; no ancient or medieval philosopher so much as considered any of the questions mentioned in the previous paragraph. First explored by the French philosopher René Descartes (1596–1650), it was not regarded as fundamental or especially important—i.e., as a problem that every philosophical system with any pretense to comprehensiveness was obliged to address—until the work of the Anglo-Irish philosopher George Berkeley (1685–1753) became widely known. Berkeley devised very able and ingenious arguments for a thoroughgoing form of idealism, according to which nothing exists but ideas (i.e., sensations and mental images), things composed of ideas, and the minds within which ideas exist. Although few philosophers accepted Berkeley’s doctrine—his arguments were notorious rather than famous—it was generally considered important that it should be refuted. The typical attitude of philosophers of the 18th century to the problem of the reality of the external world was well summarized by the German Enlightenment philosopher Immanuel Kant (1724–1804), who wrote (in a footnote to the introduction of the second edition [1787] of his Critique of Pure Reason):

It remains a scandal to philosophy, and to human reason in general, that it is necessary to take the existence of things outside us…merely on faith, and, if anyone should happen to doubt it, no adequate proof can be produced to oppose him.

Descartes’s formulation of the problem is presented in his Meditationes de Prima Philosophia (1641; Meditations on First Philosophy)—a record, in the form of a first-person narrative, of its author’s search for an absolutely reliable foundation of human knowledge. Descartes assumed that each person, in order to have knowledge, required such a foundation, and he further assumed that the foundation of each person’s knowledge would be a set of propositions whose truth it was impossible for that person to doubt and on the basis of which additional propositions (further knowledge) could be inferred. He proposed to demonstrate to each reader of the Meditations how that reader could find such a set of propositions by using himself, Descartes, as an example. He therefore set out to identify those propositions that it was impossible for him to doubt. Those propositions, Descartes argued, were precisely those that he could be certain of even in the following worst-case scenario: “I will suppose that…some malicious demon of the utmost power and cunning has employed all his energies to deceive me.” In such a case, Descartes decided, what he could be certain of (besides a few self-evident necessary truths, like “1 + 1 = 2” and “Things equal to the same thing are equal to each other”) would be only his own present existence as a thinking, sensing being and his present thoughts and sensations. Such was the foundation upon which the edifice of his knowledge was to be constructed. The “ground floor” of the building would be a proof that the sensations that he had found within himself—sensations that seemed to him to represent physical or material objects like the body he animated and the pen in his fingers and the paper and writing table before him (each of them with a determinate set of physical properties)—were veridical (truth-telling). If Descartes’s sensations were veridical, then an external world would exist, since “an external world” is no more than a name for the totality of objects of the kind (material or physical) whose existence Descartes’s sensations testified to. And if Descartes knew that his sensations were veridical, he would know that there was an external world, and he would know that it was (locally, at least) more or less as his sensations indicated that it was. (It should be noted, however, that Descartes, writing in Latin, used neither the word veridicus [“veridical”] nor any phrase that could be translated as “the external world.”)

The central argument of the Meditations aims to establish the conclusion that its author’s sensations are veridical. The core of the argument consists of two subordinate arguments, each of which seeks to prove the existence of a perfect being—that is, of God. The purpose of the current discussion does not require an exposition of those arguments; it suffices to point out that Descartes maintained that each of the subordinate arguments is valid and that one can recognize their validity without having to assume that one’s sensations are veridical.

Having demonstrated (to his own satisfaction) the existence of a perfect being, Descartes proceeded to argue that if his (Descartes’s) sensations were not veridical, the perfect being just established—the creator of all things and hence of all sensations—would be a deceiver. His argument concludes with the observation that deceit is an imperfection and hence incompatible with the nature of a perfect being. The hypothesis that his sensations are not veridical thus leads to a contradiction, from which it follows that his sensations are veridical after all (see reductio ad absurdum). Descartes assumes that each of his readers will be able to establish the same conclusion with respect to the reader’s own sensations.

Very few philosophers have found the argument of the Meditations convincing, if for no other reason than that very few of them have been convinced by either of the subordinate arguments for the existence of God (and theists have been hardly less critical of those arguments than atheists.) Moreover, very few philosophers have supposed that some other argument for the veridicality of sensations or for the existence of an external world succeeds where Descartes’s argument fails. (The above quotation from Kant reflected his belief that he had presented a new, and of course successful, argument for the reality of the external world. His argument, however, is notoriously obscure, and in any case it relies so extensively on the elaborate philosophical apparatus that is unique to Kantian philosophy that it is hardly possible for anyone who is not a full-fledged Kantian to accept it.)

Berkeleyan idealism

Although Berkeley denied the existence of anything besides ideas, things composed of ideas, and the minds within which ideas exist, he did not explicitly deny the existence of objects such as “the body Descartes animated,” “the pen in his fingers,” and “the paper and writing table before him.” Berkeley instead affirmed the existence of those objects but insisted that they were composed of ideas. His argument was straightforward. Adapted to the present case, its central point can be formulated as follows:

Take the whiteness of the sheet of paper before Descartes—or its (perceived) shape. Those properties cannot exist outside the mind—that is, outside anyone’s mind. Thus, the properties of a sheet of paper exist in the mind. Furthermore, there is nothing more to a thing than its properties—in particular, there is no imperceptible “substrate” in which properties “inhere,” as the English philosopher John Locke (1632–1704) held. (If there were such a thing, how would anyone know about it, given that all knowledge is derived from perception, and the substrate is by definition imperceptible?) Therefore, sheets of paper and all other objects of the kind that philosophers call “material” exist only in the mind. Indeed, there is nothing wrong with anyone’s calling the sheet of paper material, if by that word the speaker means that it is extended in space and impenetrable (it cannot be penetrated by another extended object without suffering damage). But extension and impenetrability are properties like any other, and as such they exist only in the mind.

In a sense, therefore, Berkeley accepted the existence of an external world, because he affirmed the existence of “material” objects, of which the external world is ordinarily said to be composed. Moreover, for Berkeley, there are things that exist partly or wholly outside each person’s mind—namely, ideas that are not in that person’s mind, and minds that are not identical to that person’s mind. But most philosophers who speak of the problem of the reality of the external world would deny that Berkeley’s idealism is consistent with the reality of an external world as they understand that phrase. Kant is a case in point. His proof of the existence of “things outside us” occurs, in the Critique of Pure Reason, under the heading “Refutation of Idealism,” and by “idealism” he meant Berkeleyan idealism (or “dogmatic” idealism, as he also called it—that is, an idealism that is defended on the basis of metaphysical reasoning of the kind that Kant’s Critique was designed to refute). Indeed, almost all philosophers who have used the phrase “external world” would join Kant in regarding Berkeleyan idealism as inconsistent with the reality of an external world. Specifically, they would insist that at least one of the two following statements (both of which Berkeley affirmed) must be false:

• 1. Extension and impenetrability exist only in the mind.

• 2. A thing is material if and only if it is both extended and impenetrable.

Berkeley never used the phrase “external world,” and he might well have said that philosophers who wished to use that term of art were free to use it in any sense that pleased them. He would, however, have vehemently rejected the thesis that either statement 1 or statement 2 must be false. His argument against that thesis would have proceeded along the following lines:

Statement 2 is true by definition, so its denial is nonsensical. As to statement 1, extension must mean either visual extension (the quality called “extension” when one is speaking of ideas presented by the sense of sight) or tactile extension (the quality called “extension” when one is speaking of ideas presented by the sense of touch). It follows that neither visual extension nor tactile extension can exist outside the mind. Similar reasoning applies to the term impenetrability. Therefore, neither extension nor impenetrability exists outside the mind; i.e., statement 1 is true.

Because Berkeley explicitly affirmed the existence of “material” objects and implicitly accepted the existence of an “external world,” the problem of the reality of an external world cannot simply be identified with the question of the truth of Berkeleyan idealism (i.e., the external world is real if and only if Berkeleyan idealism is false). As indicated above, however, most philosophers regard the problem of the reality of the external world as practically equivalent to the question of the truth of Berkeleyan idealism, in part because they reject Berkeley’s eccentric understandings of the terms in which the problem is typically formulated.

The problem in 20th-century and later philosophy

In his famous 1939 British Academy lecture, “Proof of an External World,” the English philosopher G.E. Moore (1873–1958) offered a very simple “proof” of the reality of an external world. The importance of the proof, however, lies not so much in the proof itself as in certain arguments that Moore presented to establish that it was indeed a proof. The proof was essentially this: Moore displayed one of his hands to his audience and said, “Here is one hand.” He then displayed his other hand and said, “and here is another.” He continued by presenting a careful and very precise piece of reasoning intended to establish the conclusion that the “here-is-a-hand” argument was indeed a proof of the reality of an external world—that, considered in relation to the proposition “there is an external world,” the here-is-a-hand argument satisfied all the requirements for being a proof that anyone could reasonably impose. One essential premise of the reasoning by which Moore claimed to have demonstrated that the here-is-a-hand argument was a proof of the existence of an external world was the assertion that he and everyone in his audience knew that there was a pair of hands before them.

Notwithstanding the blunt simplicity of Moore’s proof—a characteristic that struck some philosophers as slightly absurd—it is undeniable that Moore regarded the problem of the reality of the external world with deep seriousness. In his view, “Is there an external world?” is a legitimate philosophical question, just as “Did the human species die out in the 13th century?” is a legitimate historical question. Most later philosophers, however, differed from Moore on that point. In various ways, they attempted to show that the question was not genuinely philosophical or that it was not even a real question but instead a form of nonsense. Those philosophers held that the historical problem of the reality of the external world was the product of fundamental misunderstandings of the nature of human knowledge, the nature of language, or even the nature of human being (i.e., the human mode of being).

Such criticism was characteristic of logical positivism, an important school of analytic philosophy that flourished between the two World Wars. For the logical positivists, the sentences “There is an external world” and “There is not an external world” are both literally meaningless, as are many other metaphysical utterances. That position is a consequence of the logical positivists’ “verifiability principle,” according to which a sentence is literally meaningful if and only if it is either in principle empirically verifiable (or falsifiable) or a tautology. Because no possible experience (no possible experiment or observation) could either prove or disprove that there is an external world, all statements about its existence or nonexistence are nonsensical.

The Austrian-born philosopher Ludwig Wittgenstein (1889–1951) and the German philosopher Martin Heidegger (1889–1976), who are widely regarded as the two most important philosophers of the 20th century, believed that the question of the reality of the external world could be meaningfully posed only within philosophical traditions that were founded upon, and perpetuated, misapprehensions of some fundamental aspect of human experience or the human condition. For Wittgenstein, the misapprehensions concerned human language and thought; for Heidegger, they concerned human being.

Wittgenstein’s famous “private-language argument,” which appears in his posthumously published work Philosophische Untersuchungen (1953; Philosophical Investigations), can be read as implying that if there were no external world (a term, however, that Wittgenstein did not use), all language would be without meaning—from which it would follow that the question “Is there an external world?” is itself meaningless unless there is an external world. If Wittgenstein is correct, the question “Is there an external world?” is effectively answered in its being posed, as are (for example) “Is there such a thing as language?” and “Does anyone ever ask a question?” In a later work Über Gewissheit (1969; On Certainty), Wittgenstein insisted on a radical distinction between certitude and knowledge, holding that the former is not merely a surer form of the latter. Instead, certitude is the background or setting in which the “language games” of knowing, doubting, and believing (among others) take place. Ultimately, what is certain is that which is presupposed or taken for granted in the social activities of a community.

In his early masterpiece Sein und Zeit (1927; Being and Time), Heidegger characterized the philosophy of Descartes—and, by extension, all of modern epistemology—as positing a division between an “inner” world of subjective mental experiences and a hypothetical “outer” world of objective material things. The two worlds were in principle completely independent of each other (the existence of the one did not imply the existence of the other), and the only possible relation between the two was that of “representation,” whereby certain elements of mental experience could represent or correspond to certain features of the objective material world. The task of philosophy, according to the Cartesian conception (as Heidegger and others interpreted it), was to show how or to what extent the relation of representation might be veridical.

According to Heidegger, however, the two “worlds” were not at all independent; to the contrary, each was a distorted abstraction of a primordial and unified Dasein (literally, “being-there”)—the mode of human being—which was inherently already involved with and caught up in a world that the Cartesian tradition had misconceived as independent of isolated human subjects. Commenting on Kant’s “scandal to philosophy,” Heidegger wrote (in Being and Time): “The ‘scandal to philosophy’ does not lie in the fact that this proof has not yet been given, but rather in the fact that such proofs are continually expected and attempted.”

It should be remarked, however, that in the 20th century—Heidegger’s century—such proofs were not actually continually expected or attempted. Even Moore’s “proof” was best understood not as a genuine attempt to prove the existence of an external world but rather as a way of raising a pointed philosophical question about what the skeptical demand for a proof of the reality of the external world really amounted to. And that question is, “Why does a certain trivial exercise (presenting one’s hands to an audience and saying, ‘Here is one hand’ and ‘here is another’) not count as a proof of the reality of an external world?”

The remarkable revival of metaphysics among analytic philosophers in the last quarter of the 20th century did nothing to reawaken interest in the question of the reality of the external world. Subsequent analytic metaphysics was concerned either with problems that had no bearing on that question (e.g., problems regarding modality, ontology, and the nature of time) or with questions about the metaphysics of the physical or material world. (Metaphysicians writing on the metaphysics of the material world have been content to take its existence for granted and have devoted themselves entirely to questions about the kinds of objects it comprises and their properties.) The sole exception to that generalization is provided by a few defenses of idealism, such as the essay “Idealism Vindicated” (2007), by the American philosopher Robert Merrihew Adams, and A World for Us: The Case for Phenomenalistic Idealism (2008), by the English philosopher John Foster.

Mind and body

Human beings seem to have properties of two quite different kinds: physical properties, such as size and weight, and mental properties, such as feeling pain or believing that Tokyo is the capital of Japan, which imply sensation or thought. Among the properties of persons, mental properties have seemed to many philosophers to be in some sense deeper or more fundamental than physical properties. That idea is supported by a famous observation made by Descartes: that whereas it is at least conceivable that people should be mistaken about their physical properties, it is inconceivable that their mental properties should be anything other than what they seem to them to be.

There are many theories about the existence of and relation between physical and mental properties. At one extreme there are idealists, who deny the existence of physical properties, and at the other there are behaviourists and eliminative materialists, who deny the existence of mental properties (see below Types of metaphysical theory: Materialism). Most philosophers, however, believe that properties of both kinds exist. Philosophical theories of mind may be categorized according to the ways in which they conceive of the relation between physical and mental properties and according to their implications regarding the so-called mind-body problem, the problem of explaining how mental events arise from or interact with physical events. Historically, three types of theory have been most influential: psychophysical monism, property dualism, and psychophysical dualism.

According to psychophysical monism, the physical and mental properties of human beings are properties of the same thing: of their bodies or of parts of their bodies, such as the cerebral cortex or the nervous system. Psychophysical monists also believe that the mental properties of a thing are completely determined by its physical properties. Thus, a perfect physical duplicate of a thinking, feeling human being would, of necessity, have exactly the same mental properties as that human being. Psychophysical monists are almost all proponents of the identity theory, according to which mental events (i.e., the gain or loss of a mental property) are the same as or identical to physical events (i.e., the gain or loss of a physical property).

Property dualists agree with psychophysical monists that the physical and mental properties of human beings are properties of the same things (human bodies or their parts) but reject the other thesis of the monists, that the physical properties of a thing necessarily determine its mental properties. They hold that it is at least metaphysically possible to assume that there are two beings with identical physical properties but different mental properties. That possibility, moreover, implies that mental properties are nonphysical properties—hence the term property dualism. The so-called double-aspect theory of Benedict de Spinoza (1632–77) and Arthur Schopenhauer (1788–1860) is probably best categorized as a form of property dualism.

According to psychophysical dualism, the physical properties of human beings are properties of their bodies and the mental properties of human beings are properties of their minds or souls—a person’s mind or soul being an immaterial substance wholly distinct from the physical substance that is that person’s body.

Among psychophysical dualists, dualistic interactionists hold that the body and the mind interact—that the mind causally affects the body and the body causally affects the mind. Dualistic interactionists seem to be committed to the position that the physical world is not causally closed—i.e., that physical events cannot always be completely explained by reference to earlier physical events and the laws of physics. That position, however, would seem to be inconsistent with the conservation laws (e.g., conservation of energy and conservation of momentum) that are fundamental to modern physics.

Other psychophysical dualists, known as occasionalists, have maintained that the apparent causal interaction between mind and body is only apparent: mental and physical changes are coordinated by the direct action of God. (Thus, the act of willing to move one’s arm is an “occasion,” but not a cause, of the movement of one’s arm.) Like interactionists, however, occasionalists seem to be committed to the thesis that there are physical events that cannot be explained in terms of earlier physical events.

The theory of preestablished harmony, due to Gottfried Wilhelm Leibniz (1646–1716), in some ways resembles occasionalism but avoids the problem of inconsistency with the closure of the physical world by postulating separate physical and mental realms, each of which unfolds deterministically with the passage of time according to its own laws; the two realms do not interact but have been created (by God) in such a way that they are in perfect harmony with each other.

The very unclear position called epiphenomenalism is sometimes categorized as a form of psychophysical dualism according to which the body affects the mind but the mind does not affect the body. Thus, when a human being wills a certain bodily movement and that movement occurs, the movement is caused entirely by prior physical states of the body. The corresponding act of will, however, is also caused by prior physical states. As a result, the act of will seems to its subject to be the cause of the movement. It is, however, probably better to think of epiphenomenalism not as a form of psychophysical dualism but as a form of property dualism according to which both mental events (the gain or loss of a mental property) and physical events (the gain or loss of a physical property) are entirely caused by physical events. Partly because few philosophers have thought of themselves as epiphenomenalists, it is difficult to categorize that view under any familiar type of philosophical theory of mind. The best-known modern epiphenomenalist was the biologist Thomas Henry Huxley (1825–95).

Existence

Although metaphysicians have had a great deal to say about the existence of various things (e.g., of God, of the soul, of an external world), they have had less to say about existence itself—about the content of the concept of existence or about the meaning of the word existence. They have said enough, however, to make possible a taxonomy of theories of existence. Such a taxonomy can be presented as a list of pairs of opposed or contradictory theses about the nature of existence.

• 1. Some metaphysicians have affirmed, and others have denied, that existence is the same as being. It might seem obvious that “Mountains higher than Mont Blanc exist” and “There are mountains higher than Mont Blanc” are two ways of saying the same thing. But some metaphysicians believe that there are things that do not exist—fictional characters, for example, or the Greek gods. Their position is that, although such things certainly do not exist, the fact that there are such things implies that they have being. If something can “be” without existing, they argue, then existence and being must be distinguished.

• 2. Some metaphysicians have affirmed, and others have denied, that existence is a barren or empty or trivial concept. G.W.F. Hegel (1770–1831), for example, referred to being (which he did not distinguish from existence) as “the very poorest and most abstract” of all categories.

• 3. Some metaphysicians have affirmed, and others have denied, that the word exist means the same thing in all its applications. For example, mathematicians habitually speak of the “existence” of abstract, mathematical objects like numbers or functions. Metaphysicians, as well as philosophers of mathematics, differ on the question of whether existence in such assertions means the same as it does when it is applied to persons and other tangible, visible things.

• 4. Some metaphysicians have affirmed, and others have denied, that the being (or existence) of one object may be “more perfect,” or “of a higher degree,” than the being (or existence) of another. A classic expression of that idea is the analogy of the divided line, representing a fourfold hierarchy of being, from the Republic of Plato (c. 428–c. 348 bce): images and shadows participate in being very imperfectly, sensible objects less imperfectly, and “mathematicals” (geometrical lines and figures) less imperfectly still. But the eternal, unchangeable forms—and only they—exhibit being perfectly.

• 5. Some metaphysicians have affirmed, and others have denied, that existence is a property or attribute of everything that exists. Kant, the most famous critic of the thesis, identified it as the fallacy on which the ontological argument for the existence of God depends. Deniers of the thesis have maintained that “existence” statements are only apparently about the things that are their grammatical subjects and so cannot be understood as attributing a certain property to those things. Gottlob Frege (1848–1925), for example, held that the statement “Horses exist” really means “The number of objects that fall under the concept horse is not zero.”

A theory of existence may be identified with some combination of the theses discussed above. It should be noted, however, that some combinations are inconsistent, or at least apparently so. For example, anyone who accepts Frege’s account of existence seems to be committed to the theses that existence is a trivial concept, that there is no distinction to be made between being and existence, that existence means the same thing in all its applications, and that existence is not something that one thing can exhibit more perfectly or in some higher degree than another.

Universals and particulars

Many philosophers have believed that, in addition to particular things, there are “general” things of which particular things are instances or examples or cases. They have believed, for example, that, in addition to particular horses, the world contains the species Equus caballus, a general thing of which every horse is an instance (and of which only horses are instances). The Latin word for such general things is universalia (singular universale).

The complex history of the Latin term may be briefly summarized as follows.

Plato had used the (ancient Greek) adverbial phrase kath’ holou (“as a whole”) in statements such as, “I am interested not in this or that case of virtue but in virtue taken kath’ holou.” His student Aristotle (384–322 bce) used the word katholou, a noun coined from the adverbial phrase, as a name for those things that could be predicated or said of a thing—thus, “being virtuous” and “being white” are katholou. Later philosophers writing in Latin, seeking a noun corresponding to katholou, settled on universale and universalia, the neuter singular and neuter plural forms, respectively, of the adjective universalis (“universal”). They chose universalis for that purpose because it is derived from another adjective, universus, which means “taken as a whole.”

A strikingly high proportion of the writings of medieval philosophers is directed at disputes about the nature of universalia (“universals”) and the nature of their relation to the “particulars” that are their instances. The medieval interest in universals is at least partly to be explained by the respect for philosophical authority characteristic of the Middle Ages and by the fact that the two greatest authorities of antiquity, Plato and Aristotle, had disagreed about such matters.

According to Plato, when the same general word (e.g., horse, spear, river) applies to different particulars (or to the same particular at different times), it does so by virtue of the fact that those things bear a common relation to a certain form or idea—a supersensible, eternal, and changeless being. If, for example, the word horse applies to each of two particulars, it is only because both of them fall under or “participate” in the form Horse. (And if horse applies to Bucephalus on both Sunday and Monday, it is only because Bucephalus participates in Horse on both Sunday and Monday.) If the application to particular things of general terms like horse were not in some way guided by an understanding of their associated forms (Plato contended), the fact that speakers apply the word to each of two particular things would be a mere accident and would not reflect any common nature among the things so designated—as is the case with the application of the name Heraclitus to each of a dozen or so ancient Greeks. It seems to be an indisputable consequence of Plato’s theory of forms that the existence of any form does not require that there be a particular thing that participates in it. If, for example, horses were to become extinct, the form Horse, being eternal and changeless, would continue to exist.

Aristotle agreed with Plato on one important point: that when a general term is applied to many particular things, its application is “guided” by knowledge of something that those things have in common. Aristotle denied, however, that what (for example) all horses have in common is participation in a changeless, eternal, independently existing form. In his view, what all horses have in common is something that inheres in each horse—in each of the multiplicity of particular horses.

Four schools of thought emerged from the medieval disputes about universals and their relation to particulars.

• 1. Platonists, or Platonic realists, affirmed the existence of universalia ante rem (or ante res): universals “before the thing” (or “before things”). That is, they held that general things—the things that account for the fact that a general word applies to many particulars—exist independently of those particulars. According to medieval Platonic realism, before God created any horses, the species horse, or the attribute “being a horse” (or both), already existed. Some Platonists, concerned to avoid the implication that anything might exist independently of God, identified universalia ante rem with ideas in the mind of God.

• 2. Aristotelians, or Aristotelian realists, affirmed the existence of universals but contended that they were universalia in re (or in rebus): universals “in the thing” (or “in things”). According to Aristotelians, universals exist only as constituents of particulars. The word horse applies to two things by virtue of their having a certain universal as a common constituent—the species horse or the attribute “being a horse” (or both). If God had not been pleased to create horses, the Aristotelians maintained, neither the species horse nor the attribute “being a horse” would have existed.

• 3. Nominalists denied the existence of both universalia ante rem and universalia in re. Reality, they maintained, consists entirely of particulars. The word horse, then, does not refer to a universal, whether before or in things, but simply denotes all horses. Some nominalists did not so much deny the existence of universals as identify them with the general terms whose application Platonists and Aristotelians had invoked “universals” to explain. (The term nominalism is derived from the Latin word nomina, “names.”) A universal, such nominalists contended, is a mere “puff of sound” (flatus vocis).

• 4. Finally, conceptualists held that universals are mental entities, confined to individual human minds. Thus, any person’s use of the general term horse is governed by a concept that exists only in that person’s mind. Another person’s use of the word is governed by a numerically distinct concept in that other person’s mind—and those two concepts may well differ in content, with the consequence that the two speakers apply horse to different things. There is no question of a speaker’s associating the “wrong” concept with the word horse—except in so far as that concept leads the speaker to apply the word to objects different from those to which the majority of fellow speakers apply it.

The schools described above are, to a very large extent, abstractions. In practice, it is often difficult to place a given philosopher in any one of them to the complete exclusion of the others. (It is often particularly hard to decide whether a given philosopher should be called a nominalist or a conceptualist.) As a very general rule, it can be said that philosophers writing in Latin in late antiquity tended to be Platonic realists, that philosophers of the high Middle Ages tended to be Aristotelian realists, and that philosophers of the late Middle Ages tended to be nominalists.

Theories of universals received relatively little attention from philosophers of the Renaissance and modern periods (roughly from the 16th through the 19th century). That was particularly true of the empirically minded British philosophers of the 18th century, who generally adopted an uncritical nominalism and who tended to regard any attempt at serious discussion of the nature of universals as so much Scholastic quibbling.

In the 20th century there was a remarkable resurgence of interest in theories of universals. There were, on the one hand, a significant number of philosophers who defended the thesis that an appeal to Aristotelian universals explains various features of the world (e.g., that a green book and a green apple have something in common). And there was, on the other hand, a revival of Platonic realism, in large part a consequence of the realism about mathematical objects advocated by Bertrand Russell (1872–1970) and the philosophy of logic of W.V.O. Quine (1908–2000), particularly his views on quantification and “ontological commitment.”

Causation

The word causation applies to relations of two distinct kinds. To resolve the ambiguity, it is necessary to distinguish between the idea of “the” causal relation and the idea of “a” causal relation. The terms of “the” causal relation are causes and effects, and causes and effects are, by definition, events or facts or states of affairs. That relation—the relation between cause and effect—is expressed by phrases such as caused, was the cause of, was one of the causes of, led to, and had as an effect. Its converse is expressed by phrases such as was caused by, was an effect of, was due to, occurred because, was the result of, and was a consequence of. To affirm that an event or fact or state of affairs (a cause) bears the causal relation to another such item (an effect) is to imply that the former in some sense explains the latter.

It will be convenient to have an unambiguous name for the causal relation. In the remainder of the present section, this relation will be called the cause-effect relation.

By contrast, the terms of “a” causal relation—there are many of them—are substances (see below Substance) or concrete objects or particular things or entities. That is, they are items such as fingers and billiard balls and souls—as opposed to items such as a finger’s pressing a button, a billiard ball’s striking another billiard ball, and a soul’s performing an act of will. Such causal relations are expressed by words and phrases such as pushed, pulled, touched, bent, struck, cut, kissed, killed, bored a hole in, exerted a force on, acted on, affected, and brought into existence.

Again, it will be convenient to have an unambiguous name for such causal relations. In the remainder of the present section, they will be called agent-patient relations, a term that indicates that they are relations that a thing bears to another thing by virtue of the way in which the former acts on the latter.

The philosophical topic of causation comprises the cause-effect relation, the many agent-patient relations, and the relation between the two, for the cause-effect relation and the many agent-patient relations are intimately connected. Agent-patient relations, for example, often figure in descriptions of causes, as in the statement, “She died as the result of being struck by a car.” That statement asserts that the event or state of affairs “(her) being struck by a car” bore the cause-effect relation to the event or state of affairs “(her having) died,” and the former item is described in terms of an agent-patient relation (“being struck”) between a certain vehicle and a certain human being.

In Greek and medieval philosophical texts, the Greek words aition (or aitia) and the Latin word causa—each of which is usually translated as “cause”—almost always refer to agent-patient relations of one kind or another. Present-day philosophical treatments of causation, however, are devoted almost entirely to the cause-effect relation, reflecting the enormously influential work of the Scottish Enlightenment philosopher David Hume (1711–76) but also in part the influence on philosophy of Newtonian and post-Newtonian science. Although not all philosophers (even within the Anglophone philosophical tradition) accept Hume’s account of causation, most would agree with Hume on one important point: the central topic in a philosophical study of causation should be the cause-effect relation. Most philosophers would, in fact, suppose that agent-patient relations are not an important part of the topic of causation and that they should in any case be understood or analyzed in terms of the cause-effect relation. For example, they would for the most part subscribe to the following thesis:

A satisfactory philosophical analysis of the statement “The Earth exerts a gravitational force on the Moon” should take the form of a statement to the effect that some (specified) event or fact or state of affairs that involves the Earth is the cause of a certain effect—to wit, some (specified) event or fact or state of affairs that involves the Moon.

According to Hume, to say that event A is the cause of event B is to say that events that are very much like A have always been followed by events that are very much like B—that events very much like A have been “constantly conjoined” in human experience with events very much like B. For example, to say that a billiard ball’s being struck by another billiard ball was the cause of the movement of the former ball is to say that the first ball was stuck by the second and that events very much like that striking have always been followed by events very much like the first ball’s movement. Hume thus rejects the idea of a “necessary connection” between cause and effect: the concept of one ball’s coming into contact with another does not contain or imply the concept of the latter’s moving. The idea of such a connection, he contends, arises from the experience of constant conjunction, which creates a disposition in the human mind to expect an event B after having observed an event A, given that events very much like A have always been followed by events very much like B.

Many later philosophers in the Anglophone philosophical tradition have accepted some refinement of Hume’s theory of causation. (And refinements are obviously necessary: if people always hear a church bell ringing immediately after the chiming of their own clocks, it does not follow that the clocks’ chiming is the cause of the church bell’s ringing.) Contemporary Humean theories are usually framed in terms of the laws of nature. One such formulation, for example, is:

An event A is the cause of an event B if and only if there is some property F of A and some property G of B such that ‘an event with property F is always followed by an event with property G’ is a law of nature or a logical consequence of such a law.

They maintain, moreover, that laws of nature are merely the most general of the observed regularities in nature and are in no sense necessary truths.

Although he admired Hume’s analysis of causation, Kant maintained that what he called “causality” (Kausalität) did indeed include the idea of a necessary connection between cause and effect. In the Critique of Pure Reason, he argued that causality is an a priori category, or pure concept of the understanding. Because it does not derive from experience, it is possible to have the concept of causation without directly perceiving the necessity that is inherent in it. Because the categories apply only to experience, however, they cannot be used to establish the existence or nature of anything that is not itself an object of possible experience (e.g., God, freedom, and immortality). Thus, the traditional cosmological argument, which attempts to prove the existence of a “first cause” of the universe (i.e., God), is invalid, according to Kant.

Few present-day philosophers would agree with Kant that causation is an a priori category. Indeed, most contemporary philosophers of causation either accept some version of Hume’s account or at least share his assumption that the central topic in the philosophy of causation should be the analysis of the cause-effect relation. There is, however, one important exception to that generalization. Some 20th-century writers on free will revived the medieval idea of substantial causation, which can be understood as a hybrid of an agent-patient relation and the cause-effect relation. Those philosophers contended that it is possible for an event (or fact or state of affairs) to have been caused not by an earlier event (or fact or state of affairs) but by a substance. It may be, they argued, that, when people raise their arms, the people themselves—and not any event or fact or state of affairs—are the cause of their arms rising. Indeed, they maintained, that is what a free act consists of: an act caused by its agent (a substance) and not caused by any prior event or fact or state of affairs.

Substance

Although substance is one of the most important ideas in metaphysics, philosophers disagree about which entities are substances. For Aristotle, the first philosopher to make substance a central concept in his thought, the best examples of substances (among tangible, visible things) were living organisms. For Benedict de Spinoza (1632–77), who also gave the concept a central place in his philosophy, there was only one substance, which constitutes the whole of reality. Spinoza held that living organisms are mere “finite modes” of the one (infinite) substance.

If one assumes that Aristotle and Spinoza employed the same concept of substance (Aristotle holding that the best examples of substances were biological organisms, and Spinoza taking the view that the only substance was the whole of reality), then the concept must be very abstract indeed. A suitably broad concept might be set out as follows: a substance is a particular that exists “in its own right”—i.e., a particular thing that could exist independently of other particular things (although it may in fact have been brought into existence by the action of other particular things). But that attempt at explaining the concept of substance raises the following questions: What is the concept of substance opposed to? What sort of particular is not a substance? In other words, what particulars might be said to be incapable of existing independently of other particulars?

Such questions are best answered by giving examples. Some things (if they exist at all) are present only “in” other things: e.g., a smile, a wrinkle, a surface, a hole, a reflection, or a shadow. There is a clear sense in which such items, even if one is willing to grant real existence to them, do not exist in their own right. They might be called “ontological parasites,” things incapable of existing apart from the things that are their “hosts.” (A wrinkle in a carpet cannot exist apart from the carpet; a hole in a piece of cheese cannot exist apart from the cheese.) If one supposed that a carpet could, in metaphysical theory if not in physical fact, exist apart from all other things (other than its own parts), one would be supposing that the carpet was a substance, but no one would suppose that a wrinkle in that carpet could be a substance. The carpet may or may not exist in its own right, but the wrinkle certainly does not. (Spinoza would have insisted that the carpet did not exist in its own right—that only the one substance, which constitutes the whole of reality, exists in its own right, the carpet being as much an ontological parasite as the wrinkle.)

Aristotle had called things that exist in their own right prōtai ousiai (“primary beings”; singular prōtē ousia), which make up the most important of his ontological categories. Several features define prōtai ousiai: they are subjects of predication that cannot themselves be predicated of things (they are not universals); things exist “in” them, but they do not exist “in” things (they are not “accidents,” like Socrates’ wisdom or his ironic smile); and they have determinate identities (essences). The last feature could be expressed in modern terms as follows: if a prōtē ousia x exists at a certain time and a prōtē ousia y exists at some other time, there is a determinate answer to the question of whether x and y are one and the same thing, or numerically identical; and the question of whether a given prōtē ousia would exist in some specific set of counterfactual circumstances must likewise have a determinate answer. It is difficult to suppose that smiles or wrinkles or holes have this sort of determinate identity. To ask whether the smile that Socrates smiled today is the same as the smile that he smiled yesterday can be understood only as a question about descriptive identity, the relation between two distinct things whereby they are exactly like each other in every respect (see below Identity).

Aristotle used (prōtē) ousia not only as a count noun but also as a mass term. (He generally wrote ousia without qualification when he believed that the context would make it clear that he meant prōtē ousia.) For example, he asked not only questions like “Is Socrates a (prōtē) ousia?” and “What is a (prōtē) ousia?” but also questions like “What is the (prōtē) ousia of Socrates?” and “What is (prōtē) ousia?” In the count-noun sense of the term, Aristotle identified at least some (prōtai) ousiai with ta hupokeimena (“underlying things”; singular to hupokeimenon). Socrates, for example, is a to hupokeimenon in that he “lies under” the in rebus (Latin: “in the things”) universals under which he falls and the accidents that inhere in him. To hupokeimenon has an approximate Latin equivalent in substantia, “that which stands under.” Owing both to the close association of (prōtē) ousia and to hupokeimenon in Aristotle’s philosophy and to the absence of a suitable Latin equivalent of ousia (the closest analogue, essentia, a made-up Latin word formed in imitation of ousia, was used for another purpose), substantia became the customary Latin translation of the count noun (prōtē) ousia. A substantia or substance is thus a particular that is capable of “standing on its own.” A substance may indeed depend on the action of other substances for its existence: it may have been brought into existence by the prior operations of other substances, and it may depend on the concurrent operations of other substances to continue in existence. But it does not depend on other things for its existence in the manner in which a wrinkle or a hole in a carpet depends on the carpet for its existence.

Although there is no universally accepted and precise definition of “substance” (alternatively, one might say that substance is not a very clear concept), most philosophers would agree that certain kinds of things are not substances. For example, most philosophers who are willing to use the word at all would deny that any of the following (if they exist) are substances:

• 1. Universals and other abstract objects. (It should be noted that Aristotle criticized Plato for supposing that prōtai ousiai are ante res, Latin for “before things,” universals.)

• 2. Events, processes, or changes. Some philosophers have held that there are substances that are nontemporal, or outside time. But substances that are temporal are said to last or endure or to exist at various times. Events or processes, on the other hand, are said to happen, occur, or take place.

• 3. Stuffs, such as flesh, iron, or butter. Although a common meaning of “substance” is stuff or matter, Aristotle criticized earlier philosophers (specifically, the pre-Socratic cosmologists) for supposing that a prōtē ousia could be a stuff such as water, air, fire, or earth.

The question of whether there are substances continues to be one of the central problems of metaphysics. Several closely related questions are the following. How, precisely, should the concept of substance be understood? Among the sorts of things that human beings frequently encounter, which (if any) are substances? If there are substances, how many of them are there? (For example, is there only one, as Spinoza contended, or are there many, as his fellow rationalists Descartes and Leibniz supposed?) What kinds of substances are there? (For example, are there immaterial substances, eternal substances, or necessarily existent substances?)

Identity

When one says, for example, that the room in which Hegel lectured was identical with the room in which Schopenhauer lectured, there are two quite different things that one might mean. The first is that the two philosophers lectured in rooms that were in different places but were of the same dimensions and were in every other respect exact duplicates of each other. (It is in this sense of “identical” that monozygotic twins are said to be identical.) The second is that Hegel and Schopenhauer lectured in one and the same room (though presumably at different hours). Identity of the former sort is called descriptive identity, and identity of the latter sort is called numerical identity—“numerical” because, if x and y are identical in that sense, there is only one of them; some one thing is both x and y. Although the concept of descriptive identity has received a considerable amount of attention from philosophers, numerical identity is the more important of the two concepts for metaphysics.

The logical properties of numerical identity have been precisely codified by logicians, who express it by the sign “=.” The sign has been borrowed from mathematics, but (the logicians insist) without any change of meaning. According to logicians, a mathematical equation—a formula that consists of two expressions surrounding the symbol “=”—is simply a statement of numerical identity. The equation 7 + 5 = 2 × 6, for example, differs from the statement “Mark Twain is (numerically) identical with Samuel Clemens” in its subject matter—the latter is about a person (the person who was called both “Mark Twain” and “Samuel Clemens”) and the former about a number (the number that is designated by both “7 + 5” and “2 × 6”)—but not in its logical structure. The properties of “=” are, according to the standard formal logic of identity, exactly those expressed by two axioms: x = x, which says that any object x is identical with x—that is, with itself—and (x = y) ⊃ (Fx ≡ Fy), which says that if an object x and an object y are identical, then something F is true of x if and only if F is also true of y. Thus, because Mark Twain and Samuel Clemens were identical, Mark Twain was fond of buttered toast if and only if Samuel Clemens was fond of buttered toast. The latter axiom has been called both the principle of the indiscernibility of identicals and Leibniz’s law (see identity of indiscernibles). It can be intuitively stated as follows: if x is identical with y, whatever is true of x is true of y and whatever is true of y is true of x.

There are apparent exceptions to Leibniz’s law. Consider, for example, the following argument:

• 1. Mark Twain chose that name as a nom de plume.

• 2. Mark Twain was identical with Samuel Clemens.

• 3. Therefore, Samuel Clemens chose that name as a nom de plume.

It might appear that Leibniz’s law incorrectly implies that the preceding inference is valid. Almost all philosophers agree, however, that the argument is not a counterexample to Leibinz’s law, because the phrase “chose that name as a nom de plume” does not really express something that can be true of or false of someone.

The following argument, often attributed to Descartes, is widely regarded by philosophers as a similarly fallacious attempt to apply Leibinz’s law.

• 1. The following is true of my body: I can imagine that it does not really exist, though it seems to me that it does exist. (For example, I can imagine that I have been dreaming my whole life through and that the world of material things that I seem to perceive around me is no more than a figment of my long dream.)

• 2. The following is not true of me: I can imagine that I do not really exist, though it seems to me that I do exist.

• 3. Therefore, I am not identical with my body.

The argument is a “contrapositive” application of Leibniz’s law. The law implies that if a person and that person’s body are identical, then what is true of either is true of the other; it follows that if something is true of a person’s body that is not true of that person, then the person and the person’s body are not identical.

The standard criticism of this argument is that the phrase “I can imagine that x does not exist, though it seems to me that it does exist” does not express something that can be true or false of a thing. A moment’s reflection shows that if those words did in fact express something that could be true or false of a thing, then no first-person identity statement more informative than “I am I” or “I am myself” could be true. If, for example, Lee Harvey Oswald had been brought to trial for having murdered John F. Kennedy, he could have established his innocence by arguing as follows:

• 1. The following is true of the murderer of John F. Kennedy: I can imagine that he does not exist, though it seems to me that he does exist.

• 2. The following is not true of me: I can imagine that I do not really exist, though it seems to me that I do exist.

• 3. Therefore, I am not identical with the murderer of John F. Kennedy.

It is easy to prove that the two axioms of identity (Lebiniz’s law and “Everything is identical with itself”) logically imply that identity has the following features: it is symmetrical (if Mark Twain is identical with Samuel Clemens, then Samuel Clemens is identical with Mark Twain); it is transitive (if Byzantium is identical with Constantinople and if Constantinople is identical with Istanbul, then Byzantium is identical with Istanbul); and it conforms to “Euclid’s law,” or the principle that identicals may be substituted for identicals (if angle A is twice as large as angle B and if angle C is identical with angle A, then angle C is twice as large as angle B). Indeed, Leibniz’s law is nothing more than a somewhat more careful statement of Euclid’s law.

The principle of the indiscernibility of identicals must be carefully distinguished from its contrapositive, the principle of the identity of indiscernibles. The latter principle may be stated as follows: “If whatever is true of x is also true of y and if whatever is true of y is also true of x, then x and y are identical.” (Alternatively: “If x and y have all of the same properties, then x and y are identical.”) The fact that the principle of the indiscernibility of identicals is also called Leibniz’s law and the fact that the principle of the identity of indiscernibles plays a central role in Leibniz’s metaphysics have no doubt encouraged confusion between the two principles.

The principle of the identity of indiscernibles is a trivial truth if there are “individual essences”—that is, properties of a thing that consist of its being that particular thing and no other thing (e.g., Plato would have the property of being Plato, the Taj Mahal would have the property of being the Taj Mahal, and so on). If there are individual essences, then the principle would imply that each thing is identical with itself and with no other thing. However, many philosophers doubt that such individual essences really exist, and almost all philosophers who have expressed an opinion on the question believe that, individual essences apart, the principle of the identity of indiscernibles is not a necessary truth; that is, it is possible to imagine without contradiction a universe in which the principle would be false. (According to the American philosopher Max Black [1909–88], for example, the principle would not hold in a “symmetrical universe” consisting of two mathematically perfect balls of the same size and substance floating in an infinite void. If there are no individual essences, then the two balls would have exactly the same properties, including relational properties, though they would not be the same ball.)

Some of the most important philosophical debates about identity have to do with identity across time, particularly the identity of persons across time. The thesis that there is such a thing as identity across time is simply the view that one and the same entity may exist at more than one time—or, equivalently, that it is possible for a thing existing at one time and a thing existing at another time to be numerically identical. It would seem that almost everyone unreflectively believes that there are real cases of identity across time. Any history of physics, for example, will state that a certain person, Albert Einstein, formulated the special theory of relativity in 1905 and formulated the general theory of relativity in 1915. If that statement is true, then the person who formulated the special theory of relativity in 1905 was identical with the person who formulated the general theory of relativity in 1915. Nevertheless, the commonsense assumption that Einstein in 1905 was identical with Einstein in 1915 is at least apparently inconsistent with Leibniz’s law, since Einstein in 1905 and Einstein in 1915 did not have all of the same properties (e.g., Einstein in 1905 was 26 years old, whereas Einstein in 1915 was 36 years old).

Philosophers have proposed various solutions to the preceding problem. Some would say that Einstein existed at different times in virtue of having “temporal parts” that individually occupied various points in, or segments of, time. One temporal part of Einstein, some would say, formulated the special theory, and another part formulated the general theory. Other philosophers would say that there is no problem to be solved by an appeal to temporal parts: the problem, the apparent violation of Leibniz’s law, is due to a failure properly to understand what is asserted by sentences such as “The person who formulated the special theory of relativity in 1905 was 26 years old.” What that sentence “really” says, they contend, is that the person who formulated the special theory of relativity in 1905 was 26 years old when he formulated the special theory of relativity. When that fact is appreciated, they go on to say, the apparent violation of Leibniz’s law vanishes, for the person who formulated the general theory of relativity in 1915 also had that property—that is, the property of being 26 years old when he formulated the special theory of relativity.

One factor that makes problems of personal identity particularly difficult is the tension between the psychological and physical aspects of common intuitions about what it is for the same person to exist at different times. If, for example, a person’s memory is entirely obliterated by some procedure that leaves the person’s body unaffected, does that person still exist? (This is a case of physical continuity and psychological discontinuity.) Or, if a science-fictional “transporter” or “teleportation machine” should become a reality, would the human being who emerged from teleportation by such a machine be the same person as the (psychologically identical) human being who had entered the machine a spilt second earlier? (A case of psychological continuity and physical discontinuity.) Possible solutions vary with the concept of identity one employs and the metaphysics of parts and wholes one appeals to, but any plausible solution must be consistent with Leibniz’s law.

Many of the most challenging problems about identity across time are raised by cases that involve a thing’s changing its parts. An ancient example, known as “the ship of Theseus,” may be posed as follows. A new ship, made entirely of wooden planks, is named the Ariadne. The Ariadne puts to sea, and, while it is sailing, the planks of which it is constructed are replaced (gradually and one at a time) by new planks, each replacement plank being descriptively identical with the plank it replaces. The original planks are taken ashore and stored in Piraeus (the port of ancient Athens). After all of the planks have been replaced, the ship constructed entirely of the replacement planks is still sailing in the Aegean Sea (the Aegean ship). The old planks are then assembled in a dry dock in Piraeus to form a new ship (the Piraean ship). The planks that constitute the Piraean ship stand in the same spatial relations to one another as they did when they first constituted the Ariadne. The Aegean ship and the Piraean ship are obviously not the same ship, since they are in different places at the same time. But which (if either) is the Ariadne? The problem of the ship of Theseus is the problem of finding the right answer to that question.

One might argue that the Aegean ship is the Ariadne, because a ship does not cease to exist when one of its constituent planks is replaced; hence, during the gradual replacement of its planks, there was no point at which the Ariadne ceased to be the ship it originally was. But one could also argue that the Piraean ship is the Ariadne, because the Piraean ship and the Ariadne (at the first moment of its existence) are composed of exactly the same planks arranged in exactly the same way.

Again, possible solutions to the problem will vary depending on concept of identity and on the metaphysics of parts and wholes, but any solution must be consistent with Leibniz’s law.

The concept of numerical identity has also figured essentially in philosophical critiques of various Christian theological doctrines, particularly those of the Trinity, the Incarnation, and the Eucharist. Many philosophers have held that, for example, the doctrine of the Trinity (the unity in one Godhead of the Father, the Son, and the Holy Spirit) violates the principle of the transitivity of identity, since it implies, for example, that the Father and the Son are identical with God but not identical with each other.

The English Roman Catholic philosopher Peter Geach (1916–2013) proposed a radical solution to the theological problem regarding the transitivity of identity. According to Geach, there is no such thing as numerical identity; there are, instead, many relations of the form “is the same F as,” where “F” is a sortal term designating a kind of thing (e.g., “human being,” “animal,” “living organism”; “plank,” “ship,” “material object”; and so on). Geach maintained that no rule of logic licenses an inference from “x is the same F as y” to “x is the same G as y,” if “F” and “G” represent logically independent sortal terms. Accordingly, as far as logic is concerned, it is perfectly possible for there to be entities x and y such that: (1) x is the same F as y, but (2) x is not the same G as y. Geach’s theory would thus permit one to reformulate the Trinitarian implication above as follows: (1) the Father is the same God as the Son (i.e., the Father and the Son are both God), but (2) the Father is not the same person as the Son.

Geach’s theory is characterized as the view that “identity is relative to a sortal term,” or simply as the “theory of relative identity.” It has attracted some attention among philosophers and logicians, but not as much as it might have had it been clear that the theory had some application outside Christian theology, a matter of some dispute. It does seem, however, that the theory of relative identity might be applied to some of the problems of identity over time discussed above. In the case of the ship of Theseus, for example, one might propose the following: (1) since there is no such relation as numerical identity, the question of whether the Ariadne is the Aegean ship or the Piraean ship is meaningless; (2) the Ariadne, the Aegean ship, and the Piraean ship are all ships and all material things; (3) the Ariadne and the Aegean ship are the same ship but not the same material thing; and (4) the Ariadne and the Piraean ship are the same material thing but not the same ship.

Persistence through time

A thing is said to persist through time, or simply to persist, if it exists at more than one moment of time. Because persistence implies that the same object exists at more than one moment of time, persistence is often referred to as identity through (or across) time. Some philosophical problems concerning persistence or identity through time have more to do with identity than with time, and others have more to do with time than with identity. Problems of the former kind were discussed in the preceding section (see above Identity); the present section concerns problems of the latter kind.

Theories or accounts of persistence may be divided into two broad types: those based on the view that time is very much like space and those based on the view that time and space are fundamentally different.

Metaphysicians who belong to the former school regard identity across time as closely analogous to “identity across space.” The latter kind of identity is exemplified by the identity of a river that is encountered in one place with a river that is encountered in another place. What is it to say that two bridges span the same river despite the fact that they are distant from each other? The obvious answer is that the river consists of many parts or segments, and one of the bridges spans one of the segments that compose the river and the other bridge spans another of those segments. Accordingly, philosophers who regard identity across time as closely analogous to identity across space adopt a similar analysis—appealing to temporally distinct parts or segments—when analyzing problems of the former kind.

For example, suppose that a certain cat existed at the moment of its conception in 1832, at the moment of its death in 1844, at all moments in between those two moments, and at no other moments. Just as a river (considered at any moment of its existence) is composed of many spatial river-segments, a cat (considered over the whole course of its life) is composed of many temporal cat-segments, or “temporal parts” of the cat. There are, for example, the 1837-part of the cat and the 1840-part of the cat, each with a temporal extension of one year, and the June 11, 1835-part of the cat, with a temporal extension of 24 hours. To say that the kitten that Princess Victoria stroked in 1832 was identical with the dying cat that Queen Victoria stroked in 1844 is to say that Princess Victoria stroked a small, kittenish temporal part of a cat in 1832, that Queen Victoria stroked a large, moribund temporal part of a cat in 1844, and that those two temporal cat-parts were parts of the same temporal whole. That temporal whole, or whole cat, is a thing extended in time, a “space-time worm” whose endpoints are a moment in 1832 and a moment in 1844.

Thus, to persist through time is simply to have temporal parts that exist at different times. The American philosopher David Lewis (1941–2001) proposed that an object that exists at more than one time by being composed of a plurality of temporal parts should be said to “perdure,” and he called the thesis that there are persisting things—and that they persist by perduring—the perdurance theory, or “perdurantism.” Most Anglophone philosophers (whether or not they agree with Lewis) have adopted those terms.

The perdurance theory is not the only theory that treats time as being very much like space, though it is the most widely accepted theory of that kind. A rival theory maintains that, although the perdurance theory presents a correct account of what persistence would consist of if there were such a thing, there in fact is no such thing as persistence. There exists nothing in addition to the momentary things that the perdurance theory wrongly describes as temporal parts of persisting or temporally extended things. The members of the temporal sequences of momentary things that, according to the perdurance theory, compose temporally extended things are connected by a relation of causal continuity called “gen-identity,” but that fact does not imply the existence of temporally extended wholes that have them as parts.

Because the gen-identity theory denies that persistence exists, it is not, strictly speaking, a theory of persistence. It is perhaps better described as a theory of the illusion of persistence, an illusion that is due to a faulty (and frequently unconscious) inference whereby observers who encounter a temporal succession of momentary things related by gen-identity mistakenly conclude that those momentary things are parts of a temporally extended whole.

Metaphysicians who accept the reality of persistence but regard time as fundamentally different from space deny that persisting things are, as the perdurantists hold, composed of temporal parts. The idea of a temporal part, they argue, depends essentially on a belief in the fundamental similarity of time and space, for the idea of a temporal part makes sense only if things are extended in time, and things can be supposed to be extended in time only if time is sufficiently like space that the idea of extension—an idea derived from the experience of physical distances between points in space—can, by a species of analogical generalization, be applied to the intervals between moments of time.

If such opponents of the perdurance theory are challenged to produce their own account of persistence, they will typically respond that no such account is possible. And that is because a demand for an account of persistence can be understood only as a demand for an analysis of the concept of persistence in terms of simpler or more fundamental or better-understood concepts—and, according to them, no concept is simpler or more fundamental or better understood than the concept of an object’s existing at more than one time. (They will not concede that the perdurantists have provided such an analysis, because the perdurantists’ proposed analysis is intelligible only if time and space are sufficiently alike that the concept of extension, spatial in origin, can be generalized to apply to intervals of time.) Lewis called their position “endurantism,” a term that he intended to be used in opposition to “perdurantism,” and most metaphysicians have accepted the pair of terms as the standard way of referring to the two theories.

It must be said, however, that many perdurantists would object to any reference to endurantism as a “theory.” Perdurantists commonly charge that, although endurantism is obviously a thesis about persistence, it is not a theory of persistence. They contend that the entire content of endurantism is contained in the statement “persisting objects are not composed of temporal parts,” which is equivalent to the statement that a certain theory of persistence—their theory, perdurantism—is wrong. And, they point out, a statement that a particular theory of something is wrong, even if true, is not itself a theory of that something. (For example, the statement, “Newton’s theory of gravity is wrong,” even if true, is not a theory of gravity.)

In response to such objections, some endurantists have granted that endurantism is not a theory of persistence (because there could not be any theory of persistence) but have insisted that it is no worse for not being one. Endurantism, they hold, is a correct philosophical thesis about persistence, and that is all that it needs to be.

Other endurantists, however, have replied to the perdurantists by denying that the entire content of endurantism is contained in the statement that perdurantism is wrong. Endurantism, they hold, is also the positive thesis—in fact, the “theory”—that, if a persisting object exists at a certain moment, then the whole of that object, rather than merely a temporal part of it, exists at that moment (alternatively, the object is wholly present at that moment). They therefore maintain that the persistence of an object through time consists in its being wholly existent or present at different moments. And that thesis, they contend, is no less a theory of persistence than perdurantism is.

Many perdurantists (and some endurantists), however, have expressed uncertainty about how such a theory should be understood. What, they wonder, does a sentence like “Victoria’s cat was wholly present at every moment of its existence” mean? They point out that, if the sentence means only that Victoria’s cat was a persisting thing but not a temporally extended thing composed of briefer temporal parts, then the following two theses are two statements of the same thesis, two ways of saying the same thing.

• 1. The persistence of an object through time consists in its being wholly existent or present at different moments.

• 2. The persistence of an object through time does not consist in its being composed of temporal parts that exist at different moments.

And, if that is so, the former statement is a negative thesis in an affirmative disguise—a thesis about what persistence is not that has been made to look like a statement about what persistence is by verbal sleight-of-hand.

If such challenges to the concept of an object’s being wholly existent or present at a moment cannot be met, then perdurantism and endurantism should not be regarded as rival accounts of persistence. It should rather be conceded that perdurantism is the sole theory of persistence (which is not to say that it is a correct theory, of course). Endurantism, moreover, should be described as a metaphysical thesis or position—and not as a metaphysical theory—that comprises the following two merely negative theses:

• 1. Perdurantism is to be rejected, owing to the fact that it implies that persisting objects have temporal parts when, in fact, there are no such things as temporal parts. The concept of a temporal part is a product of a false picture of time, a picture that represents time as being much more like space than it really is.

• 2. There exist no concepts in terms of which a theory of persistence could be stated, for any such concept would have to be simpler or more fundamental or better understood than the concept of a persisting thing (the concept of a thing that exists at more than one moment of time), and no concept is simpler or more fundamental or better understood than the concept of a persisting thing.

Modality

The two statements “Tokyo is the capital of Japan” and “There is no largest prime number” are both true, but they differ in their relation to truth in the following important respect: whereas the former statement could have been false, the latter statement could not have been false. That is to say, the former statement is contingently true, or “contingent,” and the latter statement is necessarily true, or “necessary.”

The two statements “Yokohama is the capital of Japan” and “There is no smallest prime number” are both false. The former, however, could have been true, but the latter could not have been true. That is to say, the former statement is contingently false (it is false but possibly true, or “possible”), and the latter statement is necessarily false, or “impossible.”

The concepts expressed by the words within quotation marks in the preceding two paragraphs are called “modal” concepts. The term modal originated in a medieval theory of necessity and contingency according to which statements can be true in various “modes.” For example, the mode in which “Tokyo is the capital of Japan” is true is contingency, while the mode in which “There is no largest prime number” is true is necessity. Although philosophers no longer speak of contingency and necessity as modes of truth, the term modal—meaning “pertaining to possibility, impossibility, necessity, and contingency”—has been retained. Similarly, the noun modality is simply an abbreviated way of referring to any or all of the categories of possibility, impossibility, necessity, and contingency.

Modality that has to do with the truth or falsity of propositions is sometimes called “alethic” modality (from the Greek alētheia, “truth”). Alethic modality is contrasted with “epistemic” modality (from the Greek epistēmē, “knowledge”), which is the kind of modality expressed by phrases such as “For all anyone knows…,” “No one knows whether…,” “It must be the case that…,” “It couldn’t be the case that…,” and so on. A relatively oblique expression of epistemic modality, for example, is the statement “It is possible that this number is prime,” as uttered by a mathematician. Although the number in question is either prime or not prime, and the number could not have been not prime if it is prime or prime if it is not prime, the mathematician’s statement means only that no known mathematical consideration lends any support either to the thesis that the number is prime or to the thesis that that the number is not prime. (The notion of epistemic modality will not be further discussed in the present section; it is mentioned here only as a means of distinguishing it from, and clarifying, the notion of alethic modality.)

In addition to the modal adjectives “contingent,” “possible,” “necessary,” and “impossible,” the vocabulary of modality includes the modal operators “it is possible that” and “it is necessary that.” The following two schemas display the relation between the operators and their corresponding adjectives (the term “p” represents any proposition): (1) it is possible that p if and only if p is possible, and (2) it is necessary that p if and only p is necessary.

All modal terms can be given definitions that involve only one “basic” or “primitive” modal term, whether possible or necessary. For example, one might start with necessary and define possible as follows: “It is possible that p if and only if it is not the case that it is necessary that it is not the case that p.” Or one might start with possible and define necessary as follows: “It is necessary that p if and only if it is not the case that it is possible that it is not the case that p.” Both contingent and impossible, moreover, can easily be defined in terms of either possible or necessary.

Beginning in the second half of the 20th century, it became increasingly common for philosophers concerned with modality to approach the topic via the Leibnizian concept of possible worlds. (A possible world is usually explained intuitively as a total way that things might have been or might be, or as a possible history and future of the world. The actual world is itself a possible world, the one that represents or constitutes the way things are.) Thus, a proposition is possibly true if it is true in some (at least one) possible world, necessarily true if it is true in all possible worlds, impossible if it is true in no possible world, and contingently true if it is true in the actual world but false in some possible world. Philosophers who employ the concept of possible worlds generally think of them as abstract objects (an important exception was David Lewis), about which there are objective, mind-independent truths.

For example, assuming that time travel has been precisely defined, either there exist possible worlds in which time travel occurs or there exist no such worlds. If such worlds exist, time travel is “metaphysically” possible; if no such worlds exist, time travel is metaphysically impossible. If time travel is metaphysically possible but occurs only in worlds in which the laws of nature are different from those of the actual world, then time travel, despite its metaphysical possibility, is physically impossible. If time travel is physically possible (existing in some worlds in which the laws of nature are the actual laws) but occurs only in worlds in which technology is far in advance of the technology of the present actual world, then time travel, despite its physical possibility, is (at present) technologically or practically impossible. Physical and technological impossibility are examples of what are called “restricted” or “relative” modalities—those that are relative to one or more specifiable factors (e.g., the laws of nature or a certain level of technology). The term “metaphysical modality” is a common way of referring to absolutely unrestricted modality, or modality that is not relativized to any particular factor.

The modality that is discussed above (excepting a brief mention of epistemic modality) is the modality of propositions, or the modality of truth and falsity. The modality of propositions is sometimes thought of as being only a species of the genus modality, the other species being the modality of things. The two species are customarily designated by the medieval Latin terms de dicto (from dictum, a thing that has been said) and de re (from res, thing). The modality discussed above is therefore modality de dicto.

Whereas modality de dicto has to do with the relation of propositions to their truth-values (i.e., to truth and falsity), modality de re has to do with the relation of things to their properties (i.e., features, qualities, attributes, or characteristics). The basic concepts of modality de re are the accidental and the essential (or necessary) possession of properties: a thing has a property accidentally if it has that property in the actual world but lacks it in some possible world in which it exists, and a thing has a property essentially or necessarily if it has it in every possible world in which it exists. For example, Michelangelo’s David is now in Florence, but it has that feature (the feature of being in Florence) only accidentally, since it could at some point have been moved to some other city without ceasing to exist: there are possible worlds in which the David is in Rome or Beijing. But it seems evident that the David could not have existed without being a material thing—there is no possible world in which the David is immaterial—and that it therefore it has the property being a material thing essentially, or necessarily.

In the 20 years following World War II, owing principally to arguments of the American philosopher W.V.O. Quine, a “deflationary” theory of modality was ascendant. According to that theory, necessity is nothing more than analyticity, or the quality of a proposition whereby it is true by virtue of the meanings of the terms that are used to express it (a standard example is “All bachelors are unmarried”).

The deflationary theory was held to entail that necessity de re is an incoherent concept. The argument for that conclusion was supposed to have been established by Quine’s famous “mathematical cyclist” argument, an adaptation of which is the following:

Suppose that the proposition “All cyclists are bipedal” is analytic. The proposition “All mathematicians are bipedal” is obviously not analytic. Given that necessity is a matter of analyticity, it follows that necessity de re, if it is a coherent notion, is a matter of analyticity. Therefore, all cyclists are necessarily bipedal, and all mathematicians are not necessarily bipedal (i.e., no mathematicians are necessarily bipedal). It follows that the American cyclist and mathematician Julia Robinson (1919–85) was necessarily bipedal (because she was a cyclist) and not necessarily bipedal (because she was a mathematician)—a contradiction. Because the notion of necessity de re thus implies a contradiction (given the deflationary theory), it is incoherent.

Since about 1970, however, most philosophers in the analytical tradition have been convinced by the work of the American philosopher Saul Kripke and others that the mathematical-cyclist argument fails. Those philosophers point out that there obviously exist possible worlds in which Robinson is not bipedal or at least ceased to be bipedal at some very early age. She might, for example, have lost a leg in an accident when she was an infant. She is, therefore, accidentally bipedal. It may be plausibly stipulated that she is bipedal in every possible world in which she is a cyclist. But she is a cyclist only accidentally, since there are possible worlds in which she is not a cyclist. Accordingly, the proposition “All cyclists are bipedal,” even if it is assumed to be necessary, does not imply that all cyclists are necessarily bipedal, understood as an attribution of necessity de re. It seems, in fact, that no cyclist is necessarily bipedal: all cyclists (all people who are actually cyclists) exist in possible worlds in which they do not have two legs.