identity, in logic and metaphysics, a relation that a thing bears to itself and to no other thing. The term identical is also used to characterize two or more things that are exact duplicates or copies of each other.

If one were to say, for example, that the room in which the German philosopher G.W.F. Hegel (1770–1831) lectured was identical with the room in which the German philosopher Arthur Schopenhauer (1788–1860) 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.

Leibniz’s law

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 Leibniz’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.

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The following argument, often attributed to Descartes, is widely regarded by philosophers as a similarly fallacious attempt to apply Leibniz’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 U.S. Pres. 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 (Leibniz’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.)

Identity across time

Personal identity

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 split 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.

The ship of Theseus

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 the concept of identity and on the metaphysics of parts and wholes, but any solution must be consistent with Leibniz’s law.

Relative identity

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.

Peter van Inwagen

personal identity, in metaphysics, the problem of the nature of the identity of persons and their persistence through time.

The notion of personal identity

One makes a judgment of personal identity whenever one says that a person existing at one time is the same as a person existing at another time: e.g., that the president of the United States in 1802—namely, Thomas Jefferson—was the person who in 1776 was the primary author of the Declaration of Independence. Matters of great importance often turn on the truth of such judgments. Whether someone should be punished for a crime, for example, depends on whether he is the person who committed it, and whether someone is the owner of something now may depend on whether he is the person who purchased it at some past time. Whether there is personal immortality, or survival of death, depends on whether a person who dies can be identical with a person existing subsequent to that person’s death.

The topic of personal identity has to do with what the truth of judgments of personal identity consists of and how it can be known. Equivalently, it has to do with the nature of the persistence of persons through time and their awareness of such persistence. Some scholars, such as the 20th-century American philosopher Roderick Chisholm, have denied that there can be an informative answer to such questions; they think that personal identity is “simple and unanalyzable.” But it seems plausible that something can be said about what the sameness through time of automobiles, rivers, and cities consists of, and so it is natural to think that the same should be true of the sameness through time of persons.

Max Weber
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philosophy of mind: The soul and personal identity

Bodily and immaterial-substance theories

What one normally relies on in making judgments of personal identity in everyday life are facts about human bodies—sameness of appearance, sameness of fingerprints, sameness of DNA, and so on. This fact suggests that the sameness of persons consists of the sameness of human bodies. This suggestion of course raises the question of what the sameness of human bodies consists of. It cannot consist simply of similarity of bodily characteristics: different bodies can be alike in appearance and could be alike in fingerprints and DNA. A better answer would be that it consists of spatiotemporal continuity and continuity of bodily characteristics. A single body’s career traces a continuous path through space-time in which bodily properties change only gradually and in certain ways. Such an account would be unacceptable to those, such as the 17th-century French philosopher René Descartes, who take persons to be immaterial substances, or souls, that are only contingently connected with bodies. These philosophers would say that the persistence of a person consists of the persistence of such an immaterial substance. As to what that consists in, the most common answer is that the identity of such substances is simple and unanalyzable.

The psychological view

Both of these accounts of personal identity—the bodily theory and the immaterial-substance theory—were rejected by the 17th-century English philosopher John Locke in his Essay Concerning Human Understanding (1689), which contained the first extended treatment of the topic in Western philosophy. Book II, chapter 27, of the Essay, “Of Identity and Diversity,” introduces a famous example in which the soul of a prince, carrying with it consciousness of the prince’s past life, is transferred to the body of a cobbler. Locke argued that the post-transfer cobbler-body person would be the same person as the prince, despite not having the prince’s former body. (Updated versions of this example involve brain transplants rather than soul transfers.) He also held that consciousness can be transferred from one immaterial substance to another, so that the immaterial substance that was initially the mind of one person might become the mind of a different person.

Locke said that the identity of persons consists of sameness of consciousness. This is usually interpreted to mean that identity consists of facts about memory: someone existing now is the same as someone existing yesterday because he remembers the thoughts, experiences, or actions of the earlier person.

Traditional criticisms

The 18th-century Scottish philosopher Thomas Reid objected to this view with what has come to be known as the “brave officer” example. A small boy is flogged for stealing an apple; later, as a young officer, he remembers the flogging; later still, as an old general, he remembers acting bravely as a young officer but does not remember being flogged as a boy. According to Locke’s theory, Reid thought, the young officer is the same person as the small boy, and the old general is the same person as the young officer, but the old general is not the same person as the small boy—a contradiction, because identity is logically transitive (if A = B and B = C, then A = C). The 18th-century English bishop and philosopher Joseph Butler raised a different objection: Locke’s theory is circular, because the notion of memory it employs presupposes the notion of personal identity.

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Despite these objections, views inspired by Locke—called neo-Lockean, or psychological, accounts—have dominated discussions of personal identity since his time, and much of the subsequent history of the topic has centred on debates about whether Reid’s and Butler’s objections can be met. The first response to Reid’s brave officer example, given a prominent statement by the 20th-century British philosopher Paul Grice, was that personal identity consists of continuity of memory. A person’s life can be conceived as consisting of a series of momentary “person stages.” In order for the old general to be identical with the small boy, it is not required that the general remember experiences and actions of the boy but only that the old-general person-stage be linked to the small-boy person-stage by a series of person-stages, each member of which contains memories of something occurring in the immediately preceding stage.

In a subsequent elaboration of this response, memory continuity was replaced by psychological continuity, which includes memory continuity as a special case. Psychological continuity consists of the holding of a number of psychological relations between person-stages—e.g., relations that hold when beliefs and desires produce, through reasoning, new beliefs, desires, intentions, or decisions—as well as the holding of relations that are involved in the retention over time of personality and character traits. The shift from a simple memory theory to a psychological-continuity theory goes some way toward answering Butler’s circularity objection, since it is possible to know whether the relevant psychological relations obtain without already knowing whether the person-stages in question are stages of the same person.

Another response to Butler’s objection, advanced by the contemporary American philosopher Sydney Shoemaker, is to replace the notion of memory with that of “quasi-memory.” A person quasi-remembers a past experience or action if he has a memory experience that is caused in some appropriate way by that past action or experience. It may be theoretically possible for a person to quasi-remember past experiences or actions—i.e., to have the experience of remembering them as his own—even though they are not in fact his own (see below Fission and special concern). But remembering will be a special case—and perhaps the only actual case—of quasi-remembering. And no circularity will be involved if one uses the notion of quasi-memory in place of the notion of memory in giving one’s account of the psychological continuity that constitutes personal identity. Of course, a psychological-continuity theory based on quasi-memory will be satisfactory only if it contains provisions that determine whether a case of quasi-remembering is a case of genuine remembering.

Fission and special concern

Most contemporary versions of the psychological view of personal identity assume that persons are physical in nature. As already mentioned, Locke’s soul-transfer example was replaced in the 20th century by brain-transplant examples. The idea is that the recipient of a brain transplant could be expected to have memories corresponding to the past life of the donor, as well as a psychological history generally continuous with that of the donor before the transplant. The recipient would think that he is the donor—and, according to the psychological view, others should think the same. In addition to appealing to the possibility of brain transplants, some psychological theorists have envisaged “teletransportation” devices that move persons around by transmitting information about their neural states from one location to another.

A variant of the brain-transplant example, due to the British philosopher David Wiggins, in which the two hemispheres of a brain are transplanted into two different bodies, has been extensively discussed since the 1970s. Here the supposition is that after the transplant there are two persons who are psychologically continuous with the person who existed before. Because these two persons are not identical to each other, it is impossible for both to be identical to the original person. Yet neither of them seems to have any characteristic that would make the original person identical to him and not to the other. Because such “fission” cases seem to constitute examples of psychological continuity without personal identity, they have been regarded as a challenge to the psychological view. They also seem to provide examples of quasi-memory that is not memory: the fission products would quasi-remember the past of the original person but arguably not remember it, if neither is identical to the original person.

Some proponents of the psychological view have responded by saying that what personal identity consists of is not psychological continuity itself but “nonbranching” psychological continuity, the fission cases being examples of “branching” psychological continuity. Theorists differ, however, in how convincing they find this proposal.

Fission cases also raise questions about the special concern that people have for their own future well-being. It seems plausible that a person anticipating fission would have a special concern for the welfare of both of the fission products, even though—strictly speaking—he would be identical to neither of them.

The idea of special concern has figured prominently in the work of the contemporary English philosopher Derek Parfit. In Reasons and Persons (1984) and other works, he argued that one’s special concern is not with personal identity per se but with the psychological continuity and connectedness that is normally sufficient for personal identity but is not sufficient in cases of fission. If by “survival” is meant having what is valued, or what matters, in the prospect of continuing to exist with a life worth living, then, according to Parfit, in fission cases there is survival without identity. Parfit’s treatment of fission cases has given rise to a new criterion of adequacy for any account of personal identity: it must explain why personal identity matters in the way it does.

Amnesia

Another objection to the psychological view has to do with the possibility of amnesia: the view seems to imply that a victim of complete amnesia is not the same person as he was before he was stricken. Alternatively, the psychological theorist would be committed to saying that, despite appearances, amnesia is not really possible. Defenders of the psychological view reply that the sort of amnesia that actually occurs is compatible with the psychological view, because people can recover from ordinary amnesia—which means that their memories continue to exist in a latent state—and in any case there is more to psychological continuity than continuity of memory. In order for a case of amnesia to be apparently incompatible with the psychological view, it would have to amount to a “brain zap” that destroys not only all the subject’s memories but also all past features of his psychology. There is no reason to think that a person could survive this.

The psychological view versus animalism

Coincident entities

A powerful set of criticisms, raised in the late 20th century, has to do with the intuitively plausible assumption that persons are human animals. Although (as mentioned earlier) most versions of the psychological view assume that persons are physical entities, they are committed to holding that a person is not identical to his body, because the relations that constitute personal identity are different from those that constitute bodily identity. For similar reasons, the psychological view is also committed to holding that a person is not identical to the particular human animal (the individual Homo sapiens) that exactly coincides with his body’s physical space. If this is correct, however, then the psychological theorist must accept the existence of “coincident entities”: numerically different things (the person and the animal) that happen to occupy the same space and to be composed of the same matter. For some philosophers, this is reason enough to reject the psychological view. Others have argued that, even if coincident entities are possible, the psychological view implies the counterintuitive claim that persons are not animals.

Too many minds

Furthermore, the view also seems vulnerable to what has been called the objection from “too many minds” (or “too many thinkers”). Given that a person and his coincident human animal are physically exactly alike, it would seem (on a physicalist view about mentality) that the human animal should have the same mental states as the person and so should itself be a mental subject and a person, contrary to what the psychological view maintains. It might seem that the only way to avoid this conclusion is to assume that animals cannot think, which is also strongly counterintuitive. (The claim that the psychological view implies that animals cannot think is often referred to as the “thinking animal” objection.

Animalism

Considerations such as these have been raised by proponents of “animalism,” the theory that in the 1990s became the main competitor of the psychological view. According to the American philosopher Eric Olson and others, persons are biologically individuated animals whose persistence through time consists of biological continuity, which is constituted by the biological processes that make up an organism’s life. Animalism is additionally supported by the fact that in actual cases (not involving brain transplants and the like) sameness of person and sameness of human animal always go together.

Defenders of the psychological view, including Shoemaker, deny that they are committed to too many minds. Although persons and their coincident biological animals share the same physical properties, the result is not the instantiation of mentality in two different things, person and animal, but its instantiation in just one thing, the person. Only in the career of a creature having the persistence conditions of mental subjects—e.g., persons—are the physical-property instantiations embedded in such a way as to realize mental properties. Defenders also maintain that there is a good sense in which persons are animals, though not biologically individuated animals, and that animals in that sense can think. What they hold against animalism is the same as what Locke held against a similar view, the bodily theory: animalism is committed to rejecting the highly plausible intuition that in a brain transplant (or in a Lockean soul transfer) the person goes with the brain (or soul).

Other topics that have been addressed in contemporary discussions of personal identity include whether there can be survival of death, whether persons can exist in disembodied form, and whether there can be persons that are not constituted by organisms—possibly including computers and organized groups of organisms.

Sydney Shoemaker