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ritus, :\ristotle, and Epicurus) ma\ be viewed as compro-mises attempting to reconcile these c:onflicting claims, an

.122 .Identity

that the idea of identity originates through a comparison of the "very being" of a thing, observed existing at a de-termnate time and place, with the same thing existing at another time and place. In A Treatise of Human Nature (Book I, Part IV, Sec. 2, "Of Scepticism with regard to the Senses"), Hume proposed a similar but somewhat more subtle analysis that had much the same conclusion. Hume argued that the perception of a single object gives rise to the idea of unity, not of identity, while the perception of a number of objects conveys the idea of multiplicity. Since there can be "no medium betwixt unity and number," the idea of identity can arise neither from the perception of a single object nor from a multiplicity of objects seen simul-taneously or in a single moment of time. The solution to the dilemma is to be found in the notion of time, or dura-tion. The notion of identi.ty arises from a propensity of the mind to attribute i'nvariablness or uninterruptedness toan object while tracing it, without a'break in the span of at-tention, through a variatio~ in time. Hume termed such a propensity "a fiction ."

Almost ali the writers of the period under discussion, 'f'rm Descartes to Kat, took the term''identity" to mean that an object "is the same with itself" (Hume). These formulations were expressed by the logical principie, regarded as one of the basic laws of reasoning, [(x) x=x]. In this period queries arose as to the ontological status of this principle-whether it refers to a relation or to a prop-erty wifi~"a11 objects possess-a query that was taken up in the writings of Hegel and post-Hegelans (F. H. Brad-l~y, J. M. E. McTaggart) and that became the subject of speculation in the works of Gottlob Frege and Bertrand ,Russell at the beginning of the twentieth century.

Ickntity of indiscemibles. The question whether it is possible for two objects to be identical in ali respects and yet to differ numerically received elaborate attention in the writings of G. W. F. Leibniz (1646-1716). lt is not wholly clear what the common-sense answer to this question would be. If the common-sense view is identified with those distinctions sanctioned by our everyday speech, then the answer would appear to be yes. In ordinary speech we distinguish between "the identical automobile" (which may have been taken away for repairs and been returned) and "an identical automobile" (an acceptable replacement for one damaged beyond repair). Everyday discourse thus allows for two items to be identical and yet numerically distinct. Still, the ordinary man, if pressed, may be in-clined to agree that "an identical automobile" may not be exactly the same as the one it replaces. The Leibnizian response to the query, which emerges from and is de-manded by his general metaphysical system, maintains even more strongly that it is impossible for two things to differ only numerically . This response receives expression in his writings in a formal maxim now generally referred to as the principie of the identity of indiscernibles. Leibniz formulated this principie in a number of different ways. In the Discourse on Metaphysics (IX) he stated it as follows: "lt is not true that two substances may be exactly alike and differ only numerically, solo numero," while in the Mona-dology (9) he wrote, "lt is necessary, indeed, that each monad be different from every other. For there are never in nature two beings which are exactly alike and in which it is not possible to find an interna! difference, or one

founded upon an intrinsic: qu;,.lity (dnomination)." And in his Fourth Paper to Clarke ' Se-::. 4 ) he wrote, "There are no two individuals indiscernible from one another."

The intuitive idea whic:h these various fonnulations attempt to articulate is that where two (or more) objects are not identical, it will always be possible to discern a fea-ture, or a set of features, in one of them which the other

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1dentical" in at least two other ways . What is some-cnn . :,,nts called Leibniz' law (see Mates, op. cit., p. 215) .1s the . Jle that "things are identical if they can be substituted "'l llll I 1 " ' 1 ~ nother everywhere without change of truth-va ue, ,1r .11 '- ' , principie which applies to identity of meaning. Second, Leibniz distinguished between "identical propositions" .uid "contingent propositions" (see Monadology 31-35),

111,jntaining that the fonner are propositions whose "oppo-,1te involves an express contradiction," while the latter are propositions whose negation does not involve a contradic-tion.

"odem views. The work of Gottlob Frege, especially liis ce lebrated paper "ber Sino and Bedeutung" (trans-1.ited as "On Sense and Reference"), set the stage for mod-l'rTI resean:hes into the subject of identity. Characteristic of modern approaches to the topic is their connection and in\'olvement with the theory of meaning. From Frege's time to the present, questions about identity or sameness have been interpreted and investigated as questions about the identity of meaning. These questions stem to a great .-xtent from Frege's way of fonnulating the problem of identity. Frege asked (at the beginning of "On Sense and Reference"), "Is sameness a relation?" and if so, "a rela-tion between objects or between the names or signs of objects?" Frege maintained that identity is to be inter-preted as a relation holding between the names or signs of objects. When we utter an identity sentence such as "Ve-nus is the moming star," what we wish to express by this utterance is that the tenns "Venus" and "the moming star" both name the same thing, a certain celestial object. If the relation of identity is interpreted as holding between every object and itself, rather than as holding between names referring to a given object, one is faced with the following paradox. It is obvious that the sentences "a= a" and "a= b" generally have different cognitive significance. For instance, the sentence "The morning star is identical with the moming star" (which is an instance of "a= a") is ana-lytic and a truism, while the senfonce "The moming star is identical with the evening star" (which is an instance of "a= b") is synthetic and represents a "valuable extension of our knowledge." But if a and b are the same object, and identity is taken as a relation holding between this object and itself, then it is impossible to explain how the two sentences can differ in cognitive content, which they ob-viously do.

Granted that identity is a relation that obtains between the names of an object, how, then, are we to explain how such identity sentences can differ in their cognitive significance? Frege's solution to this difficulty takes us directly into the heart of the theory of meaning. He con-tended that one must make a distinction between the meaning (Sinn) of a term and its referent (Bedeutung). His view is that the signs "the morning star" and "the evening star" both denote the same referent, the planet Venus, but the two expressions differ in sense (have a different mean-ing or connotation). Because they differ in meaning, it is possible for "The evening star is identical with the mom-ing star" to convey infonnation, even though both "the evening star" and "the moming star" have the same ref-erent. The reason why "The moming star is identical with the morning star" is analytic, and uninfonnative, is that both of the denoting expressions in this sentence not only

Identity 123

refer to the same object (Venus ) but also have the same sense, or meaning.

The line of research initiated by Frege's seminal paper led, in the early part of the twentieth century, to a wide-spread agreement among philosophical logicians that the notion of meaning is ambiguous and that a distinction must be made between the meaning of an expression in the connotative or intensional sense and in its referential or extensional sen se. Reffection u pon Frege' s paradox and similar difficulties also led to problems about synonymity (under what circumstances, or in what contexts, expres-sions have the same meaning). One important conse-quence of such inquiries was the widespread rejection of the principie that two expressions are synonymous if and only if they denote the same object. A second important result was . that Leibniz' law that synonymous expres-sions may be interchanged in any context without change of truth-value does not generally hold and is true only of extensional contexts. These issues were discussed by Russell in his Introduction to Mathematcal Phlosophy (Ch. 16), where they led to the development of the theory of descriptions; by Rudolf Camap in Meaning and Neces-sty (esp. pp. 1-68); by W. V. O. Quine in "Notes on Existence and Necessity"; by Nelson Goodman in "On Likeness ofMeaning"; by Benson Mates in "Synonymity"; and by others. (The last three papers are reprinted in Leonard Linsky, ed., Semantics and the Philosophy of Language, Urbana, 111., 1952, pp. 77-94, 67-76, 111-138).

An interesting solution to a difficulty analogous to Frege's paradox was proposed by P. F. Strawson in "On Referring" (Mind, Vol. 59, 1950, 320-344). Strawson con-tended that the problem is to explain the differei1ce in the ordinary use of what he calls identification statements. He distinguished between (a) That is the man who swam the channel twice in one day and (b) That man swam the channel twice in one day. Strawson dismissed the "bogey of triviality," that is, one's apparently referring to the same individual twice over and hence either saying nothing about him or identifying him with himself and thus pro-ducing a trivial identity statement. Strawson' s view was that the difference between the two statements can best be explained by considering the difference between the cir-cumstances in which one would:say'(ii)'nd one would say (b). One would say (a) instead of (b) if one knew that his hearer knew or believed that someone had swum the channel twice in one day and wondered who did it, where-as one would say (b) to someone who did not know that anyone had swum the channel twice in one day. Accord-ing to Strawson, the solution to the paradox is to be found in the fact that one would say (a) to a man "whom you take to know certain things that you take to be unknown to the man to whom you say (b)."

Another fonn of Frege' s paradox is called the paradox of analysis, which maintains that all analysis is either false or trivial. The paradox states that if the expression to be analyzed (the analysandum) and the analyzing expression (the analysans) are synonymous, then no infonnation is conveyed by the analysis and it is trivial. If the analysan-dum and the analysans are not synonymous, then the analysis is false. But since the analysandum and analysans must be either synonymous or not, all analysis is either false or trivial. This difficulty, originally suggested by

1 24 I dentity of I ndiscernibles

C. H. Langford (see "Moore's Notion of Analysis," in P. A. Schilpp, ed., Philosophy of G. E. Moore, Evanston, Ill., 1942, pp. 319-342), is dealt with by various writers (Moore, Carnap, Max Black, Morton White, Leonard Lin-sky); characteristic solutions follow the lines suggested by Frege in distinguishing between the sense and referent of the terms involved.

Under the influence of ordinary language philosophers, the use (uses) of such terms as "identity," "same," and "like" have been intensively studied. Discussions of these notions are found in Ludwig Wittgenstein's Philosophical Investigations (Oxford, 1953), John Wisdom's Other Minds (Oxford, 1952), J. N. Findlay's Language, Mind and Value (New York, 1963, Ch. 1), and J. L. Austin's "The Meaning of a Word" (Philosophical Papers, Oxford, 1961, pp. 23-43) and "Truth" (ibid., pp. 85-101). Austin suggested that "same" is one of a group of words ("real," "exists") in which the "negalive' use wears the trousers." lt has no positive meaning but take.s its meaning from what it ex-cludes, being a typical device "far establishing and distin-guishing the meanings of ordinary words. Like 'real,' it is p~r,~ of our verbal ap_para~s ... for f!ng and adjusting tfie semantics of words" (Philosophical Papers, p. 88).

Bibliography

PRIMARY SOURCES, ANCIENT AND EARL Y MODERN

Descartes, Ren, Philosophical Writings, translated by Norman Kemp ~I'Qjtl;i, New York, 1958. Especially Meditation IlI and Discourse on Method:

Hera~litus, fragments in G. S. Kirk and J. E. Raven, The Preso-cratic Philosophers . Cambridge, 1957.

Hume, David, A Treatise of Human Nature, L. A. Selby-Bigge, ed. Oxford, 1946. Book I, Part I, Sec. 5; Book I, Part IV, Sec. l.

Kant, Immanuel, The Critique of Pure Reason, translated by Norman Kemp Smith. London, 1929.

Leibniz, G. W. von, Monadology. 9, 10, 14, 22, 47, 62, 71. Leibniz, G. W. von, Discourse on Metaphysics. 8, 9, 13, 33, 34. Locke, John, Essay concerning Human Understanding. Ch. 27,

esp. Secs. 9 and 10. Parmenides, fragments in G. S. Kirk and J. E. Raven, The Preso-

cratic Philosophers. Cambridge, 1957. Plato, Parmenides. Spinoza, Benedict, Ethics . Book I, Secs. 3, 5, 6, 8, 13.

PRIMARY SOURCES, LATE MODERN

Ayer, A. J., Language, Truth and Logic. London, 1936. Ch. 7. Ayer, A. J., Philosophical Essays. London, 1954. Pp. 26-35. Bosanquet, Bernard, "The Philosophical lmportance of a True

Theory of Identity," in his Essays and Addresses. London, 1891. Bradley, F. H., The Principies of Logic, 2d ed., Vol. l. Oxford,

1922. V, VI, Cap. Secs. 4 and 5. Bradley, F. H., Appearance and Reality. Oxford, 1930. VIII, IX,

X, XXII, XXIII, XXIV, Appendix C. Carnap, Rudolf, Mf!aning and Necessity . Chicago, 1947. Frege, Gottlob, "Uber Sinn und Bedeutung." Zeitschrift fr

Philosophie und philosophische Kritik (1892). Translated by Max Black as "On Sense and Reference," in Max Black and P. T. Geach, eds., Translations From the Philosophical Writings of Gottlob Frege. Oxford, 1952.

Hegel, G. W. F., Encyclopedia of Philosophy, translated by G. E. Mueller. New York. HJ59. Secs. 53-75.

McTaggart, J . M. E., The Nature of Existence. Cambridge, 1921. Ch. 10, p. 99.

Mili, John Stuart, A System of Logic. London, 1843. Ch. l, p. 201.

Russell, Bertrand, The Philosophy of Leibniz, 2d ed. London, 1937.

Russell, Bertrand, The Principies of Mathematics, 2d ed. Lon-don, 1956. Secs. 24, 64-65, 95, 209, 428.

Russell, Bertrand, and Whitehead, A. N., Principia Mathema. tica, 2d ed. Cambridge, 1962. 13.01, 13.101, 13.12, 13.15, 13 16 13.17, 13.191, 13.192, 13.19.'3, 13.195. . '

Wittgenstein, Ludwig, Tractatus Logico-philosophicus, trans-lated by D. F. Pears and B. F. McGuinness. London, 1963. Espe-cially 4.241, 4.242, 4.243, 5.53, 5.5301, 5.5302, 5.5303.

ARTICLES

Black,_ Max, "Identity of Indiscemibles." Mind, Vol. 61 (1952) 153. '

Bosanquet, Bernard, "The Philosophical lmportance of a True Theory of ldentity." Mind, Vol. 1 (1888), 356.

Bradley, F. H., "On Professor James' Doctrine of Simple Resem-blance." Mind, N. S. Vol. 2 (1893), 83-88, 366-369.

Chappell, V. C., "Sameness and Change." Philosophical Re view, Vol. 69 (1960), 351-362.

Church, R. W., "Identity and lmplications." Philosophica/ Review, Vol. 43 (1934), 229-249. . Churc?, R. W., "Bradley's Theory of Relations, etc." Philosoph ical Review, Vol. 51 (1942), 26-46. Reply to Will's article.

Hicks, L. E., "Identity as a Principie of Stable Values." Philo sophical Review, Vol. 22 (1913), 375-394.

Janes, E. E. C:, "Precise and Numerical Identity." Mind Vol. 17 (1908), 384-393. ' \ '

Lewy, C., "Equivalence and Identity." Mind Vol. 55 (1946) 223-233. ' .

Linsky, Leonard, "Hesperus and Phosphorus." Philosophical Review, Vol. 68 (1959), 515-518.

Parker, DeWitt H., "Reflexive Relations." Philosophical Rr-view, Vol. 42 (1933), 303-311, and Vol. 43 (1934), 295-300.

Qui ne, W. V., "Notes on Existence and Necessity." journal ol Philosophy, Vol. 40 (1943), 113-127.

Quine, W. V., "Identity, Ostension and Hypostasis." jouma/ of Philosophy, Vol. 47 (1950), 621-633.

Rescher, Nicholas, "Identity, Substitution and Modality." Rt--view of Metaphysics, Vol. 14 (1961).

Savery, B., "Identity and Difference." Philosophical Rei;ieu. Vol. 51 (1942), 205-212.

Smith, Norman Kemp, "The Nature of Universals." Mirad. Vol. 36 (1927), 137-157, 265-280, 393-422.

Taylor, Richard, "Disputes About Synonymity." Philosophical Review, Vol. 63 (1954), 517.

Webb, C. W., "Antinomy of Individuals." journal of Philosuphy Vol. 55 (1958), 735-739.

Wiggins, David, "Identity-Statements," in R. J. Butler. ed Analytical Philosophy, 2d series. Oxford, 1965. Pp. 40-71.

Will, F. L., "Interna! Relations and the Principie of ldentit' Philosophical Review, Vol. 49 (1940), 497.

Wilson, N. L., "Space, Time and lndividuals." ]ournal of Pl11 losophy, Vol. 52 (1955), 589-598.

Wilson, N. L., "Identity, Substitution and Modality." Ret:ieu ' '' Metaphysics, Vol. 14 (1961), 714.

Woods, M. J., "ldentity and Individuation," in R. J. Butler. ed Analytical Philosophy, 2d series. Oxford, 1965. Pp. 120-130

A VRUM STROLL Bibliography by D. Gardincr

IDENTITY OF INDISCERNIBLES. See IDE:\'TIT'

IDENTITY OF MENTAL AND BODILY STATES See MIND-BODY PROBLEM.

IDEOLOGY. "Ideology" did not begin as a tt'rm abuse, and in c:urrent usage it often so far escape .i.r.' implications of expos or denunciation that it eni br.1 ,._' any subjectively c:oherent set of political beliefs. In ni -: career, however, in the use that Karl Marx gave it. "ad"- '