ideational theory of meaning See PHILOSOPHY OF. LANGUAG. identity, the relation each thing bears just to itself. Formally, a % b Q EF(Fa P Fb); informally, the identity of a and b implies and is implied by their sharing of all their properties. Read from left to right, this biconditional asserts the indiscernibility of identicals; from right to left, the identity of indiscernibles. The indiscernibility of identicals is not to be confused with a metalinguistic principle to the effect that if a and b are names of the same object, then each may be substituted for the other in a sentence without change of truth-value: that may be false, depending on the semantics of the language under discussion. Similarly, the identity of indiscernibles is not the claim that if a and b can be exchanged in all sentential contexts without affecting truth-value, then they name the same object. For such intersubstitutability may arise when the language in question simply lacks predicates that could discriminate between the referents of a and b. In short, the identity of things is not a relation among names.
Identity proper is numerical identity, to be distinguished from exact similarity (qualitative identity). Intuitively, two exactly similar objects are ‘copies’ of each other; still they are two, hence not identical. One way to express this is via the notions of extrinsic and intrinsic properties: exactly similar objects differ in respect of the former only. But we can best explain ‘instrinsic property’ by saying that a thing’s intrinsic properties are those it shares with its copies. These notions appear virtually interdefinable. (Note that the concept of an extrinsic property must be relativized to a class or kind of things. Not being in San Francisco is an extrinsic property of persons but arguably an intrinsic property of cities.) While qualitative identity is a familiar notion, its theoretical utility is unclear. The absolute notion of qualitative identity should, however, be distinguished from an unproblematic relative notion: if some list of salient properties is fixed in a given context (say, in mechanics or normative ethics), then the exactly similar things, relative to that context, are those that agree on the properties listed.
Both the identity of indiscernibles and (less frequently) the indiscernibility of identicals are sometimes called Leibniz’s law. Neither attribution is apt. Although Leibniz would have accepted the former principle, his distinctive claim was the impossibility of exactly similar objects: numerically distinct individuals cannot even share all intrinsic properties. Moreover, this was not, for him, simply a law of identity but rather an application of his principle of sufficient reason. And the indiscernibility of identicals is part of a universal understanding of identity. What distinguishes Leibniz is the prominence of identity statements in his metaphysics and logical theory. Although identity remains a clear and basic logical notion, identity questions about problematic kinds of objects raise difficulties. One example is the identification of properties, particularly in contexts involving reduction. Although we know what identity is, the notion of a property is unclear enough to pose systematic obstacles to the evaluation of theoretically significant identity statements involving properties. Other difficulties involve personal identity or the possible identification of numbers and sets in the foundations of mathematics. In these cases, the identity questions simply inherit – and provide vivid ways of formulating – the difficulties pertaining to such concepts as person, property, or number; no rethinking of the identity concept itself is indicated. But puzzles about the relation of an ordinary material body to its constituent matter may suggest that the logician’s analysis of identity does not cleanly capture our everyday notion(s). Consider a bronze statue. Although the statue may seem to be nothing besides its matter, reflection on change over time suggests a distinction. The statue may be melted down, hence destroyed, while the bronze persists, perhaps simply as a mass or perhaps as a new statue formed from the same bronze. Alternatively, the statue may persist even as some of its bronze is dissolved in acid. So the statue seems to be one thing and the bronze another. Yet what is the bronze besides a statue? Surely we do not have two statues (or statuelike objects) in one place? Some authors feel that variants of the identity relation may permit a perspicuous description of the relation of statue and bronze: (1) tensed identity: Assume a class of timebound properties – roughly, properties an object can have at a time regardless of what properties it has at other times. (E.g., a statue’s shape, location, or elegance.) Then a % tb provided a and b share all timebound properties at time t. Thus, the statue and the bronze may be identical at time t1 but not at t2. (2) relative identity: a and b may be identical relative to one concept (or predicate) but not to another. Thus, the statue may be held to be the same lump of matter as the bronze but not the same object of art.
In each case, only detailed study will show whether the variant notion can at once offer a natural description of change and qualify as a viable identity concept. (Strong doubts arise about (2).) But it seems likely that our everyday talk of identity has a richness and ambiguity that escapes formal characterization.
See also ESSENTIALISM , IDENTITY OF INDIS- CERNIBLES , PERSONAL IDENTITY , PROPERTY , TIM. S.J.W.