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...identical to A), and reflexive (everything is identical to itself). In addition, it is governed by Leibniz's Law, the principle that says that if is identical to B, whatever is true of A is true of B. In ordinary speech, the relation is expressed by the terms 'identical' and 'same.' But in addition to being used to express 'numerical' identity, the relation that here concerns us, these terms are also used to express 'qualitative' identity, i.e., exact similarity. The phrase, 'one and the same,' on the other hand, always expresses numerical identity. When philosophers talk about identity, they are usually referring to identity in this sense.
Nonphilosophers, when offered a discussion of identity, are often puzzled and disappointed to find that it is identity in this 'logical' sense that is under consideration. They wonder how identity as the relation everything has to itself and to no other thing can be of any interest, and how, if at all, it is related to what they regard as clearly of interest, namely, the notion that figures in such expressions as 'quest for identity,' 'identity crisis,' 'loss of identity,' and (most recently) 'identity theft.'
But the 'logical' conception of identity--numerical identity--is far from foreign to ordinary folk; on the contrary, it is pervasive in everyday discourse. It is one of the notions expressed by the word 'is': it is in play whenever anyone judges that a car in the parking lot is hers, or that someone she now sees is the person she was introduced to yesterday. The adjectives 'same' and 'identical' are regularly used to communicate this concept. What is foreign to many is the use of the noun 'identity' to express it. The noun has been appropriated to articulate a different, though undoubtedly related, notion.
I will have a good deal to say about identity in--to steal a phrase from Bishop Butler--the "strict and philosophical sense." (1) (I will sometimes shorten this to 'strict.') But first I should say something about its relation to what the noun 'identity' is, these days, often used to talk about--identities as entities possessed, and sometimes lost, by individuals, usually persons.
In the latter sense, one can speak of identities in the plural, and of an identity. One might suppose that the identity of a thing is just whatever it is that makes that thing the thing it is. Then the relation between identity in this sense and identity in the strict sense would be very close. Each thing would have its own identity, and things A and B would be identical just in case the identity of A is the same as the identity of B. It is a matter of debate whether there are identities in this sense--individual essences, as they are sometimes called. But if there are, they are not things that can be lost or stolen. If someone loses his identity, the person after the loss is the same as--is numerically identical with--the person who was there before; so what is lost cannot be what makes the person the person he is.
Instead of thinking of an identity as an individual essence, we might do better to think of it as something, perhaps a set of traits, capacities, attitudes, etc., that an individual normally retains over a considerable period of time and that normally distinguishes that individual from other individuals. Identities in this sense can be lost and, to a certain extent, stolen (as when someone else gets control of one's bank accounts, credit card numbers, etc.). There is still a connection with identity in the strict sense. What makes a set of traits an identity is its being such that, normally, numerically different individuals have different sets of traits of this sort, and, normally, an individual retains the set of traits over time--where this means that numerical identity between an individual existing at a certain time and an individual at a later time goes, normally, with the individual having (more or less) the same set of traits at both times.
Of course, more is involved in the notion of an identity. It is usually...
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