- In its primary meaning, the noun 'identity' refers to the relation each thing has to itself and to no other thing. In the language of the logicians, this relation is transitive (if A is identical to B and B is identical to C, then A is identical C), symmetrical (if A is identical to B, B is 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 A 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.
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