Weakly Classical Theories of Identity

Review of Symbolic Logic 4 (4):607-644 (2011)
There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical rami cations. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity.
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DOI 10.1017/S1755020311000220
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