@MISC{Schechter_weaklyclassical, author = {Joshua B. Schechter}, title = {WEAKLY CLASSICAL THEORIES OF IDENTITY}, year = {} }

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Abstract

Abstract. 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 ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. §1. Introduction. The identity relation seems to be very straightforward. If asked to characterize this relation, we might respond with a near triviality – for example, “everything is identical to itself and to nothing else”. 1