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WEAKLY CLASSICAL THEORIES OF IDENTITY

Published online by Cambridge University Press:  26 October 2011

JOSHUA SCHECHTER
JOSHUA SCHECHTER*
Affiliation:
Department of Philosophy, Brown University
*
*DEPARTMENT OF PHILOSOPHY, BROWN UNIVERSITY, BOX 1918, PROVIDENCE, RI 02912 E-mail: [email protected]
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 4 , December 2011 , pp. 607 - 644
Copyright
Copyright © Association for Symbolic Logic 2011

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