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    Cobreros, Pablo Egré, Paul Ripley, David and Rooij, Robert 2013. Identity, Leibniz's Law and Non-transitive Reasoning. Metaphysica, Vol. 14, Issue. 2, p. 253.


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WEAKLY CLASSICAL THEORIES OF IDENTITY

  • JOSHUA SCHECHTER (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020311000220
  • Published online: 26 October 2011
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.

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*DEPARTMENT OF PHILOSOPHY, BROWN UNIVERSITY, BOX 1918, PROVIDENCE, RI 02912 E-mail: joshua_schechter@brown.edu
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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