Counterpart Theory and Quantified Modal Logic
Lewis (David)
Source: Lewis - Philosophical Papers Volume I, Part 1: Ontology, Chapter 3
Paper - Abstract

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  1. In this landmark paper, Lewis outlines his theory of modality1 and counterparts. The eight postulates constitutive of Lewis's counterpart theory are expressed in an extensional first-order language that replaces the modal2 operators (characteristic of traditional quantified modal logic)3 with four primitive predicates:
    … 'x is a possible world',
    … 'x is in possible world y',
    … 'x is actual', and
    …'x is a counterpart of y'.
  2. Upon presenting a scheme for translating sentences expressed in quantified modal logic4 into those expressed in his preferred extensional language, Lewis demonstrates that the latter is nevertheless a richer language; while every sentence of quantified modal logic5 may be translated into a sentence expressed in counterpart theory, the reverse is not the case.
  3. Lewis concludes the paper by considering the implications of his view for several well-known topics (notably, Aristotelian essentialism).
  4. The postscript includes numerous additions and emendations (including a specification of the primitive predicate, 'x is in possible world y').


Also in "Loux (Michael), Ed. - The Possible and the Actual: Readings in the Metaphysics of Modality".

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