Counterpart Theory and Quantified Modal Logic

Abstract

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