Quantificational Logic and Empty Names

Abstract

In a number of recent articles Timothy Williamson has built a strong case for the claim that everything necessarily exists. His argument rests on a combination of the derivability of this claim from quantificational logic, with standard modal principles and a robust understanding of the Kripke semantics for quantified modal logic. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. It is argued that although certain names and free variables do not actually denote anything they might have actually done so, allowing one to interpret the contingentist claims without quantifying over non-existent possibilia. 1 The classical theory of quantification is subject to a number of difficulties relating to contingent existence and to the treatment of both empty and nonempty names. In this paper I propose and defend a modal metaphysics, couched in a weakening of classical logic, that avoids these objections. It is well known that classical quantification theory does not provide a

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