Necessary Identity -- A Logical and Philosophical Investigation

Abstract

A derivation of the necessity of identity that dates back to Ruth Barcan challenges the once consensus view that identical object(s) are contingently identical. This dissertation argues against the once consensus view and defends its denial. To accomplish this, the main body of the dissertation is split into two parts, one philosophical and the other logical. In the philosophical part, I first clarify the notion of identity by presenting and analysing four classes of supposed identity statements from a novel perspective, which naturally leading to a definitive definition of identity in its capacity for representing reality; in the logical part, I defend the necessity of identity thesis by offering an alternative derivation in a typed higher-order context. In developing the derivation, syntactic distinctions dismissed by existing derivations are identified, formalized, and discussed; syntactic transitions based on these distinctions receive justifications. Toward the end, a property of quantified self-identity propositions is exploited to generate a necessity operator. This necessity operator is at least as strong as a quantified logical necessity and has an additional advantage in that it is neutral to metaphysical necessity.