The Paradox of Identity

Epistemologia:207-226 (1996)
Abstract
Call a semantics for singular terms *extensionalist* if it embraces (1) and *classical* if it embraces (2). 1. The meaning of a singular term is exhausted by its reference. 2. The reference of a singular term is an entity that is logically simple. Call a semantics *adequate* if it distinguishes material identity (a = b) from formal identity (a = a). Frege reacts to the inadequacy of classical extensionalist semantics by rejecting (1). This he does without a sideways glance at (2), whose background ontology, an "ontology of individuals" (van Heijenoort's term), Frege implicitly accepts. In contrast, my account of the difference between material and formal identity replaces that background ontology with one whose ground-level objects are ontologically differentiated and logically complex. The semantics I urge for singular terms, while *extensionalist* in the sense of (1), is thus a non-classical semantics in which singular terms take structured individuals, or complexes (as I will say), as their referents. For such individuals, unlike those of Frege's ontology, keep a = b and a = a apart.
Keywords material identity  formal identity  Frege  names  meaning  reference  semantic extensionalism  complex individuals  ontology
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