The Paradox of Identity

Epistemologia (2):207-226 (1996)
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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