What Frege's Theory of Identity is Not

The analysis of identity as coreference is strongly associated with Frege; it is the view in Begriffsschrift, and, some have argued, henceforth throughout his work. This thesis is incorrect: Frege never held that identity is coreference. The case is made not by interpretation of “proof-quotes”, but rather by exploring how Frege actually deploys the concept. Two cases are considered. The first, from Grundgesetze, are the definitions of the core concepts, zero and truth; the second, from Begriffsschrift, is the validity of Leibniz's Law. In both cases, if identity is coreference, results ensue that would be unacceptable to Frege.