Logicism, Frege and the Logical Composition of Informative Identities

Abstract

Informative, non-trivial identities (like the definition of number) form the core of Frege's logicist program. This is why it is important to be able to dissipate any impression that there might be something paradoxical about them. However, it is easy to have such an impression : informative identities seem to be able to have either correctness (because the two elements involved in the identity really are identical) or informativeness (because the two elements involved in the identity are not exactly identical). This problem is sometimes called ‘the paradox of analysis.’ The first step in the direction of a Fregean solution to the paradox is, I argue, the elucidation of the status of ‘fruitful definitions’ as informative identities in Frege.