The Caesar-problem Problem

Abstract

Hume’s Principle (HP) does not determine the truth values of ‘mixed’ identity statements like ‘$ \#F $ = Caesar’. This is the Caesar Problem (CP). Still, neologicists such as Hale and Wright argue that (1) HP is a priori, and (2) HP introduces the pure sortal concept Number. We argue that Neologicism faces a Caesar-problem Problem (CPP): if neologicists solve CP by establishing that ‘$ \#F\neq $ Caesar’ is true, (1) and (2) cannot be retained simultaneously. We examine various responses neologicists might provide and show that they do not address CPP. We conclude that CP uncovers a fatal tension in Neologicism.