Generality and Objectivity in Frege’s Foundations of Arithmetic

Abstract

This chapter argues for two principal contentions, both of which mark points of divergence from the neo-Fregean position first developed in Crispin Wright’s monograph Frege’s Conception of Numbers as Objects, and developed further in an extended series of works by Wright and Bob Hale. First, that Frege can be regarded as addressing the apriority of arithmetic in a manner that is independent of the ideas that numbers are logical objects or that arithmetic is analytic or a part of logic. Second, that Frege can secure the objectivity of arithmetic in a way that is independent of the idea that numbers are logical objects.