The Negation of Number 2 in Grundgesetze e § 46 de Grundlagen: Reply to Pedro Barbalho

Abstract

In his comment on my article A Negação Fregeana do Número 2, Pedro Barbalho has criticized my attempt to show that, given the reconstruction of the syntax and the semantics of the system in Grundgesetze that I have presented in a former paper, Frege’s assumption that “|Ø-- 2” is a well-formed expression having both a sense and as reference can be satisfactorily explained. Pedro Barbalho offers an alternative explanation that is suggested by Frege’s claim in Grundlagen that a statement of number contains an assertion about a concept that I did not consider. In this reply my aim is to show that this strategy for making sense of “|Ø-- 2” does not actually work.