Charles Explorer logo
🇬🇧

Can logicism be saved?

Publication at Faculty of Arts |
2005

Abstract

The objective of my article is to show why there is no possibility of saving the doctrine of logicism. Since I am keenly aware that such general claims concerning the epistemic nature of mathematics do not usually solve the problem, but ordinarily cause a new one, I refer explicitly to Crispin Wright's neologicism, George Boolos' Fregean studies and Paul Lorenzen's operativist account of mathematics.

My main thesis then rests on the observation that logicism undervalued the practical, calculational character of arithmetic: I demonstrate in detail why inductive definition, i. e. exactly the Kantian operative element, is not meaningfully eliminable from the foundations of arithmetic, at least not by means of the Fregean logicism or its alleged (Wright's and Hale's) successor.

Keywords