Amending Frege's Grundgesetze der Arithmetik

Fernando Ferreira

pp. 3-19

in: Reflections on Frege and Hilbert, Synthese 147 (1), 2005.

Abstract

Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this extended system.

Cited authors

Frege Gottlob