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Amending Frege’s Grundgesetze der Arithmetik

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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.

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  1. Departamento de Matemática, Universidade de Lisboa, Rua Ernesto de Vasconcelos, C1-3, P-1749-016, Lisboa, Portugal

    Fernando Ferreira

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  1. Fernando Ferreira
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Correspondence to Fernando Ferreira.

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Ferreira, F. Amending Frege’s Grundgesetze der Arithmetik . Synthese 147, 3–19 (2005). https://doi.org/10.1007/s11229-004-6204-8

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