Amending Frege’s Grundgesetze der Arithmetik

Synthese 147 (1):3-19 (2005)
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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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Citations of this work

Ramified Frege Arithmetic.Richard G. Heck - 2011 - Journal of Philosophical Logic 40 (6):715-735.

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References found in this work

Frege.Michael Dummett - 1981 - Cambridge, Mass.: Harvard University Press.
Introduction to logic.Patrick Suppes - 1957 - Mineola, N.Y.: Dover Publications.
Philosophy of Logic.W. V. O. Quine - 1970 - In Simon Blackburn & Keith Simmons (eds.), Truth. Oxford University Press.
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 1980 - New York: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.

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