Amending Frege's grundgesetze der arithmetik
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. | |||||||||
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Similar books and articlesGottlob Frege (1950). Frege Against the Formalists (II): A Translation of Part of Grundgesetze der Arithmetik. Philosophical Review 59 (2):202-220.
G. Frege (1960). Grundgesetze der Arithmetik. Section 56ff. In P. Geach & M. Black (eds.), Translations From the Philosophical Writings of Gottlob Frege. Blackwell.
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Kai F. Wehmeier (2004). Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik. In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter.
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Richard Heck (1996). The Consistency of Predicative Fragments of Frege's Grundgesetze der Arithmetik. History and Philosophy of Logic 17 (1):209-220.
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