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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Keywords | Predicative definitions finite reducibility Frege logicism |
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DOI | 10.1007/s11229-004-6204-8 |
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References found in this work BETA
Making It Explicit: Reasoning, Representing, and Discursive Commitment.Robert Brandom - 1994 - Harvard University Press.
Philosophy of Logic.W. Quine - 1970 - In Simon Blackburn & Keith Simmons (eds.), Truth. Oxford University Press.
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2002 - Cambridge University Press.
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Citations of this work BETA
What Russell Should Have Said to Burali–Forti.Salvatore Florio & Graham Leach-Krouse - 2017 - Review of Symbolic Logic 10 (4):682-718.
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