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The Consistency of predicative fragments of frege’s grundgesetze der arithmetik
History and Philosophy of Logic 17 (1-2):209-220 (1996)
Abstract
As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...Author's Profile
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Grundgesetze der Arithmetik. Section 56ff.Gottlob Frege - 1960 - In P. Geach & M. Black (eds.), Translations From the Philosophical Writings of Gottlob Frege. Blackwell.
On the consistency of the Δ11-CA fragment of Frege's grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - Journal of Philosophical Logic 31 (4):301-311.
Russell's paradox in consistent fragments of Frege's grundgesetze der arithmetik.Kai F. Wehmeier - 2004 - In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter.
Consistent fragments of grundgesetze and the existence of non-logical objects.Kai F. Wehmeier - 1999 - Synthese 121 (3):309-328.
The development of arithmetic in Frege's Grundgesetze der Arithmetik.Richard Heck - 1993 - Journal of Symbolic Logic 58 (2):579-601.
Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Definition by Induction in Frege's Grundgesetze der Arithmetik.Richard Heck - 1995 - In William Demopoulos (ed.), Frege's philosophy of mathematics. Cambridge: Harvard University Press.
Die Grundlagen der Arithmetik §§82-83.Richard Heck & George Boolos - 1998 - In Matthias Schirn (ed.), The Philosophy of mathematics today. New York: Clarendon Press.
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Citations of this work
In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic.Sean Walsh - 2016 - Journal of Philosophical Logic 45 (3):277-326.
References found in this work
The development of arithmetic in Frege's Grundgesetze der Arithmetik.Richard Heck - 1993 - Journal of Symbolic Logic 58 (2):579-601.
On the consistency of the first-order portion of Frege's logical system.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
On the consistency of the Δ11-CA fragment of Frege's grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - Journal of Philosophical Logic 31 (4):301-311.
Whence the Contradiction?George Boolos - 1993 - Aristotelian Society Supplementary Volume 67:211--233.
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