History and Philosophy of Logic 17 (1):209-220 (1996)

Authors
Richard Kimberly Heck
Brown University
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 differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed
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DOI 10.1080/01445349608837265
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References found in this work BETA

Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
The Basic Laws of Arithmetic.Gottlob Frege - 1893 - Berkeley: University of California Press.
Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
Frege: Philosophy of Mathematics. [REVIEW]Charles Parsons - 1996 - Philosophical Review 105 (4):540.

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Citations of this work BETA

Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.
Impredicativity and Paradox.Gabriel Uzquiano - 2019 - Thought: A Journal of Philosophy 8 (3):209-221.
Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.

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