Realism and Paradox

Notre Dame Journal of Formal Logic 41 (3):227-241 (2000)
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This essay addresses the question of the effect of Russell's paradox on Frege's distinctive brand of arithmetical realism. It is argued that the effect is not just to undermine Frege's specific account of numbers as extensions (courses of value) but more importantly to undermine his general means of explaining the object-directedness of arithmetical discourse. It is argued that contemporary neo-Fregean attempts to revive that explanation do not successfully avoid the central problem brought to light by the paradox. Along the way, it is argued that the need to fend off an eliminative construal of arithmetic can help explain the so-called Caesar problem in the Grundlagen, and that the "syntactic priority thesis" is insufficient to establish the claim that numbers are objects



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Patricia Blanchette
University of Notre Dame

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Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
On concept and object.Gottlob Frege - 1951 - Mind 60 (238):168-180.
Ontological commitments.William P. Alston - 1958 - Philosophical Studies 9 (1-2):8 - 17.
Is Hume's principle analytic?G. Boolos - 1998 - Logic, Logic, and Logic:301--314.
New V, ZF and Abstraction.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293-321.

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