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2000 Realism and Paradox
Patricia A. Blanchette
Notre Dame J. Formal Logic 41(3): 227-241 (2000). DOI: 10.1305/ndjfl/1038336843


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 A. Blanchette. "Realism and Paradox." Notre Dame J. Formal Logic 41 (3) 227 - 241, 2000.


Published: 2000
First available in Project Euclid: 26 November 2002

zbMATH: 1009.03007
MathSciNet: MR1943494
Digital Object Identifier: 10.1305/ndjfl/1038336843

Primary: 00A30
Secondary: 03A05

Rights: Copyright © 2000 University of Notre Dame


Vol.41 • No. 3 • 2000
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