Notre Dame Journal of Formal Logic

Realism and Paradox

Patricia A. Blanchette

Abstract

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 41, Number 3 (2000), 227-241.

Dates
First available in Project Euclid: 26 November 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1038336843

Digital Object Identifier
doi:10.1305/ndjfl/1038336843

Mathematical Reviews number (MathSciNet)
MR1943494

Zentralblatt MATH identifier
1009.03007

Subjects
Primary: 00A30: Philosophy of mathematics [See also 03A05]
Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}

Keywords
Frege realism logicism platonism paradox

Citation

Blanchette, Patricia A. Realism and Paradox. Notre Dame J. Formal Logic 41 (2000), no. 3, 227--241. doi:10.1305/ndjfl/1038336843. https://projecteuclid.org/euclid.ndjfl/1038336843


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