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2003 Neo-Fregeanism: An Embarrassment of Riches
Alan Weir
Notre Dame J. Formal Logic 44(1): 13-48 (2003). DOI: 10.1305/ndjfl/1082637613

Abstract

Neo-Fregeans argue that substantial mathematics can be derived from a priori abstraction principles, Hume's Principle connecting numerical identities with one:one correspondences being a prominent example. The embarrassment of riches objection is that there is a plurality of consistent but pairwise inconsistent abstraction principles, thus not all consistent abstractions can be true. This paper considers and criticizes various further criteria on acceptable abstractions proposed by Wright settling on another one—stability—as the best bet for neo-Fregeans. However, an analogue of the embarrassment of riches objection resurfaces in the metatheory and I conclude by arguing that the neo-Fregean program, at least insofar as it includes a platonistic ontology, is fatally wounded by it.

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Alan Weir. "Neo-Fregeanism: An Embarrassment of Riches." Notre Dame J. Formal Logic 44 (1) 13 - 48, 2003. https://doi.org/10.1305/ndjfl/1082637613

Information

Published: 2003
First available in Project Euclid: 21 April 2004

zbMATH: 1071.03006
MathSciNet: MR2060054
Digital Object Identifier: 10.1305/ndjfl/1082637613

Subjects:
Primary: 03A05
Secondary: 03E65, 03E70

Rights: Copyright © 2003 University of Notre Dame

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Vol.44 • No. 1 • 2003
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