Notre Dame Journal of Formal Logic

Neo-Fregeanism: An Embarrassment of Riches

Alan Weir

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.

Article information

Source
Notre Dame J. Formal Logic Volume 44, Number 1 (2003), 13-48.

Dates
First available: 21 April 2004

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1082637613

Digital Object Identifier
doi:10.1305/ndjfl/1082637613

Mathematical Reviews number (MathSciNet)
MR2060054

Zentralblatt MATH identifier
02187138

Subjects
Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 03E65: Other hypotheses and axioms 03E70: Nonclassical and second-order set theories

Keywords
neologicism Frege abstraction

Citation

Weir, Alan. Neo-Fregeanism: An Embarrassment of Riches. Notre Dame Journal of Formal Logic 44 (2003), no. 1, 13--48. doi:10.1305/ndjfl/1082637613. http://projecteuclid.org/euclid.ndjfl/1082637613.


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