Neo-Fregeanism: an embarrassment of riches

Weir, A.J. (2003) Neo-Fregeanism: an embarrassment of riches. Notre Dame Journal of Formal Logic, 44(1), pp. 13-48. (doi: 10.1305/ndjfl/1082637613)

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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.

Item Type:Articles
Keywords:neologicism, Frege, abstraction
Glasgow Author(s) Enlighten ID:Weir, Professor Alan
Authors: Weir, A.J.
Subjects:B Philosophy. Psychology. Religion > B Philosophy (General)
College/School:College of Arts & Humanities > School of Humanities > Philosophy
Journal Name:Notre Dame Journal of Formal Logic
ISSN (Online):1939-0726

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