Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 44, Number 1 (2003), 13-48.
Neo-Fregeanism: An Embarrassment of Riches
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.
Notre Dame J. Formal Logic Volume 44, Number 1 (2003), 13-48.
First available in Project Euclid: 21 April 2004
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Weir, Alan. Neo-Fregeanism: An Embarrassment of Riches. Notre Dame J. Formal Logic 44 (2003), no. 1, 13--48. doi:10.1305/ndjfl/1082637613. https://projecteuclid.org/euclid.ndjfl/1082637613