Bad company and neo-Fregean philosophy

Synthese 170 (3):393-414 (2009)
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Abstract

A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on a priori justification; the idea of abstraction as reconceptualization, the idea that truth is prior to reference in the sense associated with Frege's context principle; and various broadly relativistic views. The conclusions are by and large negative.

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Matti Eklund
Uppsala University

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References found in this work

Truth and objectivity.Crispin Wright - 1992 - Cambridge, Mass.: Harvard University Press.
Truth and Objectivity.Crispin Wright - 1992 - Cambridge, Mass.: Harvard University Press.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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