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Hilbert, Detlefsen and a Fregean response

University of British Columbia

This thesis examines Frege's objections to Hilbert's program. It argues that Frege's concerns can best be understood as questioning Hilbert's implicit importing of content into ideal mathematics. A contemporary defense of Hilbert, Michael Detlefsen's Hilbert's Program, is taken as representative of an anti-Fregean view. Detlefsen, following Hilbert, develops the finitary/ideal distinction in mathematics. Finitary mathematics, unlike ideal mathematics, is claimed to involve genuine propositions. Frege's objections are thus primarily directed against ideal mathematics. More accurately, Frege's objections are seen as demonstrating the need for explicitly identifying the background language in which Hilbert's program, and thus model theory, are carried out.

Thesis/Dissertation

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2008-09-16

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http://hdl.handle.net/2429/2108

Philosophy

University of British Columbia

UBCV

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