Hilbert, Detlefsen, and a Fregean Response
Researcher: Rudy Vogt
- Date Complete: 1993/04
- Degree Awarded: M.A.
- Research Supervisor: A.D. Irvine
Abstract
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.
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