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The Philosophical Fundamentals of Hilbert’s Program

  • Michael Detlefsen
Part of the Synthese Library book series (SYLI, volume 182)

Abstract

In this chapter I shall attempt to set out Hilbert’s Program in a way that is more revealing than previous treatments. Specificially, I shall try to improve upon preceding accounts of Hilbert’s Porgram in each of the following respects: (1) in isolating and developing the distinctive form of mathematical instrumentalism which is basic to Hilbert’s Program, (2) in defining the central problems which must be overcome in order to successfully defend any form of mathematical instrumentalism, (3) in showing how Hilbert’s finitism can be related to his instrumentalism by natural and illuminating means, and (4) in identifying some important philosophical implications of the program which have hitherto not been brought to light.

Keywords

Ideal Method Justify Belief Epistemic Attitude Conservative Extension Ideal Mathematic 
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Notes

  1. 11.
    For Frege, a judgement is the acknowledgement of the truth of a thought (cf. Frege [1903], p. 86; [1928], p. 539).Google Scholar
  2. 28.
    Cf. Putnam [1971], pp. 38–43.Google Scholar
  3. 32.
    The statement of these two theses and the ensuing conclusion is taken from Hart [1979], pp. 154–5.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • Michael Detlefsen
    • 1
  1. 1.Department of PhilosophyUniversity of Notre DameUSA

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