On an alleged refutation of Hilbert's program using gödel's first incompleteness theorem

Journal of Philosophical Logic 19 (4):343 - 377 (1990)
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Abstract

It is argued that an instrumentalist notion of proof such as that represented in Hilbert's viewpoint is not obligated to satisfy the conservation condition that is generally regarded as a constraint on Hilbert's Program. A more reasonable soundness condition is then considered and shown not to be counter-exemplified by Godel's First Theorem. Finally, attention is given to the question of what a theory is; whether it should be seen as a "list" or corpus of beliefs, or as a method for selecting beliefs. The significance of this question for assessing "intensional" results like Godel's Second Theorem, and their bearing on Hilbert's Program are discussed.

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Michael Detlefsen
Last affiliation: University of Notre Dame

Citations of this work

Hilbert’s Program.Richard Zach - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
Universism and extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - 2021 - Review of Symbolic Logic 14 (1):112-154.
Hilbert's program then and now.Richard Zach - 2006 - In Dale Jacquette (ed.), Philosophy of Logic. North Holland. pp. 411–447.
Is Mathematics Problem Solving or Theorem Proving?Carlo Cellucci - 2017 - Foundations of Science 22 (1):183-199.

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References found in this work

The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
Fragments of arithmetic.Wilfried Sieg - 1985 - Annals of Pure and Applied Logic 28 (1):33-71.

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