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

Journal of Philosophical Logic 19 (4):343 - 377 (1990)
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.
Keywords Gödel's incompleteness theorems  Gödel's first incompleteness theorem  Gödel's second incompleteness theorem  Smorynski  Hilbert's Program
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DOI 10.1007/BF00263316
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Alexander Paseau (2011). Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence. Studies in History and Philosophy of Science Part A 42 (1):140-149.

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