The Gödelian Inferences

History and Philosophy of Logic 30 (3):241-256 (2009)
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Abstract

I attribute an 'intensional reading' of the second incompleteness theorem to its author, Kurt G del. My argument builds partially on an analysis of intensional and extensional conceptions of meta-mathematics and partially on the context in which G del drew two familiar inferences from his theorem. Those inferences, and in particular the way that they appear in G del's writing, are so dubious on the extensional conception that one must doubt that G del could have understood his theorem extensionally. However, on the intensional conception, the inferences are straightforward. For that reason I conclude that G del had an intensional understanding of his theorem. Since this conclusion is in tension with the generally accepted view of G del's understanding of mathematical truth, I explain how to reconcile that view with the intensional reading of the theorem that I attribute to G del. The result is a more detailed account of G del's conception of meta-mathematics than is currently available

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Curtis Franks
University of Notre Dame

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References found in this work

From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: London.
From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
Solution of a problem of Leon Henkin.M. H. Löb - 1955 - Journal of Symbolic Logic 20 (2):115-118.

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