The Gödelian Inferences

Abstract

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