Gödel on intuition and on Hilbert's finitism

Abstract

There are some puzzles about Gödel's published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, Gödel's writings represent a smooth evolution, with just one rather small double-reversal, of his view of finitism. He used the term "finit" (in German) or "finitary" or "finitistic" primarily to refer to Hilbert's conception of finitary mathematics. On two occasions (only, as far as I know), the lecture notes for his lecture at Zilsel's (Gödel [*1938a]) and the lecture notes for a lecture at Yale (Gödel [*1941]), he used it in a way that he knew—in the second case, explicitly—went beyond what Hilbert meant.