Piergiorgio Odifreddi: "Gödel's Mathematics of Philosophy"
AbstractMathematicians with an interest in philosophy, such as the present author, find an interest in the latter when they see it as a metaphor or, even better, an inspiration for the former. Gödel provides a study case, since he is well known to have declared that (part of) his mathematical work was a direct consequence of his philosophical assumptions. If one takes this to mean Gödel's own philosophy in the academic sense, then it is difficult to make precise sense of his remark. The following observations intend to show that the difficulties disappear if one interprets Gödel's philosophical assumption in a more popular sense, to mean assumptions of philosophers whose thought he happened to know and find interesting. We claim that some of Gödel's main results can be seen as mathematically precise formulations of intuitions of Aristotle, Leibniz and Kant. What we really care about, as non professional philosophers, is to show that (part of) philosophy can be reinterpreted as asking questions and suggesting answers that mathematics makes precise. Or, to put it more generally, that in intellectual history everything happens twice: first as philosophy, and then as mathematics.