The Key Problems of KC

Abstract

The aim of the present paper is to show the limitations of the attempt made by Juliet
Floyd and Hilary Putnam (Floyd and Putnam 2000) to defend Wittgenstein’s remarks
concerning Gödel’s first theorem. Two objections can be raised against this
interpretation of Wittgenstein. One (paragraph 1) is that the key claim that Floyd
and Putnam (KC) attribute to Wittgenstein is compatible with mathematical realism, a
type of philosophy of mathematics that the philosopher explicitly rejected. The other
(paragraph 2) is that Floyd and Putnam’s claim hinges upon an untenable way of
distinguishing between mathematical theorems and metaphysical theses. Successively,
(paragraph 3), I argue that some of Wittgenstein’s pivotal theses in the philosophy
of mathematics are involved in his discussion of Gödel’s theorem and at the end of
the day I cast some doubts on the alleged non-revisionist nature of his reflection on
mathematics.