Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein

Abstract

The long-standing issue of Wittgenstein's controversial remarks on Godel's Theorem has recently heated up in a number of different and interesting directions [(Floyd and Putnam, 2000), (Steiner, 2001), (Floyd, 2001)]. In their (2000), Juliet Floyd and Hilary Putnam purport to argue that Wittgenstein's 'notorious' (RFM App. III, 8) contains a philosophical claim of great interest, namely, if one assumed... that - P is provable in Russell's system one should... give up the translation of P by the English sentence 'P is not provable', because if ? P is provable in PM, PM is ω-inconsistent, and if PM is ω-inconsistent, we cannot translate 'P' as 'P is not provable in PM' because the predicate 'NaturalNo.(x)' in 'P' cannot be... interpreted as x is a natural number. Though Floyd and Putnam do not clearly distinguish the two tasks, they also argue for The Floyd-Putnam Thesis, namely, that in the 1930's Wittgenstein had a particular (correct) understanding of Godel's First Incompleteness Theorem. In this paper, I endeavour to show, first, that the most natural and most defensible interpretation of Wittgenstein's (RFM App. III, 8) and the rest of (RFM App. III) is incompatible with the Floyd-Putnam attribution and, second, that evidence from Wittgenstein's Nachlass (i.e., a hitherto unknown proof sketch of Godel's reasoning, Wittgenstein's only mention of ω-inconsistency, and Wittgenstein's only mention of K provable) strongly indicates that the Floyd-Putnam attribution and the Floyd-Putnam Thesis are false. By way of this examination, we shall see that despite a failure to properly understand Godel's proof - perhaps because, as Kreisel says, Wittgenstein did not read Godel's 1931 paper prior to 1942 - Wittgenstein's 1937-38, 1941 and 1944 remarks indicate that Godel's result makes no sense from Wittgenstein's own (idiosyncratic) perspective.