Proof Research Papers - Academia.edu (original) (raw)

The long-standing issue of Wittgenstein's controversial remarks on Gödel'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 ωP 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 Gödel'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 Nachla (i.e., a hitherto unknown “proof sketch” of Gödel'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 Gödel's proof—perhaps because, as Kreisel says, Wittgenstein did not read Gödel's 1931 paper prior to 1942-Wittgenstein's 1937–38, 1941 and 1944 remarks indicate that Gödel's result makes no sense from Wittgenstein's own (idiosyncratic) perspective.