Titre du document / Document title

Misunderstanding Gödel: New arguments about Wittgenstein and new remarks by Wittgenstein = Gödel incompris : les nouveaux arguments sur Wittgenstein et les nouvelles remarques de Wittgenstein

Auteur(s) / Author(s)

RODYCH Victor ⁽¹⁾ ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

⁽¹⁾ Department of Philosophy, University of Lethbridge, Alberta, CANADA

Résumé / Abstract

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, <pilcrow>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 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, <pilcrow>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 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.

Revue / Journal Title

Dialectica    ISSN  0012-2017 

Source / Source

2003, vol. 57, n^o3, pp. 279-313 [35 page(s) (article)] (1 p.1/4)

Langue / Language

Anglais

Editeur / Publisher

Blackwell, Oxford, ROYAUME-UNI  (1947) (Revue)

Mots-clés anglais / English Keywords

Self reference

;

Mathematics

;

Truth

;

Natural Number

;

Inconsistency

;

Putnam (H.)

;

Proof

;

Incompleteness

;

Gödel's Theorem

;

Wittgenstein (L.)

;

Mots-clés français / French Keywords

Floyd (J.)

;

Autoréférence

;

Mathématiques

;

Vérité

;

Nombre naturel

;

Inconsistance

;

Putnam (H.)

;

Preuve

;

Incomplétude

;

Théorème de Gödel

;

Wittgenstein (L.)

;

Localisation / Location

INIST-CNRS, Cote INIST : 2446, 35400011926731.0020