What he could have said (but did not say) about Gödel’s second theorem: A note on Floyd-Putnam’s Wittgenstein

Wittgenstein-Studien 12 (1):121-129 (2021)
  Copy   BIBTEX

Abstract

In several publications, Juliet Floyd and Hilary Putnam have argued that the so-called ‘notorious paragraph’ of the Remarks on the Foundations of Mathematics contains a valuable philosophical insight about Gödel’s informal proof of the first incompleteness theorem – in a nutshell, the idea they attribute to Wittgenstein is that if the Gödel sentence of a system is refutable, then, because of the resulting ω-inconsistency of the system, we should give up the translation of Gödel’s sentence by the English sentence “I am unprovable”.I will argue against Floyd and Putnam’s use of the idea, and I will indirectly question its attribution to Wittgenstein. First, I will point out that the idea is inefficient in the context of the first incompleteness theorem because there is an explicit assumption of soundness in Gödel’s informal discussion of that theorem. Secondly, I will argue that of he who makes the observation that Floyd and Putnam think Wittgenstein has made about the first theorem, one will expect to see an analogous observation about Gödel’s second incompleteness theorem – yet we see nothing to that effect in Wittgenstein’s remarks. Incidentally, that never-made remark on the import of the second theorem is of genuine logical significance.‏

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,174

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
More on ‘The Philosophical Significance of Gödel’s Theorem’.A. W. Moore - 1999 - Grazer Philosophische Studien 55 (1):103-126.
More on ‘The Philosophical Significance of Gödel’s Theorem’.A. W. Moore - 1999 - Grazer Philosophische Studien 55 (1):103-126.
Kurt Gödel, Paper on the Incompleteness Theorems (1931).Richard Zach - 2005 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. Amsterdam: North-Holland. pp. 917-925.

Analytics

Added to PP
2021-02-10

Downloads
41 (#281,857)

6 months
4 (#170,426)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Kaave Lajevardi
University of Toronto, St. George Campus (PhD)

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references