Philosophia Mathematica:nkaa041 (forthcoming)

Authors
Saeed Salehi
University of Tabriz
Kaave Lajevardi
University of Toronto, St. George Campus (PhD)
Abstract
We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkaa041
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

An Introduction to Gödel's Theorems.Peter Smith - 2007 - Cambridge University Press.
The Incompleteness Theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.
Arithmetization of Metamathematics in a General Setting.S. Feferman - 1966 - Journal of Symbolic Logic 31 (2):269-270.
Maximal Consistent Sets of Instances of Tarski's Schema (T).Vann McGee - 1992 - Journal of Philosophical Logic 21 (3):235 - 241.
Another Look at the Second Incompleteness Theorem.Albert Visser - 2020 - Review of Symbolic Logic 13 (2):269-295.

View all 17 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Socrates Did It Before Gödel.Josef Wolfgang Degen - 2011 - Logic and Logical Philosophy 20 (3):205-214.
On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
Herbrand Consistency of Some Arithmetical Theories.Saeed Salehi - 2012 - Journal of Symbolic Logic 77 (3):807-827.
A Non-Arithmetical Gödel Logic.Peter Hájek - 2005 - Logic Journal of the IGPL 13 (4):435-441.
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.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
Heterologicality and Incompleteness.Cezary Cieśliński - 2002 - Mathematical Logic Quarterly 48 (1):105-110.
Is G True by Gödel’s Theorem?Virgil Drăghici - 2018 - Proceedings of the XXIII World Congress of Philosophy 55:11-16.
Lucas Against Mechanism II: A Rejoinder.J. R. Lucas - 1984 - Canadian Journal of Philosophy 14 (2):189-191.
Lucas Against Mechanism II: A Rejoinder.John R. Lucas - 1984 - Canadian Journal of Philosophy 14 (June):189-91.

Analytics

Added to PP index
2021-02-15

Total views
77 ( #138,020 of 2,445,393 )

Recent downloads (6 months)
33 ( #22,404 of 2,445,393 )

How can I increase my downloads?

Downloads

My notes