Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-08-04T15:06:56.307Z Has data issue: false hasContentIssue false
  • English
  • Français

GÖDEL’S THEOREM AND DIRECT SELF-REFERENCE

Part of: Mathematical Logic and Foundations

Published online by Cambridge University Press:  02 December 2021

SAUL A. KRIPKE Open the ORCID record for SAUL A. KRIPKE [Opens in a new window]
SAUL A. KRIPKE*
Affiliation:
THE SAUL KRIPKE CENTER, THE GRADUATE CENTER CUNY, 365 FIFTH AVE., ROOM 7118 NEW YORK, NY 10016, USA
*
E-mail: kripkecenter@gc.cuny.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In his paper on the incompleteness theorems, Gödel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that ‘direct’ self-reference can actually be used to prove his result.

Keywords

direct self-referenceGödel numberingIncompleteness

MSC classification

Primary: 03-03: Historical (must also be assigned at least one classification number from Section 01)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 2 , June 2023 , pp. 650 - 654
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Gödel, K. (1986). On formally undecidable propositions of Principia Mathematica and related systems I. In Feferman, S., et al., editors. Kurt Gödel: Collected Works, Volume I. New York: Oxford University Press, translated by Jean van Heijenoort, pp. 145–195.Google Scholar
Grabmayr, B., & Visser, A. (2021). Self-reference upfront: A study of self-referential Gödel numberings. Review of Symbolic Logic, doi: 10.1017/S1755020321000393.CrossRefGoogle Scholar
Halbach, V., & Visser, A. (2014). Self-reference in arithmetic I. Review of Symbolic Logic 7, 671–691.CrossRefGoogle Scholar
Halbach, V., & Visser, A. (2014). Self-reference in arithmetic II. Review of Symbolic Logic 7, 692–712.CrossRefGoogle Scholar
Heck, R. (2004). Self-reference and the languages of arithmetic. Philosophia Mathematica 15, 1–29.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. The Journal of Philosophy 72, 696–716. Reprinted in Kripke, S. (2011). Philosophical Troubles. New York: Oxford University Press, pp. 75–98.CrossRefGoogle Scholar
Picollo, L. (2018). Reference in arithmetic. Review of Symbolic Logic 11, 573–603.CrossRefGoogle Scholar
Visser, A. (2004). Semantics and the liar paradox. In Gabbay, D. and Guenthner, F., editors. Handbook of Philosophical Logic, Vol. 11 (second edition). Heidelberg: Springer, pp. 149–240.Google Scholar