Saul Kripke
CUNY Graduate Center
In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.
Keywords mathematical incompleteness  independence results  first-order Peano arithmetic  Gentzen  Goodstein
Categories (categorize this paper)
DOI 10.1080/01445340.2021.1976052
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,107
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

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
The Shortest Definition of a Number in Peano Arithmetic.Dev K. Roy - 2003 - Mathematical Logic Quarterly 49 (1):83-86.
A Mathematical Incompleteness in Peano Arithmetic.Jeff Paris & Leo Harrington - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 90--1133.
Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
Arithmetic with Fusions.Jeff Ketland & Thomas Schindler - 2016 - Logique Et Analyse 234:207-226.
Heterologicality and Incompleteness.Cezary Cieśliński - 2002 - Mathematical Logic Quarterly 48 (1):105-110.


Added to PP index

Total views
29 ( #379,426 of 2,454,583 )

Recent downloads (6 months)
29 ( #26,127 of 2,454,583 )

How can I increase my downloads?


My notes