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Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History.
- Source :
- History & Philosophy of Logic; May2022, Vol. 43 Issue 2, p175-182, 8p
- Publication Year :
- 2022
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- INCOMPLETENESS theorems
NOTIONS (Philosophy)
MATHEMATICIANS
LOGICIANS
Subjects
Details
- Language :
- English
- ISSN :
- 01445340
- Volume :
- 43
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- History & Philosophy of Logic
- Publication Type :
- Academic Journal
- Accession number :
- 157137840
- Full Text :
- https://doi.org/10.1080/01445340.2021.1976052