On Godel Sentences and What They Say

Citation

Milne P (2007) On Godel Sentences and What They Say. Philosophia Mathematica, 15 (2), pp. 193-226. https://doi.org/10.1093/philmat/nkm015

Abstract
Proofs of Gödel’s First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable and that they are true; otherwise a false theory can yield false gödel sentences.

Keywords
Gödel sentences; Gödel, Kurt.; Incompleteness theorem; Gödel’s theorem; Mathematics Philosophy

Journal
Philosophia Mathematica: Volume 15, Issue 2

People

Professor Peter Milne

Emeritus Professor, Philosophy