On Gödel Sentences and What They Say

Philosophia Mathematica 15 (2):193-226 (2007)

Authors
Peter Milne
University of Stirling
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   Journal Article   Gödel, Kurt.   Incompleteness theorem   Gödel’s theorem   Mathematics Philosophy
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DOI 10.1093/philmat/nkm015
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Self-Reference in Arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
Reference in Arithmetic.Lavinia Picollo - 2018 - Review of Symbolic Logic 11 (3):573-603.
Between Proof and Truth.Julien Boyer & Gabriel Sandu - 2012 - Synthese 187 (3):821-832.

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