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Philosophia Mathematica Advance Access originally published online on April 10, 2007
Philosophia Mathematica 2007 15(2):193-226; doi:10.1093/philmat/nkm015
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Copyright © The Author 2007. Published by Oxford University Press.

On Gödel Sentences and What They Say{dagger}

Peter Milne*

* Department of Philosophy, University of Stirling, Stirling FK9 4AL, U.K.

Correspondence: Peter.Milne{at}stir.ac.uk

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.

{dagger} For comments on earlier versions of this article I should like to thank Jeffrey Ketland, Panu Raatikainen, Philosophia Mathematica’s referees, and especially the late Torkel Franzén


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