On a Fallacy Concerning I-Am-Unprovable Sentences: Reflections on Gödel's Introduction

History and Philosophy of Logic (forthcoming)
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Abstract

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a certain property F, and A does in fact have the property F; therefore A is true. We then examine an argument of this form in Gödel's introduction to his classic paper on incompleteness and examine some auxiliary premises which might have been at work in that context. Philosophically significant as it may be, that particular informal argument plays no rôle in Gödel's technical results. Going deeper into the issue and investigating truth conditions of Gödelian sentences (i.e. those sentences which are provably equivalent to their own unprovability) will provide us with insights regarding the philosophical debate on the truth of Gödelian sentences of systems – a debate which goes back at least to Dummett in the 1960s.

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Gödel’s Theorem and Direct Self-Reference.Saul A. Kripke - 2023 - Review of Symbolic Logic 16 (2):650-654.

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