On a fallacy concerning I-am-unprovable sentences: what to take home from Goedel's introduction

Kaave Lajevardi; Saeed Salehi

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arXiv · 2311.06568

On a fallacy concerning I-am-unprovable sentences: what to take home from Goedel's introduction

Kaave Lajevardi·Saeed Salehi

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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 the informal introduction of Goedel's classic (1931) 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 role in Goedel's technical results. Going deeper into the issue and investigating truth conditions of Goedelian 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 Goedelian sentences of systems--a debate which is at least as old as Dummett (1963).

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Kaave Lajevardi, Saeed Salehi. 2023-11-11. On a fallacy concerning I-am-unprovable sentences: what to take home from Goedel's introduction. https://arxiv.org/abs/2311.06568

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