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  1. 1 Logic and Logical Philosophy

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  1. 1 Degen J. W.

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  1. 1 2011

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Socrates Did it Before Gödel

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Degen J. W.
Logic and Logical Philosophy
|
2011
|
vol. 20
|
issue 3
205-214
EN
We translate Socrates’ famous saying I know that I know nothing into the arithmetical sentence I prove that I prove nothing. Then it is easy to show that this translated saying is formally undecidable in formal arithmetic, using Gödel’s Second Incompleteness Theorem. We investigate some variations of this Socrates-Gödel sentence. In an appendix we sketch a ramified epistemic logic with propositional quantifiers in order to analyze the Socrates-Gödel sentence in a more logical way, separated from the arithmetical context.
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