Degen W (2011)
Publication Type: Journal article
Publication year: 2011
Publisher: Versita
Book Volume: 20
Pages Range: 205-214
URI: https://www10.informatik.uni-erlangen.de/Publications/Papers/2011/Degen_LLP.pdf
Abstract. 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.
APA:
Degen, W. (2011). Socrates Did It Before Gödel. Logic and Logical Philosophy, 20, 205-214. https://dx.doi.org/10.12775/LLP.2011.011
MLA:
Degen, Wolfgang. "Socrates Did It Before Gödel." Logic and Logical Philosophy 20 (2011): 205-214.
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