Socrates Did It Before Gödel - Degen, Wolfgang (Logic and Logical Philosophy, 2011)
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.
UnivIS-Import:2015-03-09:Pub.2011.tech.IMMD.lsinfs.socrat
Keywords: Gödel's Second Incompleteness Theorem. A ramified epistemic logic with propositional quantifiers; The "paradoxon" of Socrates