Socrates Did it Before Gödel

• Authors: Josef Wolfgang Degen
• Languages of publication: EN

Abstracts

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.

Keywords

EN

The “paradoxon” of Socrates; Gödel’s Second Incompleteness Theorem. A ramified epistemic logic with propositional quantifiers

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2011
• Volume: 20
• Issue: 3
• Pages: 205-214

Dates

published

2011-09-01

online

2013-07-02

Contributors

author

Josef Wolfgang Degen

• Erlangen University Department of Computer Science

References

• [1] Kurt Gödel, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, Monatshefte für Mathematik und Physik 38 (1931): 173-198.
• [2] Craig Smorynski, “The incompleteness theorems”, in: Jon Barwise (editor), Handbook of Mathematical Logic, North-Holland, 1977.
• [3] Craig Smorynski, Self-Reference and Modal Logic, Springer, 1985.

Identifiers

DOI

10.12775/LLP.2011.011