Description

• Title:
  Socrates did it before Gödel
• Creator:
  Degen, Josef Wolfgang
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2011.11.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 20 No. 3 (2011); 205-214;
  Logic and Logical Philosophy; Tom 20 Nr 3 (2011); 205-214;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2011.011/802
• Subject:
  the “paradoxon” of Socrates;
  Gödel’s Second Incompleteness Theorem;
  a ramified epistemic logic with propositional quantifiers
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2011.011
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text