SOCRATES DID IT BEFORE GODEL

被引：0

作者：

Degen, Josef Wolfgang ^{[1
]}

机构：

[1] Erlangen Univ, Dept Comp Sci, Erlangen, Germany

来源：

LOGIC AND LOGICAL PHILOSOPHY | 2011年 / 20卷 / 03期

关键词：

The "paradoxon" of Socrates; Godel's Second Incompleteness;

D O I：

10.12775/LLP.2011.011

中图分类号：

B81 [逻辑学（论理学）];

学科分类号：

010104 ; 010105 ;

摘要：

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 Godel's Second Incompleteness Theorem. We investigate some variations of this Socrates-Godel sentence. In an appendix we sketch a ramified epistemic logic with propositional quantifiers in order to analyze the Socrates-Godel sentence in a more logical way, separated from the arithmetical context.

引用

页码：205 / 214

页数：10