A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points

2003/05/19 by Noson S. Yanofsky · 4 voices
Mathematics · #math.LO

paper · pdf · doi:10.2178/bsl/1058448677

Abstract

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

Discussions

• Universal Approach to Self-Referential Paradoxes (2003) [hn, 2 points, 0 comments]
• The article is great! Self-reference, undecidability etc. come from Lawvere's fixed-point theorem - which is a category-theoretic generalization from Gödel, Tarski, Russell, Cantor etc. arxiv.org/abs/ [bsky, 1 points, 0 comments]
• A Universal Approach to Self-Referential Paradoxes - Noson S. Yanofsky [2003] [hn, 1 points, 0 comments]
• A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points | Abstract arxiv.org/abs/math/030... 今頃読んで後悔してるけど、丁寧な解説論文がここにあった。 [bsky, 0 points, 0 comments]