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

Published online by Cambridge University Press:  15 January 2014

Noson S. Yanofsky
Noson S. Yanofsky*
Affiliation:
Department of Computer and Information Science, Brooklyn College, Cuny Brooklyn, N.Y. 11210 Department of Computer Science, The Graduate Center, Cuny 365 Fifth Avenue, New york, N.Y. 10016, E-mail: noson@sci.brooklyn.cuny.edu
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Abstract

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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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 9 , Issue 3 , September 2003 , pp. 362 - 386
Copyright
Copyright © Association for Symbolic Logic 2003

References

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