A universal approach to self-referential paradoxes, incompleteness and fixed points

Bulletin of Symbolic Logic 9 (3):362-386 (2003)
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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

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References found in this work

Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Introduction to Mathematical Logic.D. van Dalen - 1964 - Journal of Symbolic Logic 45 (3):631-631.
Handbook of Mathematical Logic.Akihiro Kanamori - 1984 - Journal of Symbolic Logic 49 (3):971-975.
Notes on the mathematical aspects of Kripke’s theory of truth.Melvin Fitting - 1986 - Notre Dame Journal of Formal Logic 27 (1):75-88.
Understanding the Infinite.Stewart Shapiro - 1996 - Philosophical Review 105 (2):256.

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