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

DOI10.2178/bsl/1058448677zbMath1067.03012arXivmath/0305282OpenAlexW2159080528WikidataQ112739923 ScholiaQ112739923MaRDI QIDQ4650304

Noson S. Yanofsky

Publication date: 9 February 2005

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0305282

zbMATH Keywords

fixed point theoremssemantic paradoxesincompletenessself-referencediagonal arguments

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Categorical semantics of formal languages (18C50) Set theory (03E99) Gödel numberings and issues of incompleteness (03F40)

Related Items (14)

Logic in Category Theory ⋮ DIAGONALIZATION EXHIBITED IN THE LIAR PARADOX, RUSSELL’S PARADOX AND GÖDEL’S INCOMPLETENESS THEOREM ⋮ An impossibility theorem on beliefs in games ⋮ Fixed points in lambda calculus. an eccentric survey of problems and solutions ⋮ A Yabloesque paradox in epistemic game theory ⋮ Why Categories? ⋮ Epistemic horizons and the foundations of quantum mechanics ⋮ At the Limits of Thought ⋮ The scope of Gödel's first incompleteness theorem ⋮ Zeno machines and hypercomputation ⋮ Burali-Forti as a purely logical paradox ⋮ A negation-free proof of Cantor's theorem ⋮ From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference ⋮ Aspects of Categorical Recursion Theory

Cites Work

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• On Gödel incompleteness and finite combinatorics
• A note on inconsistencies caused by fixpoints in a cartesian closed category
• A note on Russell's paradox in locally Cartesian closed categories
• Notes on the mathematical aspects of Kripke's theory of truth
• General computability
• On the structure of paradoxes
• Categorical fixed point semantics
• An existence theorem for recursion categories
• Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question
• Existence and feasibility in arithmetic

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