A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points
Article
Formal Antecedent
Category Theory
Citation
Noson S. Yanofsky. (2003). A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points. Bulletin of Symbolic Logic. 9(3). pp. 362–386.
Why this reference is included
Yanofsky’s 2003 A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points, published in Bulletin of Symbolic Logic, is one of the program’s working technical references. Cited across Book I (Categorical Foundations), Part 18, Chapter The Self-Hosting Landscape; Book I (Categorical Foundations), Part 18, Chapter Star-Autonomous Categories and the Diagonal Barrier — the central framing is “Yanofsky (2003). Yanofsky showed that Cantor’s diagonal argument, Russell’s paradox, G"odel’s incompleteness theorem, Tarski’s undefinability theorem, and Turing’s halting…”.
Cited in
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Book I — Categorical Foundations Part 18Chapter The Self-Hosting Landscape
Yanofsky (2003). Yanofsky showed that Cantor's diagonal argument, Russell's paradox, G\"odel's incompleteness theorem, Tarski's undefinability theorem, and Turing's halting problem are all instances of a single abstract pattern — Lawvere's fixed-point theorem applied in appropriate categories
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Book I — Categorical Foundations Part 18Chapter Star-Autonomous Categories and the Diagonal Barrier
Yanofsky reformulated Lawvere's theorem using sets and functions, showing that every classical diagonal-argument result — Cantor's theorem, Russell's paradox, G\"odel's first incompleteness theorem, Turing's halting problem, Tarski's undefinability of truth — is an instance of a single abstract scheme