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74This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders the proof of the so–called fixed point theorem transparent. We also point out various historical details and make some observations on circularity and some comparisons with natural language. The sketch does not include the messy details of the arithmetization of the language, but the motive for arithmetization and what it should accomplish are made obvious. We s…Read more
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61The semantic paradoxes, whose paradigm is the Liar, played a crucial role at a crucial juncture in the development of modern logic. In his 1908 seminal paper, Russell outlined a system, soon to become that of the Principia Mathematicae, whose main goal was the solution of the logical paradoxes, both semantic and settheoretic. Russell did not distinguish between the two and his theory of types was designed to solve both kinds in the same uniform way. Set theoreticians, however, were content to tr…Read more
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202005–06 Winter Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 12 (3): 503-516. 2006.
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86Self-reference and the acyclicity of rational choiceAnnals of Pure and Applied Logic 96 (1-3): 117-140. 1999.Self-reference in semantics, which leads to well-known paradoxes, is a thoroughly researched subject. The phenomenon can appear also in decision theoretic situations. There is a structural analogy between the two and, more interestingly, an analogy between principles concerning truth and those concerning rationality. The former can serve as a guide for clarifying the latter. Both the analogies and the disanalogies are illuminating.
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1Operational pointer semantics: Solution to self-referential puzzles IIn M. Y. Vardi (ed.), Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge, Morgan Kaufman. 1988.
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Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Philosophy of Probability |