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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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212005–06 Winter Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 12 (3): 503-516. 2006.
New York City, New York, United States of America
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Philosophy of Probability |