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40William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Gdel
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39Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational CalculiZeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5): 28-38. 1961.
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38Review: J. P. Mayberry, The Foundations of Mathematics in the Theory of Sets (review)Bulletin of Symbolic Logic 8 (3): 424-426. 2002.
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37The reduction of the lambda calculus to the theory of combinators in [Sch¨ onfinkel, 1924] applies to positive implicational logic, i.e. to the typed lambda calculus, where the types are built up from atomic types by means of the operation A −→ B, to show that the lambda operator can be eliminated in favor of combinators K and S of each type A −→ (B −→ A) and (A −→ (B −→ C)) −→ ((A −→ B) −→ (A −→ C)), respectively.1 I will extend that result to the case in which the types are built up by means o…Read more
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32Plato's Second Best MethodReview of Metaphysics 39 (3). 1986.AT PHAEDO 96A-C Plato portrays Socrates as describing his past study of "the kind of wisdom known as περὶ φυσέως ἱστορία." At 96c-97b, Socrates says that this study led him to realize that he had an inadequate understanding of certain basic concepts which it involved. In consequence, he says at 97b, he abandoned this method and turned to a method of his own. But at this point in the dialogue, instead of proceeding immediately to describe his method, Plato has him interjecting a complaint concern…Read more
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32Kurt Godel. Collected Works. Volume IV: Selected Correspondence AG; Volume V: Selected Correspondence HZPhilosophia Mathematica 14 (1): 76. 2006.
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30The Palmer House Hilton Hotel, Chicago, Illinois April 19–21, 2007Bulletin of Symbolic Logic 13 (4). 2007.
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30Meeting of the Association for Symbolic Logic, Chicago, 1977Journal of Symbolic Logic 43 (3). 1978.
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24The Hilton New York Hotel New York, NY December 27–29, 2005Bulletin of Symbolic Logic 12 (3). 2006.
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23Review: Steven Orey, On $omega$-Consistency and Related Properties (review)Journal of Symbolic Logic 23 (1): 40-41. 1958.
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22Meeting of the Association for Symbolic Logic, Chicago 1975Journal of Symbolic Logic 41 (2): 551-560. 1976.
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22Review: S. C. Kleene, Extension of an Effectively Generated Class of Functions by Enumeration (review)Journal of Symbolic Logic 25 (3): 279-280. 1960.
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22Orey Steven. On ω-consistency and related propertiesJournal of Symbolic Logic 23 (1): 40-41. 1958.
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22Extensional Equality in the Classical Theory of TypesVienna Circle Institute Yearbook 3 219-234. 1995.The classical theory of types in question is essentially the theory of Martin-Löf [1] but with the law of double negation elimination. I am ultimately interested in the theory of types as a framework for the foundations of mathematics and, for this purpose, we need to consider extensions of the theory obtained by adding ‘well-ordered types,’ for example the type N of the finite ordinals; but the unextended theory will suffice to illustrate the treatment of extensional equality
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19Mayberry J. P.. The foundations of mathematics in the theory of sets. Encyclopedia of mathematics and its applications, vol. 82. Cambridge University Press, Cambridge 2000, New York 2001, etc., xx + 424 pp (review)Bulletin of Symbolic Logic 8 (3): 424-426. 2002.
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19Early Analytic Philosophy: Frege, Russell, Wittgenstein : Essays in Honor of Leonard LinskyOpen Court Publishing Company. 1997.These essays present new analyzes of the central figures of analytic philosophy -- Frege, Russell, Moore, Wittgenstein, and Carnap -- from the beginnings of the analytic movement into the 1930s. The papers do not reflect a single perspective, but rather express divergent interpretations of this controversial intellectual milieu.
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16Kleene S. C.. Extension of an effectively generated class of functions by enumeration. Colloquium mathematicum, vol. 6 , pp. 68–78 (review)Journal of Symbolic Logic 25 (3): 279-280. 1960.
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15A Nonconstructive Proof of Gentzen's Hauptsatz for Second Order Predicate LogicJournal of Symbolic Logic 33 (2): 289-290. 1968.
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13J. P. Mayberry. The foundations of mathematics in the theory of sets. Encyclopedia of mathematics and its applications, vol. 82. Cambridge University Press, Cambridge 2000, New York 2001, etc., xx + 424 pp (review)Bulletin of Symbolic Logic 8 (3): 424-426. 2002.
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12Review: H. G. Rice, On Completely Recursively Enumerable Classes and Their Key Arrays (review)Journal of Symbolic Logic 23 (1): 48-48. 1958.
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11Chicago 1967 meeting of the Association for Symbolic LogicJournal of Symbolic Logic 36 (2): 359-368. 1971.
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8Review: A. Grzegorczyk, Some Proofs of Undecidability of Arithmetic (review)Journal of Symbolic Logic 23 (1): 46-47. 1958.
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1What Hilbert and Bernays Meant by "Finitism"In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, De Gruyter. pp. 249-261. 2019.
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To appear in the Proceedings of Logic Colloquium 2006. (28 pages).
Chicago, Illinois, United States of America