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William Tait [17]William W. Tait [8]William D. Tait [1]
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Profile: William W. Tait (University of Chicago)
  1. William Tait, On Cut Elimination for Subsystems of Second-Order Number Theory.
    To appear in the Proceedings of Logic Colloquium 2006. (32 pages).
     
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  2. William Tait, Takeuti’s Consistency Proof for Pi^.
    To appear in the Proceedings of Logic Colloquium 2006. (28 pages).
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  3. William Tait, Takeuti’s Consistency Proof for Pi^11 NCA.
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  4. William Tait, Constructing Cardinals From Below.
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  5. William Tait, Cantor's Grundlagen and the Paradoxes of Set Theory.
    Foundations of a General Theory of Manifolds [Cantor, 1883], which I will refer to as the Grundlagen, is Cantor’s first work on the general theory of sets. It was a separate printing, with a preface and some footnotes added, of the fifth in a series of six papers under the title of “On infinite linear point manifolds”. I want to briefly describe some of the achievements of this great work. But at the same time, I want to discuss its connection (...)
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  6. William Tait, Frege Versus Cantor and Dedekind: On the Concept of Number.
    There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, (...)
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  7. William Tait, Remarks on Finitism.
    The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, P RA; and in 1981, in “Finitism” [28], I expanded on the argument. But some recent discussions and some of the more recent literature on the subject lead me to think that a few further remarks would be useful.
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  8. William Tait, The Five Questions.
    1. A Road to Philosophy of Mathematics l became interested in philosophy and mathematics at more or less the same time, rather late in high school; and my interest in the former certainly influenced my attitude towards the latter, leading me to ask what mathematics is really about at a fairly early stage. I don ’t really remember how it was that I got interested in either subject. A very good math teacher came to my school when I was in (...)
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  9. William Tait, Variable-Free Formalization of the Curry-Howard Theory.
    The 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)), (...)
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  10. Yiannis Moschovakis, Richmond H. Thomason, Steffen Lempp, Steve Awodey, Jean-Pierre Marquis & William Tait (2007). The Palmer House Hilton Hotel, Chicago, Illinois April 19–21, 2007. Bulletin of Symbolic Logic 13 (4).
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  11. Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman (2006). Of the Association for Symbolic Logic. Bulletin of Symbolic Logic 12 (3-4):503.
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  12. Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman (2006). The Hilton New York Hotel New York, NY December 27–29, 2005. Bulletin of Symbolic Logic 12 (3).
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  13. William Tait (2006). Godel's Interpretation of Intuitionism. Philosophia Mathematica 14 (2):208-228.
    Gödel regarded the Dialectica interpretation as giving constructive content to intuitionism, which otherwise failed to meet reasonable conditions of constructivity. He founded his theory of primitive recursive functions, in which the interpretation is given, on the concept of computable function of finite type. I will (1) criticize this foundation, (2) propose a quite different one, and (3) note that essentially the latter foundation also underlies the Curry-Howard type theory, and hence Heyting's intuitionistic conception of logic. Thus the Dialectica interpretation (in (...)
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  14. William W. Tait (2006). Gödel's Correspondence on Proof Theory and Constructive Mathematics Kurt Gödel. Collected Works. Volume IV: Selected Correspondence A–G; Volume V: Selected Correspondence H–Z. Solomon Feferman, John W. Dawson, Warren Goldfarb, Charles Parsons, and Wilfried Sieg, Eds. Oxford: Oxford University Press, 2002. Pp. Xi+ 662; Xxiii+ 664. ISBN 0-19-850073-4; 0-19-850075-0. [REVIEW] Philosophia Mathematica 14 (1):76-111.
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  15. William W. Tait (2006). Proof-Theoretic Semantics for Classical Mathematics. Synthese 148 (3):603 - 622.
    We discuss the semantical categories of base and object implicit in the Curry-Howard theory of types and we derive derive logic and, in particular, the comprehension principle in the classical version of the theory. Two results that apply to both the classical and the constructive theory are discussed. First, compositional semantics for the theory does not demand ‘incomplete objects’ in the sense of Frege: bound variables are in principle eliminable. Secondly, the relation of extensional equality for each type is definable (...)
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  16. William Tait (2005). The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History. OUP USA.
    William 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 Gödel. Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This (...)
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  17. William W. Tait (2002). The Myth of the Mind. Topoi 21 (1-2):65-74.
    Of course, I do not mean by the title of this paper to deny the existence of something called.
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  18. William Tait (2001). Godel's Unpublished Papers on Foundations of Mathematics. Philosophia Mathematica 9 (1):87-126.
  19. William W. Tait (1993). Some Recent Essays in the History of the Philosophy of Mathematics: A Critical Review. [REVIEW] Synthese 96 (2):293 - 331.
  20. William W. Tait (1986). Wittgenstein and the 'Skeptical Paradoxes'. Journal of Philosophy 83 (September):475-488.
  21. Daniel Halpern, William Tait & John T. Baldwin (1981). Meeting of the Association for Symbolic Logic: Biloxi, 1979. Journal of Symbolic Logic 46 (1):191-198.
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  22. Carl G. Jockusch Jr, Robert I. Soare, William Tait & Gaisi Takeuti (1978). Meeting of the Association for Symbolic Logic: Chicago, 1977. Journal of Symbolic Logic 43 (3):614 - 619.
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  23. Georg Kreisel & William W. Tait (1961). Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):28-38.
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  24. William W. Tait (1960). Review: S. C. Kleene, Extension of an Effectively Generated Class of Functions by Enumeration. [REVIEW] Journal of Symbolic Logic 25 (3):279-280.
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  25. William W. Tait (1959). Review: Leon Henkin, A Generalization of the Concept of $Omega$-Completeness. [REVIEW] Journal of Symbolic Logic 24 (2):172-173.
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  26. William D. Tait (1928). Psychology, Leadership and Democracy. Australasian Journal of Philosophy 6 (1):28 – 34.
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