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William Tait [19]William W. Tait [13]William D. Tait [2]
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William W. Tait
University of Chicago
  1.  25
    The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and its History.William Tait - 2005 - 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 Gdel.
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  2. Frege Versus Cantor and Dedekind: On the Concept of Number.William Tait - manuscript
    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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  3.  58
    Remarks on Finitism.William Tait - manuscript
    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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  4.  98
    Gödel's Correspondence on Proof Theory and Constructive Mathematics †Charles Parsons Read Part of an Early Draft of This Review and Made Important Corrections and Suggestions.William W. Tait - 2006 - Philosophia Mathematica 14 (1):76-111.
  5.  58
    Cantor's Grundlagen and the Paradoxes of Set Theory.William Tait - manuscript
    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.  45
    Constructing Cardinals From Below.William Tait - manuscript
  7.  44
    Godel's Interpretation of Intuitionism.William Tait - 2006 - 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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  8. The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History.William Tait - 2006 - Bulletin of Symbolic Logic 12 (4):608-611.
     
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  9.  84
    Proof-Theoretic Semantics for Classical Mathematics.William W. Tait - 2006 - 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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  10. Early Analytic Philosophy Frege, Russell, Wittgenstein : Essays in Honor of Leonard Linsky.Leonard Linsky & William W. Tait - 1997
     
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  11. The Myth of the Mind.William W. Tait - 2002 - 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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  12.  26
    Variable-Free Formalization of the Curry-Howard Theory.William Tait - manuscript
    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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  13. Early Analytic Philosophy: Frege, Russell, Wittgenstein.William W. Tait (ed.) - 1996 - Open Court.
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  14.  26
    Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi.Georg Kreisel & William W. Tait - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):28-38.
  15.  81
    Wittgenstein and the 'Skeptical Paradoxes'.William W. Tait - 1986 - Journal of Philosophy 83 (September):475-488.
  16.  66
    Some Recent Essays in the History of the Philosophy of Mathematics: A Critical Review. [REVIEW]William W. Tait - 1993 - Synthese 96 (2):293 - 331.
  17.  33
    Meeting of the Association for Symbolic Logic: Biloxi, 1979.Daniel Halpern, William Tait & John T. Baldwin - 1981 - Journal of Symbolic Logic 46 (1):191-198.
  18.  21
    The Palmer House Hilton Hotel, Chicago, Illinois April 19–21, 2007.Yiannis Moschovakis, Richmond H. Thomason, Steffen Lempp, Steve Awodey, Jean-Pierre Marquis & William Tait - 2007 - Bulletin of Symbolic Logic 13 (4).
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  19.  16
    Extensional Equality in the Classical Theory of Types.William Tait - 1995 - Vienna Circle Institute Yearbook 3:219-234.
    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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  20.  13
    Kleene S. C.. Extension of an Effectively Generated Class of Functions by Enumeration. Colloquium Mathematicum, Vol. 6 , Pp. 68–78. [REVIEW]William W. Tait - 1960 - Journal of Symbolic Logic 25 (3):279-280.
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  21.  35
    The Five Questions.William Tait - 2007 - In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/Vip.
    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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  22.  17
    Review: S. C. Kleene, Extension of an Effectively Generated Class of Functions by Enumeration. [REVIEW]William W. Tait - 1960 - Journal of Symbolic Logic 25 (3):279-280.
  23.  17
    Of the Association for Symbolic Logic.Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman - 2006 - Bulletin of Symbolic Logic 12 (3-4):503.
  24.  4
    Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi.Georg Kreisel & William W. Tait - 1967 - Journal of Symbolic Logic 32 (2):270-271.
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  25.  10
    Psychology, Leadership and Democracy.William D. Tait - 1928 - Australasian Journal of Psychology and Philosophy 6 (1):28-34.
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  26.  14
    The Hilton New York Hotel New York, NY December 27–29, 2005.Sergei Artemov, Peter Koellner, Michael Rabin, Jeremy Avigad, Wilfried Sieg, William Tait & Haim Gaifman - 2006 - Bulletin of Symbolic Logic 12 (3).
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  27.  13
    Psychology, Leadership and Democracy.William D. Tait - 1928 - Australasian Journal of Philosophy 6 (1):28 – 34.
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  28.  16
    Meeting of the Association for Symbolic Logic, Chicago, 1977.Carl G. Jockusch, Robert I. Soare, William Tait & Gaisi Takeuti - 1978 - Journal of Symbolic Logic 43 (3):614 - 619.
  29. Lectures on the Philosophy of the Mind.Thomas Brown, David Welsh & William Tait - 1846 - William Tait, 107, Prince's Street.
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  30. On Cut Elimination for Subsystems of Second-Order Number Theory.William Tait - manuscript
    To appear in the Proceedings of Logic Colloquium 2006. (32 pages).
     
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  31. Takeuti’s Consistency Proof for Pi^.William Tait - manuscript
    To appear in the Proceedings of Logic Colloquium 2006. (28 pages).
     
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  32. Takeuti’s Consistency Proof for Pi^11 NCA.William Tait - manuscript
     
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  33. What Hilbert and Bernays Meant by "Finitism".William W. Tait - 2019 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics. Berlin, Boston: De Gruyter. pp. 249-261.
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