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William W. Tait
University of Chicago
  1. Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
  2. Truth and Proof: The Platonism of Mathematics.W. W. Tait - 1986 - Synthese 69 (3):341 - 370.
  3.  67
    Intensional Interpretations of Functionals of Finite Type I.W. W. Tait - 1967 - Journal of Symbolic Logic 32 (2):198-212.
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  4.  76
    Gödel's Reformulation of Gentzen's First Consistency Proof for Arithmetic: The No-Counterexample Interpretation.W. W. Tait - 2005 - Bulletin of Symbolic Logic 11 (2):225-238.
    The last section of “Lecture at Zilsel’s” [9, §4] contains an interesting but quite condensed discussion of Gentzen’s first version of his consistency proof for P A [8], reformulating it as what has come to be called the no-counterexample interpretation. I will describe Gentzen’s result (in game-theoretic terms), fill in the details (with some corrections) of Godel's reformulation, and discuss the relation between the two proofs.
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  5. Against Intuitionism: Constructive Mathematics is Part of Classical Mathematics. [REVIEW]W. W. Tait - 1983 - Journal of Philosophical Logic 12 (2):173 - 195.
  6.  18
    Kurt Godel. Collected Works. Volume IV: Selected Correspondence AG; Volume V: Selected Correspondence HZ.W. W. Tait - 2006 - Philosophia Mathematica 14 (1):76.
  7. Zermelo's Conception of Set Theory and Reflection Principles.W. W. Tait - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
  8.  88
    Gödel on Intuition and on Hilbert's Finitism.W. W. Tait - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
    There are some puzzles about G¨ odel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, G¨ odel’s writings represent a smooth evolution, with just one rather small double-reversal, of his view of finitism. He used the term “finit” (in German) or “finitary” or “finitistic” primarily to (...)
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  9. Functionals Defined by Transfinite Recursion.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):155-174.
  10.  63
    Beyond the Axioms: The Question of Objectivity in Mathematics.W. W. Tait - 2001 - Philosophia Mathematica 9 (1):21-36.
    This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter (...)
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  11.  31
    The Law of Excluded Middle and the Axiom of Choice.W. W. Tait - 1994 - In Alexander George (ed.), Mathematics and Mind. Oxford University Press. pp. 45--70.
  12. Meeting of the Association for Symbolic Logic.John Baldwin, D. A. Martin, Robert I. Soare & W. W. Tait - 1976 - Journal of Symbolic Logic 41 (2):551-560.
  13. The Completeness of Heyting First-Order Logic.W. W. Tait - 2003 - Journal of Symbolic Logic 68 (3):751-763.
    Restricted to first-order formulas, the rules of inference in the Curry-Howard type theory are equivalent to those of first-order predicate logic as formalized by Heyting, with one exception: ∃-elimination in the Curry-Howard theory, where ∃x : A.F (x) is understood as disjoint union, are the projections, and these do not preserve firstorderedness. This note shows, however, that the Curry-Howard theory is conservative over Heyting’s system.
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  14.  5
    Alan Cobham. Some Remarks Concerning Theories with Recursively Enumerable Complements. The Journal of Symbolic Logic, Vol. 28 No. 1 , Pp. 72–74. [REVIEW]W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):255-255.
  15.  16
    The Substitution Method.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):175-192.
  16.  46
    Noesis: Plato on Exact Science.W. W. Tait - 2002 - In David B. Malament (ed.), Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics. Open Court. pp. 11--31.
  17.  16
    Plato's Second Best Method.W. W. Tait - 1986 - Review of Metaphysics 39 (3):455 - 482.
    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 (...)
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  18.  6
    Frege's Philosophy of Mathematics.W. Demopoulos & W. W. Tait - 2002 - Synthese 133 (3):441-452.
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  19.  7
    Infinitely Long Terms of Transfinite Type.W. W. Tait, J. N. Crossley & M. A. E. Dummett - 1975 - Journal of Symbolic Logic 40 (4):623-624.
  20.  16
    Mathematics in Philosophy. Charles Parsons.W. W. Tait - 1986 - Philosophy of Science 53 (4):588-606.
  21.  17
    Set Existence.R. O. Gandy, G. Kreisel & W. W. Tait - 1962 - Journal of Symbolic Logic 27 (2):232-233.
  22.  30
    Kant and Finitism.W. W. Tait - 2016 - Journal of Philosophy 113 (5/6):261-273.
    An observation and a thesis: The observation is that, whatever the connection between Kant’s philosophy and Hilbert’s conception of finitism, Kant’s account of geometric reasoning shares an essential idea with the account of finitist number theory in “Finitism”, namely the idea of constructions f from ‘arbitrary’ or ‘generic’ objects of various types. The thesis is that, contrary to a substantial part of contemporary literature on the subject, when Kant referred to number and arithmetic, he was not referring to the natural (...)
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  23.  4
    Wittgenstein and the "Skeptical Paradoxes".W. W. Tait - 1986 - Journal of Philosophy 83 (9):475.
  24.  25
    A Counterexample to a Conjecture of Scott and Suppes.W. W. Tait - 1959 - Journal of Symbolic Logic 24 (1):15-16.
  25.  4
    Nested Recursion.W. W. Tait - 1963 - Journal of Symbolic Logic 28 (1):103-104.
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  26.  49
    Curtis Franks The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited.W. W. Tait - 2011 - History and Philosophy of Logic 32 (2):177 - 183.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 177-183, May 2011.
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  27.  2
    A Nonconstructive Proof of Gentzen's Hauptsatz for Second Order Predicate Logic.W. W. Tait - 1968 - Journal of Symbolic Logic 33 (2):289-290.
  28.  5
    Intensional Interpretations of Functionals of Finite Type I.W. W. Tait - 1975 - Journal of Symbolic Logic 40 (4):624-625.
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  29.  14
    Functionals Defined by Transfinite Recursion.R. E. Vesley & W. W. Tait - 1966 - Journal of Symbolic Logic 31 (3):509.
  30.  10
    Eckart Menzler-Trott. Translated by Craig Smoryński and Edward Griffor. Logic's Lost Genius: The Life of Gerhard Gentzen. History of Mathematics, Vol. 33. American Mathematical Society, Providence, RI, 2007, Xxii+441 Pp. [REVIEW]W. W. Tait - 2010 - Bulletin of Symbolic Logic 16 (2):270-275.
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  31.  23
    Review: J. P. Mayberry, The Foundations of Mathematics in the Theory of Sets. [REVIEW]W. W. Tait - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.
  32.  18
    The Logic of Provability.W. W. Tait - 1999 - Journal of Philosophy 96 (1):50-53.
  33.  7
    Henkin Leon. A Generalization of the Notion of Ω-Consistency.W. W. Tait - 1958 - Journal of Symbolic Logic 23 (1):40-40.
  34.  6
    Meeting of the Association for Symbolic Logic, Chicago 1975.John Baldwin, D. A. Martin, Robert I. Soare & W. W. Tait - 1976 - Journal of Symbolic Logic 41 (2):551-560.
  35.  6
    Chicago 1967 Meeting of the Association for Symbolic Logic.W. W. Tait - 1971 - Journal of Symbolic Logic 36 (2):359-368.
  36.  5
    Mayberry 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]W. W. Tait - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.
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  37.  5
    Orey Steven. On Ω-Consistency and Related Properties.W. W. Tait - 1958 - Journal of Symbolic Logic 23 (1):40-41.
  38.  4
    Grzegorczyk A.. Some Proofs of Undecidability of Arithmetic. Fundamenta Mathematicae, Vol. 43 , Pp. 166–177.W. W. Tait - 1958 - Journal of Symbolic Logic 23 (1):46-47.
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  39.  10
    Book Review:Wittgenstein on Meaning. Colin McGinn. [REVIEW]W. W. Tait - 1987 - Ethics 97 (3):675-.
  40.  1
    Review: Steven Orey, On $Omega$-Consistency and Related Properties. [REVIEW]W. W. Tait - 1958 - Journal of Symbolic Logic 23 (1):40-41.
  41.  2
    Review: H. G. Rice, On Completely Recursively Enumerable Classes and Their Key Arrays. [REVIEW]W. W. Tait - 1958 - Journal of Symbolic Logic 23 (1):48-48.
  42.  1
    A Counterexample to a Conjecture of Scott and Suppes.W. W. Tait - 1968 - Journal of Symbolic Logic 33 (2):288-288.
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  43. Book Review on Potter 2004. [REVIEW]W. W. Tait - 2005 - History and Philosophy of Logic 26 (2):164.
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  44. Review: A. Grzegorczyk, Some Proofs of Undecidability of Arithmetic. [REVIEW]W. W. Tait - 1958 - Journal of Symbolic Logic 23 (1):46-47.
  45. REVIEWS: E. Menzler-Trott-Logic's Lost Genius: The Life of Gerhard Gentzen. [REVIEW]W. W. Tait - 2010 - Bulletin of Symbolic Logic 16 (2).