Results for 'William Tait'

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  1. 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.
  2. What Hilbert and Bernays Meant by "Finitism".William W. Tait - 2019 - In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 249-261.
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  3.  6
    What Hilbert and Bernays Meant by “Finitism”.William Tait - 2019 - In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 249-262.
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  4.  17
    Early Analytic Philosophy: Frege, Russell, Wittgenstein : Essays in Honor of Leonard Linsky.William W. Tait - 1997 - Open Court Publishing Company.
    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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  5.  39
    The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and its History.William Walker Tait - 2004 - Oxford, England: 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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  6. 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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  7.  89
    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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  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.  67
    Constructing cardinals from below.William Tait - manuscript
  10.  67
    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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  11.  84
    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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  12.  37
    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.
  13.  35
    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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  14. 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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  15.  9
    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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  16.  23
    Early Analytic Philosophy: Frege, Russell, Wittgenstein : Essays in Honor of Leonard Linsky.William W. Tait (ed.) - 1996 - Open Court.
    These essays present new analyses 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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  17.  42
    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.  95
    Wittgenstein and the 'skeptical paradoxes'.William W. Tait - 1986 - Journal of Philosophy 83 (September):475-488.
  19. 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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  20.  21
    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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  21. 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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  22.  27
    Psychology, leadership and democracy.William D. Tait - 1928 - Australasian Journal of Philosophy 6 (1):28 – 34.
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  23.  15
    Psychology, leadership and democracy.William D. Tait - 1928 - Australasian Journal of Psychology and Philosophy 6 (1):28-34.
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  24. Takeuti’s consistency proof for pi^.William Tait - manuscript
    To appear in the Proceedings of Logic Colloquium 2006. (28 pages).
     
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  25. Takeuti’s consistency proof for pi^11 NCA.William Tait - manuscript
     
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  26.  49
    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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  27.  1
    Lectures on the Philosophy of the Mind.Thomas Brown, David Welsh & William Tait - 1851 - William Tait, 107, Prince's Street.
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  28.  15
    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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  29.  22
    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.
  30.  77
    Some recent essays in the history of the philosophy of mathematics: A critical review. [REVIEW]William W. Tait - 1993 - Synthese 96 (2):293 - 331.
  31.  28
    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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  32.  54
    Proceedings of the 4th World Conference on Research Integrity: Brazil, Rio de Janeiro. 31 May - 3 June 2015.Lex Bouter, Melissa S. Anderson, Ana Marusic, Sabine Kleinert, Susan Zimmerman, Paulo S. L. Beirão, Laura Beranzoli, Giuseppe Di Capua, Silvia Peppoloni, Maria Betânia de Freitas Marques, Adriana Sousa, Claudia Rech, Torunn Ellefsen, Adele Flakke Johannessen, Jacob Holen, Raymond Tait, Jillon Van der Wall, John Chibnall, James M. DuBois, Farida Lada, Jigisha Patel, Stephanie Harriman, Leila Posenato Garcia, Adriana Nascimento Sousa, Cláudia Maria Correia Borges Rech, Oliveira Patrocínio, Raphaela Dias Fernandes, Laressa Lima Amâncio, Anja Gillis, David Gallacher, David Malwitz, Tom Lavrijssen, Mariusz Lubomirski, Malini Dasgupta, Katie Speanburg, Elizabeth C. Moylan, Maria K. Kowalczuk, Nikolas Offenhauser, Markus Feufel, Niklas Keller, Volker Bähr, Diego Oliveira Guedes, Douglas Leonardo Gomes Filho, Vincent Larivière, Rodrigo Costas, Daniele Fanelli, Mark William Neff, Aline Carolina de Oliveira Machado Prata, Limbanazo Matandika, Sonia Maria Ramos de Vasconcelos & Karina de A. Rocha - 2016 - Research Integrity and Peer Review 1 (Suppl 1).
    Table of contentsI1 Proceedings of the 4th World Conference on Research IntegrityConcurrent Sessions:1. Countries' systems and policies to foster research integrityCS01.1 Second time around: Implementing and embedding a review of responsible conduct of research policy and practice in an Australian research-intensive universitySusan Patricia O'BrienCS01.2 Measures to promote research integrity in a university: the case of an Asian universityDanny Chan, Frederick Leung2. Examples of research integrity education programmes in different countriesCS02.1 Development of a state-run “cyber education program of research ethics” in (...)
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  33.  24
    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.
  34.  23
    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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  35.  27
    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.
  36.  12
    Combinatory logic with polymorphic types.William R. Stirton - 2022 - Archive for Mathematical Logic 61 (3):317-343.
    Sections 1 through 4 define, in the usual inductive style, various classes of object including one which is called the “combinatory terms of polymorphic type”. Section 5 defines a reduction relation on these terms. Section 6 shows that the weak normalizability of the combinatory terms of polymorphic type entails the weak normalizability of the lambda terms of polymorphic type. The entailment is not vacuous, because the combinatory terms of polymorphic type are indeed weakly normalizable, as is proven in Sect. 7 (...)
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  37.  85
    William Tait. The provenance of pure reason. Essays on the philosophy of mathematics and on its history.Charles Parsons - 2009 - Philosophia Mathematica 17 (2):220-247.
    William Tait's standing in the philosophy of mathematics hardly needs to be argued for; for this reason the appearance of this collection is especially welcome. As noted in his Preface, the essays in this book ‘span the years 1981–2002’. The years given are evidently those of publication. One essay was not previously published in its present form, but it is a reworking of papers published during that period. The Introduction, one appendix, and some notes are new. Many of (...)
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  38.  16
    Tait William. The provenance of pure reason: essays in the philosophy of mathematics and its history. Oxford University Press, Oxford, 2005, x+ 332 pp. [REVIEW]Jeremy Avigad - 2006 - Bulletin of Symbolic Logic 12 (4):608-611.
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  39.  13
    Georg Kreisel and William W. Tait. Finite definability of number-theoretic functions and parametric completeness of equational calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 7 , pp. 28–38. [REVIEW]Rohit Parikh - 1967 - Journal of Symbolic Logic 32 (2):270-271.
  40.  4
    Review: Georg Kreisel, William W. Tait, Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi. [REVIEW]Rohit Parikh - 1967 - Journal of Symbolic Logic 32 (2):270-271.
  41.  35
    A consistency proof for some restrictions of Tait's reflection principles.Rupert McCallum - 2013 - Mathematical Logic Quarterly 59 (1-2):112-118.
    In 5, Tait identifies a set of reflection principles called equation image-reflection principles which Peter Koellner has shown to be consistent relative to the existence of κ, the first ω-Erdős cardinal 1. Tait also defines a set of reflection principles called equation image-reflection principles; however, Koellner has shown that these are inconsistent when m > 2, but identifies restricted versions of them which he proves consistent relative to κ 2. In this paper, we introduce a new large-cardinal property, (...)
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  42.  26
    P. G. Tait and edinburgh natural philosophy, 1860–1901.David B. Wilson - 1991 - Annals of Science 48 (3):267-287.
    Though P. G. Tait was in a seemingly perfect position to teach both William Thomson's thermodynamics and James Clerk Maxwell's electromagnetic theory of light, he did not. Tait probably first encountered the new thermodynamics in the 1850s at Queen's College, Belfast, and presented the ideas in his inaugural lecture at Edinburgh in 1860, soon making energy theory the centre-piece of his course there. The comprehensiveness of energy theory plus Thomson's opposition to Maxwell's electromagnetic theory evidently combined in (...)
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  43.  13
    Logic, Philosophy of Mathematics, and Their History: Essays in Honor of W. W. Tait.Erich H. Reck (ed.) - 2018 - College Publications.
    In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched (...)
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  44. Frege versus Cantor and Dedekind: On the Concept of Number.W. W. Tait - 1996 - In Matthias Schirn (ed.), Frege: importance and legacy. New York: Walter de Gruyter. pp. 70-113.
  45. Constructive Reasoning.W. W. Tait - 1968 - In B. Van Rootselaar & J. F. Staal (eds.), Logic, Methodology and Philosophy of Science III. Amsterdam: North-Holland. pp. 185-99.
  46.  20
    Logic's lost genius: The life of Gerhard Gentzen. History of mathematics, vol. 33.W. Tait - 2010 - Bulletin of Symbolic Logic 16 (2):270-275.
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  47. The Emergent Self.William Hasker - 2001 - London: Cornell University Press.
    In The Emergent Self, William Hasker joins one of the most heated debates in contemporary analytic philosophy, that over the nature of mind.
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  48. Judgement and justification.William G. Lycan - 1988 - New York: Cambridge University Press.
    Toward theory a homuncular of believing For years and years, philosophers took thoughts and beliefs to be modifications of incorporeal Cartesian egos. ...
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  49. The Will to Believe: And Other Essays in Popular Philosophy.William James - 1979 - New York: Cambridge University Press. Edited by Frederick Burkhardt, Fredson Bowers & Ignas K. Skrupskelis.
    For this 1897 publication, the American philosopher William James brought together ten essays, some of which were originally talks given to Ivy League societies. Accessible to a broader audience, these non-technical essays illustrate the author's pragmatic approach to belief and morality, arguing for faith and action in spite of uncertainty. James thought his audiences suffered 'paralysis of their native capacity for faith' while awaiting scientific grounds for belief. His response consisted in an attitude of 'radical empiricism', which deals practically (...)
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  50.  12
    J. 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]W. W. Tait - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.
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