Order:
Disambiguations
Carl J. Posy [24]Carl Posy [10]Carl Jeffrey Posy [1]
  1.  3
    Mathematical Intuitionism.Carl J. Posy - 2020 - Cambridge University Press.
    L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  2.  89
    Kant’s Mathematical Realism.Carl J. Posy - 1984 - The Monist 67 (1):115-134.
    Though my title speaks of Kant’s mathematical realism, I want in this essay to explore Kant’s relation to a famous mathematical anti-realist. Specifically, I want to discuss Kant’s influence on L. E. J. Brouwer, the 20th-century Dutch mathematician who built a contemporary philosophy of mathematics on constructivist themes which were quite explicitly Kantian. Brouwer’s theory is perhaps most notable for its belief that constructivism requires us to abandon the traditional logic of mathematical reasoning in favor of different canon of reasoning, (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  3.  47
    Intuitionism and Philosophy.Carl Posy - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 319--355.
    After sketching the essentials of L. E. J. Brouwer’s intuitionistic mathematics—separable mathematics, choice sequences, the uniform continuity theorem, and the intuitionistic continuum—this chapter outlines the main philosophical tenets that go hand in hand with Brouwer’s technical achievements. It presents his views about general and mathematical phenomenology and shows how these views ground his positive epistemological and ontological positions and his stinging criticisms of classical mathematics and logic. The chapter then turns to intuitionistic logic and its philosophical side. It first sets (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  4.  84
    Brouwer's Constructivism.Carl J. Posy - 1974 - Synthese 27 (1-2):125 - 159.
  5.  33
    Varieties of Indeterminacy in the Theory of General Choice Sequences.Carl J. Posy - 1976 - Journal of Philosophical Logic 5 (1):91 - 132.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  6. Kant's Philosophy of Mathematics Modern Essays.Carl J. Posy - 1992
  7. Immediacy and the Birth of Reference in Kant: The Case for Space.Carl Posy - 2000 - In Gila Sher & Richard Tieszen (eds.), Between Logic and Intuition: Essays in Honor of Charles Parsons. Cambridge University Press. pp. 155-185.
     
    Export citation  
     
    Bookmark   8 citations  
  8.  41
    Dancing to the Antinomy: A Proposal for Transcendental Idealism.Carl Posy - 1983 - American Philosophical Quarterly 20 (1):81 - 94.
  9.  16
    The Infinite, the Indefinite and the Critical Turn: Kant Via Kripke Models.Carl Posy - forthcoming - Tandf: Inquiry:1-31.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10. A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics.Carl J. Posy - 1982 - Topoi 1 (1-2):30-43.
    IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  11. Intuition and Infinity: A Kantian Theme with Echoes in the Foundations of Mathematics.Carl Posy - 2008 - Royal Institute of Philosophy Supplement 63:165-193.
    Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  12.  25
    Intuition and Infinity: A Kantian Theme with Echoes in the Foundations of Mathematics.Carl Posy - 2008 - Royal Institute of Philosophy Supplement 63:165-193.
    Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’. And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can have (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  13.  54
    Where Have All the Objects Gone?Carl J. Posy - 1987 - Southern Journal of Philosophy 25 (S1):17-36.
  14.  33
    Between Leibniz and Mill: Kant's Logic and the Rhetoric of Psychologism.Carl J. Posy - 1997 - Philosophy and Rhetoric 30 (3):243 - 270.
  15.  7
    The Infinite, the Indefinite and the Critical Turn: Kant Via Kripke Models.Carl Posy - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):743-773.
    ABSTRACT This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant’s ‘Critical Philosophy’. Part I reviews some old work of mine that applies these models to provide a reading of Kant’s second antinomy about the divisibility of matter and to answer several attacks on Kant’s antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant’s second antinomy claim that matter is divisible ‘ad infinitum’ and (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  16.  15
    Epistemology, Ontology and the Continuum.Carl J. Posy - 2000 - In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge. Kluwer Academic Publishers. pp. 199--219.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  17.  78
    The Language of Appearances and Things in Themselves.Carl J. Posy - 1981 - Synthese 47 (2):313 - 352.
  18.  21
    On Brouwer's Definition of Unextendable Order.Carl J. Posy - 1980 - History and Philosophy of Logic 1 (1-2):139-149.
    It is argued that the tensed theory of the creative subject provides a natural formulation of the logic underlying Brouwer's notion of unextendable order and explains the link between that notion and virtual order. The tensed theory of the creative subject is also shown to be a useful tool for interpreting recent evidence about the stages of Brouwer's thinking concerning these two notions of order.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  19.  9
    Where Have All the Objects Gone?Carl J. Posy - 1987 - Southern Journal of Philosophy 25 (S1):17-36.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  20.  20
    The Theory of Empirical Sequences.Carl J. Posy - 1977 - Journal of Philosophical Logic 6 (1):47 - 81.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  21. Transcendental Idealism and Causality: An Interpretation of Kant's Argument in the Second Analogy.Carl J. Posy - 1984 - In William A. Harper & Ralf Meerbote (eds.), Kant on Causality, Freedom, and Objectivity. University of Minnesota Press. pp. 20-41.
     
    Export citation  
     
    Bookmark   1 citation  
  22.  19
    Desmond Paul Henry. The Truncation of Truth-Functional Calculation. Notre Dame Journal of Formal Logic, Vol. 2 , Pp. 193–205. [REVIEW]Gerald J. Massey & Carl J. Posy - 1974 - Journal of Symbolic Logic 39 (1):174.
  23.  33
    Van Dalen Dirk. Intuitionistic Logic. Handbook of Philosophical Logic, Volume III, Alternatives to Classical Logic, Edited by Gabbay D. And Guenthner F., Synthese Library, Vol. 166, D. Reidel Publishing Company, Dordrecht Etc. 1986, Pp. 225–339. Felscher Walter. Dialogues as a Foundation for Intuitionistic Logic. Handbook of Philosophical Logic, Volume III, Alternatives to Classical Logic, Edited by Gabbay D. And Guenthner F., Synthese Library, Vol. 166, D. Reidel Publishing Company, Dordrecht Etc. 1986 .. [REVIEW]Carl J. Posy - 1992 - Journal of Symbolic Logic 57 (2):754-756.
  24.  6
    Kant's Philosophy of Mathematics: Volume 1: The Critical Philosophy and its Roots.Carl Posy & Ofra Rechter (eds.) - 2019 - Cambridge University Press.
    The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  25. Mathematical Knowledge, Objects and Applications.Carl Posy & Yemima Ben-Menahem (eds.) - forthcoming - Springer.
    No categories
     
    Export citation  
     
    Bookmark  
  26. Review: Dirk van Dalen, Intuitionistic Logic; Walter Felscher, Dialogues as a Foundation for Intuitionistic Logic. [REVIEW]Carl J. Posy - 1992 - Journal of Symbolic Logic 57 (2):754-756.
  27. Strong Completeness for Some Intuitionistic Free Logics.Carl J. Posy - 1991 - In Karel Lambert (ed.), Philosophical Applications of Free Logic. Oxford University Press. pp. 49.
     
    Export citation  
     
    Bookmark  
  28.  39
    Authenticity or Autonomy? Leibniz and Kant on Practical Rationality.Carl J. Posy - 2008 - In Marcelo Dascal (ed.), Leibniz: What Kind of Rationalist? Springer. pp. 293--313.
    Direct download  
     
    Export citation  
     
    Bookmark  
  29.  52
    Introduction.Carl J. Posy - 1984 - Topoi 3 (2):97-98.
  30. Kant and Conceptual Semantics.Carl J. Posy - 1991 - Topoi 10 (1):67-78.
  31.  47
    Editors' Introduction.Carl J. Posy & Michael T. Ferejohn - 1993 - Synthese 96 (3):333-334.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  32.  15
    Essay Review.Carl J. Posy - 1983 - History and Philosophy of Logic 4 (1-2):83-90.
    MICHAEL DUMMETT, Elements of intuitionism. With the assistance of Robert Minio. Oxford: Oxford University Press, 1977. xii + 466 pp. No price stated.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  33.  7
    Unity, Identity, Infinity.Carl Posy - 1995 - Proceedings of the Eighth International Kant Congress 1:621-642.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  34.  8
    Review: Desmond Paul Henry, The Truncation of Truth-Functional Calculation. [REVIEW]Gerald J. Massey & Carl J. Posy - 1974 - Journal of Symbolic Logic 39 (1):174-174.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark