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Carl J. Posy [25]Carl Jeffrey Posy [1]
  1.  51
    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, (...)
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  2.  60
    Varieties of indeterminacy in the theory of general choice sequences.Carl J. Posy - 1976 - Journal of Philosophical Logic 5 (1):91 - 132.
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  3. Brouwer's constructivism.Carl J. Posy - 1974 - Synthese 27 (1-2):125 - 159.
  4.  11
    Kant’s Philosophy of Mathematics: Modern Essays.Carl J. Posy - 1992 - Springer.
    Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. (...)
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  5. 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).
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  6.  23
    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 (...)
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  7. The language of appearances and things in themselves.Carl J. Posy - 1981 - Synthese 47 (2):313 - 352.
  8. Kant and conceptual semantics.Carl J. Posy - 1991 - Topoi 10 (1):67-78.
  9.  46
    Between Leibniz and Mill: Kant's Logic and the Rhetoric of Psychologism.Carl J. Posy - 1997 - Philosophy and Rhetoric 30 (3):243 - 270.
  10.  34
    Epistemology, ontology and the continuum.Carl J. Posy - 2000 - In Emily Grosholz & Herbert Breger (eds.), The growth of mathematical knowledge. Boston: Kluwer Academic Publishers. pp. 199--219.
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  11.  73
    Where have all the objects gone?Carl J. Posy - 1986 - Southern Journal of Philosophy 25 (S1):17-36.
  12.  34
    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.
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  13. Transcendental Idealism and Causality: An Interpretation of Kant's Argument in the Second Analogy.Carl J. Posy - 1984 - In William Leonard Harper & Ralf Meerbote (eds.), Kant on Causality, Freedom, and Objectivity. Univ of Minnesota Press. pp. 20-41.
     
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  14.  26
    Platonism and the Proto-ontology of Mathematics: Learning from the Axiom of Choice.Carl J. Posy - 2023 - In Carl Posy & Yemima Ben-Menahem (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner. Springer. pp. 99-134.
    Benacerraf’s Problem about mathematical truth displays a tension, indeed a seemingly unbridgeable gap, between Platonist foundations for mathematics on the one hand and Hilbert’s ‘finitary standpoint’ on the other. While that standpoint evinces an admirable philosophical unity, it is ultimately an effete rival to Platonism: It leaves mathematical practice untouched, even the highly non-constructive axiom of choice. Brouwer’s intuitionism is a more potent finitist rival, for it engenders significant deviation from standard (classical) mathematics. The essay illustrates three sorts of intuitionistic (...)
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  15.  36
    The theory of empirical sequences.Carl J. Posy - 1977 - Journal of Philosophical Logic 6 (1):47 - 81.
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  16.  29
    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.
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  17.  49
    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.
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  18.  56
    Editors' introduction.Carl J. Posy & Michael T. Ferejohn - 1993 - Synthese 96 (3):333-334.
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  19.  67
    Introduction.Carl J. Posy - 1984 - Topoi 3 (2):97-98.
  20. Kant's philosophy of mathematics.Carl J. Posy & Ofra Rechter (eds.) - 2019 - New York, NY: Cambridge University Press.
    volume 1. The critical philosophy and its roots.
     
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  21. Strong Completeness for Some Intuitionistic Free Logics.Carl J. Posy - 1991 - In Karel Lambert (ed.), Philosophical applications of free logic. New York: Oxford University Press. pp. 49.
     
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  22.  24
    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.  18
    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.
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  24. (1 other version) Intuitionistic Logic by Dirk van Dalen;Dialogues as a Foundation for Intuitionistic Logic by Walter Felscher. [REVIEW]Carl J. Posy - 1992 - Journal of Symbolic Logic 57 (2):754-756.