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  1.  31
    Problems and Riddles: Hilbert and the Du Bois-Reymonds.D. C. McCarty - 2005 - Synthese 147 (1):63 - 79.
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  2.  54
    Intuitionistic Completeness and Classical Logic.D. C. McCarty - 2002 - Notre Dame Journal of Formal Logic 43 (4):243-248.
    We show that, if a suitable intuitionistic metatheory proves that consistency implies satisfiability for subfinite sets of propositional formulas relative either to standard structures or to Kripke models, then that metatheory also proves every negative instance of every classical propositional tautology. Since reasonable intuitionistic set theories such as HAS or IZF do not demonstrate all such negative instances, these theories cannot prove completeness for intuitionistic propositional logic in the present sense.
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  3.  28
    On Theorems of Gödel and Kreisel: Completeness and Markov's Principle.D. C. McCarty - 1994 - Notre Dame Journal of Formal Logic 35 (1):99-107.
    In 1957, Gödel proved that completeness for intuitionistic predicate logic HPL implies forms of Markov's Principle, MP. The result first appeared, with Kreisel's refinements and elaborations, in Kreisel. Featuring large in the Gödel-Kreisel proofs are applications of the axiom of dependent choice, DC. Also in play is a form of Herbrand's Theorem, one allowing a reduction of HPL derivations for negated prenex formulae to derivations of negations of conjunctions of suitable instances. First, we here show how to deduce Gödel's results (...)
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  4.  45
    Undecidability and intuitionistic incompleteness.D. C. McCarty - 1996 - Journal of Philosophical Logic 25 (5):559 - 565.
    Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is many-one (...)
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  5.  40
    Optics of Thought: Logic and Vision in Müller, Helmholtz, and Frege.D. C. McCarty - 2000 - Notre Dame Journal of Formal Logic 41 (4):365-378.
    The historical antecedents of Frege's treatment of binocular vision in "The thought" were the physiological writings of Johannes Mueller, Hermann von Helmholtz, and Emil du Bois-Reymond. In their research on human vision, logic was assigned an unexpected role: it was to be the means by which knowledge of a world extended in three dimensions arises from stimuli that are at best two-dimensional. An examination of this literature yields a richer understanding of Frege's insistence that a proper epistemology requires us to (...)
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  6.  44
    A review of Michael Peters and James Marshall, 1999, Wittgenstein: Philosophy, Postmodernism, Pedagogy, None of the Above , London: Bergin and Garvey. [REVIEW]D. C. McCarty - 2002 - Studies in Philosophy and Education 21 (3):253-262.