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  1. Charles McCarty (forthcoming). Structuralism and Isomorphism. Philosophia Mathematica:nkt024.
    If structuralism is a true view of mathematics on which the statements of mathematicians are taken ‘at face value’, then there are both structures on which classical second-order arithmetic is a correct report, and structures on which intuitionistic second-order arithmetic is correct. An argument due to Dedekind then proves that structures and structures are isomorphic. Consequently, first- and second-order statements true in structures must hold in , and conversely. Since instances of the general law of the excluded third fail in (...)
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  2. Charles Mccarty (2013). Antirealism and Constructivism: Brouwer's Weak Counterexamples. Review of Symbolic Logic 6 (1):147-159.
    Strictly intuitionistic inferences are employed to demonstrate that three conditionsare together inconsistent. Therefore, if the logical signs in mathematical statements governed by the recognition condition are constructive in that they satisfy the clauses of the BHK, then every relevant instance of the classical principle Test is true intuitionistically, and the antirealistic critique of conventional logic, once thought to yield such weak counterexamples, is seen, in this instance, to fail.
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  3. Charles Mccarty (2013). Brouwer's Weak Counterexamples and Testability: Further Remarks. Review of Symbolic Logic 6 (3):513-523.
    Straightforwardly and strictly intuitionistic inferences show that the BrouwerKolmogorov (BHK) interpretation, in the presence of a formulation of the recognition principle, entails the validity of the Law of Testability: that the form s original weak counterexample reasoning was fallacious. The results of the present article extend and refine those of McCarty, C. (2012). Antirealism and Constructivism: Brouwer’s Weak Counterexamples. The Review of Symbolic Logic. First View. Cambridge University Press.
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  4. Charles McCarty (2013). Paradox and Potential Infinity. Journal of Philosophical Logic 42 (1):195-219.
    We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.
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  5. Charles McCarty (2009). Two Questions From Dana Scott: Intuitionistic Topologies and Continuous Functions. Journal of Symbolic Logic 74 (2):689-692.
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  6. Charles McCarty (2008). Intuitionism and Logical Syntax. Philosophia Mathematica 16 (1):56-77.
    , Rudolf Carnap became a chief proponent of the doctrine that the statements of intuitionism carry nonstandard intuitionistic meanings. This doctrine is linked to Carnap's ‘Principle of Tolerance’ and claims he made on behalf of his notion of pure syntax. From premises independent of intuitionism, we argue that the doctrine, the Principle, and the attendant claims are mistaken, especially Carnap's repeated insistence that, in defining languages, logicians are free of commitment to mathematical statements intuitionists would reject. I am grateful to (...)
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  7. Charles McCarty (2008). Completeness and Incompleteness for Intuitionistic Logic. Journal of Symbolic Logic 73 (4):1315-1327.
    We call a logic regular for a semantics when the satisfaction predicate for at least one of its nontheorems is closed under double negation. Such intuitionistic theories as second-order Heyting arithmetic HAS and the intuitionistic set theory IZF prove completeness for no regular logics, no matter how simple or complicated. Any extensions of those theories proving completeness for regular logics are classical, i.e., they derive the tertium non datur. When an intuitionistic metatheory features anticlassical principles or recognizes that a logic (...)
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  8. Charles McCarty (2007). Carnap and Quine on Intuitionism. Soochow Journal of Philosophical Studies 16:93 - 109.
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  9. Charles McCarty (2006). At the Heart of Analysis: Intuitionism and Philosophy. Philosophia Scientiae:81-94.
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  10. Charles McCarty (2006). The Coherence of Antirealism. Mind 115 (460):947-956.
    The project of antirealism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of the excluded third and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity. Using principles of intuitionistic mathematics and employing only intuitionistically correct inferences, we show that prima facie reasonable formulations of (1), (2), and (3) are inconsistent. Therefore, it should (...)
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  11. Charles McCarty (1988). Constructive Validity is Nonarithmetic. Journal of Symbolic Logic 53 (4):1036-1041.
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  12. Charles McCarty (1988). Markov's Principle, Isols and Dedekind Finite Sets. Journal of Symbolic Logic 53 (4):1042-1069.
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  13. Charles McCarty (1987). Variations on a Thesis: Intuitionism and Computability. Notre Dame Journal of Formal Logic 28 (4):536-580.
  14. Charles McCarty & Neil Tennant (1987). Skolem's Paradox and Constructivism. Journal of Philosophical Logic 16 (2):165 - 202.
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  15. Charles McCarty (1986). Subcountability Under Realizability. Notre Dame Journal of Formal Logic 27 (2):210-220.
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  16. Charles McCarty (1986). Realizability and Recursive Set Theory. Annals of Pure and Applied Logic 32:153-183.
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  17. Charles McCarty (1983). Intuitionism: An Introduction to a Seminar. [REVIEW] Journal of Philosophical Logic 12 (2):105 - 149.
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  18. Charles McCarty (1981). Wittgenstein on the Foundations of Mathematics. Grazer Philosophische Studien 14:165-175.
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