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  1. Colin Mclarty, What Does It Take to Prove Fermat's Last Theorem?
    Does the proof of Fermat’s Last Theorem (FLT) go beyond Zermelo Fraenkel set theory (ZFC)? Or does it merely use Peano Arithmetic (PA) or some weaker fragment of that? The answers depend on what is meant by “proof ” and “use,” and are not entirely known. This paper surveys the current state of these questions and briefly sketches the methods of cohomological number theory used in the existing proof. The existing proof of FLT is Wiles [1995] plus improvements that do (...)
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  2. Colin Mclarty (2013). Foundations as Truths Which Organize Mathematics. Review of Symbolic Logic 6 (1):76-86.
    The article looks briefly at Fefermans own foundations. Among many different senses of foundations, the one that mathematics needs in practice is a recognized body of truths adequate to organize definitions and proofs. Finding concise principles of this kind has been a huge achievement by mathematicians and logicians. We put ZFC and categorical foundations both into this context.
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  3. Colin Mclarty (2010). What Does It Take to Prove Fermat's Last Theorem? Grothendieck and the Logic of Number Theory. Bulletin of Symbolic Logic 16 (3):359-377.
    This paper explores the set theoretic assumptions used in the current published proof of Fermat's Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.
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  4. Colin Mclarty (2008). In Arithmetic. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oup Oxford. 370.
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  5. Colin McLarty (2008). Philosophical Relevance of Category Theory. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oup Oxford.
     
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  6. Colin McLarty (2008). Review of S. Duffy, Virtual Mathematics: The Logic of Difference. [REVIEW] Australasian Journal of Philosophy 86 (2):332-336.
    This book is important for philosophy of mathematics and for the study of French philosophy. French philosophers are more concerned than most Anglo-American with mathematical practice outside of foundations. This contradicts the fashionable claim that French intellectuals get science all wrong and we return below to a germane example from Sokal and Bricmont [1999]. The emphasis on practice goes back to mid-20th century French historians of science including those Kuhn cites as sources for his orientation in philosophy of science [Kuhn (...)
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  7. Colin McLarty (2007). Saunders Mac Lane. Saunders Mac Lane: A Mathematical Autobiography. Philosophia Mathematica 15 (3):400-404.
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  8. Colin McLarty (2007). The Last Mathematician From Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics. British Journal for the Philosophy of Science 58 (1):77-112.
    While Saunders Mac Lane studied for his D.Phil in Göttingen, he heard David Hilbert's weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether's algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most efficient path to valuable specific results—while he sees that the question of which results are (...)
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  9. Colin McLarty (2006). Emmy Noether's “Set Theoretic” Topology: From Dedekind to the First Functors. In José Ferreirós Domínguez & Jeremy Gray (eds.), The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford University Press. 187--208.
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  10. Colin McLarty (2006). Two Constructivist Aspects of Category Theory. Philosophia Scientiae:95-114.
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  11. Colin McLarty (2005). Learning From Questions on Categorical Foundations. Philosophia Mathematica 13 (1):44-60.
    We can learn from questions as well as from their answers. This paper urges some things to learn from questions about categorical foundations for mathematics raised by Geoffrey Hellman and from ones he invokes from Solomon Feferman.
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  12. Colin McLarty (2005). `Mathematical Platonism' Versus Gathering the Dead: What Socrates Teaches Glaucon. Philosophia Mathematica 13 (2):115-134.
    Glaucon in Plato's Republic fails to grasp intermediates. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. He says mathematical objects are eternal. Socrates urges a seriously debatable, and seriously defensible, alternative centered on the destruction of hypotheses. He offers his version of geometry and astronomy as refuting the charge that he impiously ‘ponders things up in the sky and investigates things under the earth and makes the weaker argument the stronger’. We relate his account (...)
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  13. Colin McLarty (2005). Poor Taste as a Bright Character Trait: Emmy Noether and the Independent Social Democratic Party. Science in Context 18 (3):429.
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  14. Colin McLarty (2005). Saunders Mac Lane (1909–2005): His Mathematical Life and Philosophical Works. Philosophia Mathematica 13 (3):237-251.
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  15. Warren Goldfarb, Erich Reck, Jeremy Avigad, Andrew Arana, Geoffrey Hellman, Colin McLarty, Dana Scott & Michael Kremer (2004). Palmer House Hilton Hotel, Chicago, Illinois April 23–24, 2004. Bulletin of Symbolic Logic 10 (3).
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  16. Colin McLarty (2004). Review of Charles S. Chihara, A Structural Account of Mathematics. [REVIEW] Notre Dame Philosophical Reviews 2004 (8).
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  17. Colin McLarty (2003). Muller FA. Sets, Classes, and Categories. British Journal for the Philosophy of Science, Vol. 52 (2001), Pp. 539–573. Bulletin of Symbolic Logic 9 (1):43-44.
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  18. Michael Detlefsen, Erich Reck, Colin McLarty, Rohit Parikh, Larry Moss, Scott Weinstein, Gabriel Uzquiano, Grigori Mints & Richard Zach (2001). 2000-2001 Spring Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 7 (3).
     
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  19. Michael Detlefsen, Erich Reck, Colin McLarty, Rohit Parikh, Larry Moss, Scott Weinstein, Gabriel Uzquiano, Grigori Mints & Richard Zach (2001). The Minneapolis Hyatt Regency, Minneapolis, Minnesota May 3–4, 2001. Bulletin of Symbolic Logic 7 (3).
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  20. Colin McLarty (2000). Voir-Dire in the Case of Mathematical Progress. In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge. Kluwer Academic Publishers. 269--280.
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  21. Colin McLarty (1999). Book Review:Real Numbers, Generalizations of the Reals, & Theories of Continua Philip Ehrlich. [REVIEW] Philosophy of Science 66 (3):500-.
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  22. Chin-Tai Kim & Colin McLarty (1997). Raymond J. Nelson 1917-1997. Proceedings and Addresses of the American Philosophical Association 71 (2):125 - 126.
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  23. Colin McLarty (1997). Book Review: Shaughan Lavine. Understanding the Infinite. [REVIEW] Notre Dame Journal of Formal Logic 38 (2):314-324.
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  24. Colin Mclarty (1997). Poincaré: Mathematics & Logic & Intuition. Philosophia Mathematica 5 (2):97-115.
    often insisted existence in mathematics means logical consistency, and formal logic is the sole guarantor of rigor. The paper joins this to his view of intuition and his own mathematics. It looks at predicativity and the infinite, Poincaré's early endorsement of the axiom of choice, and Cantor's set theory versus Zermelo's axioms. Poincaré discussed constructivism sympathetically only once, a few months before his death, and conspicuously avoided committing himself. We end with Poincaré on Couturat, Russell, and Hilbert.
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  25. Colin Mclarty (1994). Category Theory in Real Time. Philosophia Mathematica 2 (1):36-44.
    The article surveys some past and present debates within mathematics over the meaning of category theory. It argues that such conceptual analyses, applied to a field still under active development, must be in large part either predictions of, or calls for, certain programs of further work.
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  26. Colin McLarty (1993). Anti-Foundation and Self-Reference. Journal of Philosophical Logic 22 (1):19 - 28.
    This note argues against Barwise and Etchemendy's claim that their semantics for self-reference requires use of Aczel's anti-foundational set theory, AFA, semantics for self-reference requires use of Aczel's anti-foundational set theory, AFA, ones irrelevant to the task at hand" (The Liar, p. 35). Switching from ZF to AFA neither adds nor precludes any isomorphism types of sets. So it makes no difference to ordinary mathematics. I argue against the author's claim that a certain kind of 'naturalness' nevertheless makes AFA preferable (...)
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  27. Colin McLarty (1993). Numbers Can Be Just What They Have To. Noûs 27 (4):487-498.
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  28. Colin McLarty (1992). Failure of Cartesian Closedness in NF. Journal of Symbolic Logic 57 (2):555-556.
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  29. Colin McLarty (1991). Axiomatizing a Category of Categories. Journal of Symbolic Logic 56 (4):1243-1260.
    Elementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed topos with separation axiom and natural numbers are. The theory is not finitely axiomatizable. Each axiom is independent of the others. Further independence and definability results are proved. Relations (...)
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  30. Colin McLarty (1990). Review of [Bell, 1988]. [REVIEW] Notre Dame Journal of Formal Logic 31:151-161.
     
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  31. Colin McLarty (1990). The Uses and Abuses of the History of Topos Theory. British Journal for the Philosophy of Science 41 (3):351-375.
    The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led both to study Grothendieck's foundations for algebraic geometry. I end with remarks on a categorical view of (...)
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  32. Colin McLarty (1989). Book Review: John Bell. Introduction to Toposes and Local Set Theory. [REVIEW] Notre Dame Journal of Formal Logic 31 (1):150-161.
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  33. Colin McLarty (1988). Defining Sets as Sets of Points of Spaces. Journal of Philosophical Logic 17 (1):75 - 90.
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  34. Colin McLarty (1987). Elementary Axioms for Canonical Points of Toposes. Journal of Symbolic Logic 52 (1):202-204.
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