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6Formal Logic: Its Scope and Limits (edited book)Hackett Publishing Company. 2006.The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and the decidability proof is ex…Read more
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6Chapter Five. Relevantistic LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 99-120. 1969.
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6Shapiro Stewart. Foundations without foundationalism. A case for second-order logic. Oxford logic guides, no. 17. Clarendon Press, Oxford University Press, Oxford and New York 1991, xx + 277 pp (review)Journal of Symbolic Logic 58 (1): 363-365. 1993.
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6Saul KripkeIn John Shand (ed.), Central Works of Philosophy, Vol. 5: The Twentieth Century: Quine and After, Acumen Publishing. pp. 166-186. 2006.
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6Making the Best of It: Following Christ in the Real WorldJournal of the Society of Christian Ethics 31 (1): 225-227. 2011.
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5Set TheoryIn Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell. 2017.Set theory is the branch of mathematics concerned with the general properties of aggregates of points, numbers, or arbitrary elements. It was created in the late nineteenth century, mainly by Georg Cantor. After the discovery of certain contradictions euphemistically called paradoxes, it was reduced to axiomatic form in the early twentieth century, mainly by Ernst Zermelo and Abraham Fraenkel. Thereafter it became widely accepted as a framework ‐ or ‘foundation’ ‐ for the development of the othe…Read more
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5Kripke on FunctionalismCritica 48 (144): 3-18. 2016.En el texto se exponen las opiniones de Saul Kripke acerca del funcionalismo en la filosofía de la mente, que aún permanecen en gran parte sin publicarse, con base en la transcripción de una charla suya de 1984 sobre este tema, y se identifican algunas preguntas sin resolver.
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4Christ and Culture RevisitedJournal of the Society of Christian Ethics 31 (2): 55-74. 2011.WESTERN SCHOLARS HAVE POINTED OUT BOTH THE USEFULNESS AND limitations of H. Richard Niebuhr's Christ and Culture. This essay relates Niebuhr's five types to discussions of church and culture in contemporary Russian Orthodoxy. I propose a sixth type, Christ in culture, that best illuminates the Church's current program of votserkovlenie. To its Russian representatives, "Christ in culture" enabled the Christian faith to survive communist efforts to destroy the Church, and this cultural legacy cont…Read more
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2A Subject with No Object: Strategies for Nominalistic Interpretation of MathematicsPhilosophical Quarterly 50 (198): 124-126. 1997.
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2A Subject with No Object: Strategies for Nominalistic Interpretation of MathematicsStudia Logica 67 (1): 146-149. 2001.
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1Review: Robert Vaught, A. R. D. Mathias, H. Rogers, Descriptive Set Theory in $L{omega1omega}$; Robert Vaught, Invariant Sets in Topology and Logic (review)Journal of Symbolic Logic 47 (1): 217-218. 1982.
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Review: The limits of abstraction by Kit fine (review)Notre Dame Journal Fo Formal Logic 44 227-251. 2003.
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Set TheoryCambridge University Press. 2022.Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, con…Read more
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Frege and arbitrary functionsIn William Demopoulos (ed.), Frege's philosophy of mathematics, Harvard University Press. pp. 89--107. 1995.
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Logic, Mathematics, Science. Quine's Philosophy of Logic and MathematicsIn Gilbert Harman & Ernest LePore (eds.), A Companion to W. V. O. Quine, Wiley-blackwell. 2013.
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Mathematics, Models, and Modality: Selected Philosophical EssaysCambridge University Press. 2008.John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be o…Read more
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