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37The middle chapters of Soames’s The World Philosophy Made are briefly summarized and examined. There are some local slips, but globally the work displays an impressive knowledge of and a distinctive viewpoint on a wide range of important intellectual disciplines and their original roots in and continuing connections with philosophy.
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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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61Measurable Selections: A Bridge Between Large Cardinals and Scientific Applications?†Philosophia Mathematica 29 (3): 353-365. 2021.There is no prospect of discovering measurable cardinals by radio astronomy, but this does not mean that higher set theory is entirely irrelevant to applied mathematics broadly construed. By way of example, the bearing of some celebrated descriptive-set-theoretic consequences of large cardinals on measurable-selection theory, a body of results originating with a key lemma in von Neumann’s work on the mathematical foundations of quantum theory, and further developed in connection with problems of…Read more
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Cats, Dogs, and So OnIn Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4, Oxford University Press. 2008.
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51Luca Incurvati* Conceptions of Set and the Foundations of MathematicsPhilosophia Mathematica 28 (3): 395-403. 2020.
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65Platonism and Anti-Platonism in MathematicsPhilosophical Review 110 (1): 79. 2001.Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.
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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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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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61Truth and the Absence of FactPhilosophical Review 111 (4): 602-604. 2002.This volume reprints a dozen of the author’s papers, most with substantial postscripts, and adds one new one. The bulk of the material is on topics in philosophy of language, but there are also two papers on philosophy of mathematics written after the appearance of the author’s collected papers on that subject, and one on epistemology. As to the substance of Field’s contributions, limitations of space preclude doing much more below than indicating the range of issues addressed, and the general o…Read more
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32Platonism and anti-platonism in mathematicsPhilosophical Review 110 (1): 79-82. 2001.Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.
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34Charles Parsons, Mathematics in Philosophy: Selected Essays. Ithaca, NY: Cornell University Press (2005), 368 pp., $35.00 (paper) (review)Philosophy of Science 74 (4): 549-552. 2007.
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24C. L. Hamblin. The modal “probably.”Mind, n.s. vol. 68 , pp. 234–240Journal of Symbolic Logic 35 (4): 582-583. 1970.
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16Robert Vaught. Descriptive set theory in Lω,1ω, Cambridge summer school in mathematical logic, held in Cambridge/England, August 1–21, 1971, edited by A.R.D. Mathias and H. Rogers, Lecture notes in mathematics, vol. 337, Springer-Verlag, Berlin, Heidelberg, and New York, 1973, pp. 574–598. - Robert Vaught. Invariant sets in topology and logic. Fundamenta mathematicae, vol. 82 no. 3 , pp. 269–294 (review)Journal of Symbolic Logic 47 (1): 217-218. 1982.
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50George Boolos. To be is to be a value of a variable . The journal of philosophy, vol. 81 , pp. 430–449. - George Boolos. Nominalist Platonism, The philosophical review, vol. 94 , pp. 327–344 (review)Journal of Symbolic Logic 54 (2): 616-617. 1989.
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26Hailperin Theodore. Sentential probability logic. Origins, development, current status, and technical applications. Lehigh University Press, Bethlehem, Pennsylvania, and Associated University Presses, London, 1996, 304 pp (review)Journal of Symbolic Logic 62 (3): 1040-1041. 1997.
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12Jody Azzouni. Deflating existential consequence: a case for nominalism. Oxford University Press, Oxford, 2004, viii + 342 pp (review)Bulletin of Symbolic Logic 10 (4): 573-577. 2004.
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42Jonathan Bennett. A philosophical guide to conditionals. Clarendon Press, Oxford, 2003, viii + 388 pp (review)Bulletin of Symbolic Logic 10 (4): 565-570. 2004.
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100New Foundations for Physical Geometry: The Theory of Linear Structures, by Tim Maudlin: Oxford: Oxford University Press, 2014, pp. x + 363, £50.00 (review)Australasian Journal of Philosophy 93 (1): 187-190. 2015.
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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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21Which Modal Models are the Right Ones (for Logical Necessity)?Theoria 18 (2): 145-158. 2010....
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16Axioms of Infinity as the Starting Point for Rigorous MathematicsAnnals of the Japan Association for Philosophy of Science 20 17-28. 2012.
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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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2A Subject with No Object: Strategies for Nominalistic Interpretation of MathematicsStudia Logica 67 (1): 146-149. 2001.
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