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20Review: Theodore Hailperin, Sentential Probability Logic. Origins, Development, Current Status, and Technical Applications (review)Journal of Symbolic Logic 62 (3): 1040-1041. 1997.
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20Adapated from talks at the UCLA Logic Center and the Pitt Philosophy of Science Series. Exposition of material from Fixing Frege, Chapter 2 (on predicative versions of Frege’s system) and from “Protocol Sentences for Lite Logicism” (on a form of mathematical instrumentalism), suggesting a connection. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.
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20Saul Kripke: puzzles and mysteriesPolity. 2013.Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, Naming and Necessity, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection Philosophical Troubles. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burge…Read more
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19Chapter Four. Conditional LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 71-98. 1969.
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18Review: C. L. Hamblin, The Modal "Probably." (review)Journal of Symbolic Logic 35 (4): 582-583. 1970.
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17Careful choices---a last word on Borel selectorsNotre Dame Journal of Formal Logic 22 (3): 219-226. 1981.
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17European and American PhilosophersIn Robert L. Arrington (ed.), A Companion to the Philosophers, Blackwell. 2017.Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categ…Read more
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17Chapter Two. Temporal LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 13-39. 1969.
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16Review of Paul A. Gregory, Quine's Naturalism: Language, Theory, and the Knowing Subject (review)Notre Dame Philosophical Reviews 2009 (5). 2009.
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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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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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14Wang Hao. From mathematics to philosophy. International library of philosophy and scientific method. Humanities Press, New York 1974, xiv + 428 pp (review)Journal of Symbolic Logic 42 (4): 579-580. 1977.
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13Review: Hao Wang, From Mathematics to Philosophy (review)Journal of Symbolic Logic 42 (4): 579-580. 1977.
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13Rescher Nicholas. A probabilistic approach to modal logic. Proceedings of a Colloquium on Modal and Many-valued Logics, Helsinki, 23–26 August, 1962, Acta philosophica Fennica, no. 16, Helsinki 1963, pp. 215–226 (review)Journal of Symbolic Logic 35 (4): 583-583. 1970.
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12Chapter Three. Modal LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 40-70. 1969.
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12It is shown that for invariance under the action of special groups the statements "Every invariant PCA is decomposable into (1 invariant Borel sets" and "Every pair of invariant PCA is reducible by a pair of invariant PCA sets" are independent of the axioms of set theory.
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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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11Review: Nicholas Rescher, A Probabilistic Approach to Modal Logic (review)Journal of Symbolic Logic 35 (4): 583-583. 1970.
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10Quine's Philosophy of Logic and MathematicsIn Ernie Lepore & Gilbert Harman (eds.), A Companion to W. V. O. Quine, Wiley-blackwell. 2013.Thomas Kelly, “Quine and Epistemology”: For Quine, as for many canonical philosophers since Descartes, epistemology stands at the very center of philosophy. In this chapter, I discuss some central themes in Quine's epistemology. I attempt to provide some historical context for Quine's views, in order to make clear why they were seen as such radical challenges to then prevailing orthodoxies within analytic philosophy. I also highlight aspects of his views that I take to be particularly relevant t…Read more
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9Fixing FregePrinceton University Press. 2005.The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previous…Read more
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9Chapter Six. Intuitionistic LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 121-142. 1969.
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8Retrieving the Martyrs in Order to Rethink the Political Order: The Russian Orthodox CaseJournal of the Society of Christian Ethics 34 (2): 177-201. 2014.This essay argues that in retrieving the new martyrs and confessors, the approximately two thousand people who suffered directly for their faith under Soviet communist oppression, the Russian Orthodox Church has made publicly available symbols and narratives that bear democratizing potential. The Church's "Icon of the New Martyrs and Confessors" can be interpreted as calling for broad representation of all parts of society in Church and political life, and freedom of the Church to represent its …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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