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7Which modal models are the right ones (for logical necessity)?Theoria 18 (2): 145-158. 2003.Recently it has become almost the received wisdom in certain quarters that Kripke models are appropriate only for something like metaphysical modalities, and not for logical modalities. Here the line of thought leading to Kripke models, and reasons why they are no less appropriate for logical than for other modalities, are explained. It is also indicated where the fallacy in the argument leading to the contrary conclusion lies. The lessons learned are then applied to the question of the status o…Read more
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33. Cats, Dogs, and so onIn Dean W. Zimmerman (ed.), Oxford Studies in Metaphysics, Oxford University Press. pp. 4--56. 2008.
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16The truth is never simpleJournal of Symbolic Logic 51 (3): 663-681. 1986.The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.
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3Careful choices---a last word on Borel selectorsNotre Dame Journal of Formal Logic 22 (3): 219-226. 1981.
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6No requirement of relevanceIn Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press. pp. 727--750. 2005.There are schools of logicians who claim that an argument is not valid unless the conclusion is relevant to the premises. In particular, relevance logicians reject the classical theses that anything follows from a contradiction and that a logical truth follows from everything. This chapter critically evaluates several different motivations for relevance logic, and several systems of relevance logic, finding them all wanting.
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4Synthetic mechanics revisitedJournal of Philosophical Logic 20 (2). 1991.Earlier results on eliminating numerical objects from physical theories are extended to results on eliminating geometrical objects
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9KripkePolity. 2012.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. B…Read more
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3Review of B. Hale and A. Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology (review)Notre Dame Philosophical Reviews 2010 (10). 2010.
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22E pluribus unum: Plural logic and set theoryPhilosophia Mathematica 12 (3): 193-221. 2004.A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory
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3Charles Parsons. Mathematical thought and its objectsPhilosophia Mathematica 16 (3): 402-409. 2008.This long-awaited volume is a must-read for anyone with a serious interest in philosophy of mathematics. The book falls into two parts, with the primary focus of the first on ontology and structuralism, and the second on intuition and epistemology, though with many links between them. The style throughout involves unhurried examination from several points of view of each issue addressed, before reaching a guarded conclusion. A wealth of material is set before the reader along the way, but a revi…Read more
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15Quick completeness proofs for some logics of conditionalsNotre Dame Journal of Formal Logic 22 (1): 76-84. 1981.
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13Probability logicJournal of Symbolic Logic 34 (2): 264-274. 1969.In this paper we introduce a system S5U, formed by adding to the modal system S5 a new connective U, Up being read “probably”. A few theorems are derived in S5U, and the system is provided with a decision procedure. Several decidable extensions of S5U are discussed, and probability logic is related to plurality quantification.
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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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1Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in GeometryPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988. 1988.The consequences for the theory of sets of points of the assumption of sets of sets of points, sets of sets of sets of points, and so on, are surveyed, as more generally are the differences among the geometric theories of points, of finite point-sets, of point-sets, of point-set-sets, and of sets of all ranks.
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8Hintikka et Sandu versus Frege in re Arbitrary FunctionsPhilosophia Mathematica 1 (1): 50-65. 1993.Hintikka and Sandu have recently claimed that Frege's notion of function was substantially narrower than that prevailing in real analysis today. In the present note, their textual evidence for this claim is examined in the light of relevant historical and biographical background and judged insufficient.
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12Review: Hao Wang, From Mathematics to Philosophy (review)Journal of Symbolic Logic 42 (4): 579-580. 1977.
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17Chapter Two. Temporal LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 13-39. 1969.
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4The decision problem for linear temporal logicNotre Dame Journal of Formal Logic 26 (2): 115-128. 1985.
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20Quine, analyticity and philosophy of mathematicsPhilosophical Quarterly 54 (214). 2004.Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific the…Read more
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26On a derivation of the necessity of identitySynthese 191 (7): 1-19. 2014.The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view
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16TruthPrinceton University Press. 2011.This is a concise, advanced introduction to current philosophical debates about truth. A blend of philosophical and technical material, the book is organized around, but not limited to, the tendency known as deflationism, according to which there is not much to say about the nature of truth. In clear language, Burgess and Burgess cover a wide range of issues, including the nature of truth, the status of truth-value gaps, the relationship between truth and meaning, relativism and pluralism about …Read more
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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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2Review 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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12What is the simplest and most natural axiomatic replacement for the set-theoretic definition of the minimal fixed point on the Kleene scheme in Kripke’s theory of truth? What is the simplest and most natural set of axioms and rules for truth whose adoption by a subject who had never heard the word "true" before would give that subject an understanding of truth for which the minimal fixed point on the Kleene scheme would be a good model? Several axiomatic systems, old and new, are examined and ev…Read more
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7Charles S. Chihara. A structural account of mathematics. Oxford: Oxford university press, 2004. Pp. XIV + 380. ISBN 0-19-926753- (review)Philosophia Mathematica 13 (1): 78-90. 2005.
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1Review: C. L. Hamblin, The Modal "Probably." (review)Journal of Symbolic Logic 35 (4): 582-583. 1970.
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