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134Charles 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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74Probability 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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103Quick completeness proofs for some logics of conditionalsNotre Dame Journal of Formal Logic 22 (1): 76-84. 1981.
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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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74Hintikka 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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42Sets 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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11Review: 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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224Quine, 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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35The decision problem for linear temporal logicNotre Dame Journal of Formal Logic 26 (2): 115-128. 1985.
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306On 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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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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112TruthPrinceton 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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156What 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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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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18Review: C. L. Hamblin, The Modal "Probably." (review)Journal of Symbolic Logic 35 (4): 582-583. 1970.
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61Charles 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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207Philosophical LogicPrinceton University Press. 2009.Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic, focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choi…Read more
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120Mary Leng. Mathematics and Reality. Oxford: Oxford University Press, 2010. ISBN 978-0-19-928079-7. Pp. x + 278: Critical Studies/Book Reviews (review)Philosophia Mathematica 18 (3): 337-344. 2010.(No abstract is available for this citation)
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33Axioms for tense logic. I. "Since" and "until"Notre Dame Journal of Formal Logic 23 (4): 367-374. 1982.
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46How Foundational Work in Mathematics Can Be Relevant to Philosophy of SciencePSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992. 1992.Foundational work in mathematics by some of the other participants in the symposium helps towards answering the question whether a heterodox mathematics could in principle be used as successfully as is orthodox mathematics in scientific applications. This question is turn, it will be argued, is relevant to the question how far current science is the way it is because the world is the way it is, and how far because we are the way we are, which is a central question, if not the central question, o…Read more
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18Saul 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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75Decidability for branching timeStudia Logica 39 (2-3): 203-218. 1980.The species of indeterminist tense logic called Peircean by A. N. Prior is proved to be recursively decidable
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10Rescher 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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120Quinus ab Omni Nævo VindicatusCanadian Journal of Philosophy 27 (sup1): 25-65. 1997.Today there appears to be a widespread impression that W. V. Quine's notorious critique of modal logic, based on certain ideas about reference, has been successfully answered. As one writer put it some years ago: “His objections have been dead for a while, even though they have not yet been completely buried.” What is supposed to have killed off the critique? Some would cite the development of a new ‘possible-worlds’ model theory for modal logics in the 1960s; others, the development of new ‘dir…Read more
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