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160What 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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18Review: C. L. Hamblin, The Modal "Probably." (review)Journal of Symbolic Logic 35 (4): 582-583. 1970.
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64Charles 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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213Philosophical 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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33Axioms for tense logic. I. "Since" and "until"Notre Dame Journal of Formal Logic 23 (4): 367-374. 1982.
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121Mary 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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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 Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection Philosophical Troubles.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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48How 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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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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77Decidability 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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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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98Dummett's case for intuitionismHistory and Philosophy of Logic 5 (2): 177-194. 1984.Dummett's case against platonism rests on arguments concerning the acquisition and manifestation of knowledge of meaning. Dummett's arguments are here criticized from a viewpoint less Davidsonian than Chomskian. Dummett's case against formalism is obscure because in its prescriptive considerations are not clearly separated from descriptive. Dummett's implicit value judgments are here made explicit and questioned. ?Combat Revisionism!? Chairman Mao
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23On the Hanf number of souslin logicJournal of Symbolic Logic 43 (3): 568-571. 1978.We show it is consistent with ZFC that the Hanf number of Ellentuck's Souslin logic should be exactly $\beth_{\omega_2}$
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128The Development of Modern LogicHistory and Philosophy of Logic 32 (2). 2011.History and Philosophy of Logic, Volume 32, Issue 2, Page 187-191, May 2011
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38Rigor and StructureOxford University Press UK. 2015.While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the …Read more
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73Fixing FregePrinceton University Press. 2005.This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in ...
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9Chapter Six. Intuitionistic LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 121-142. 1969.
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43Philosophy of Mathematics in the Twentieth Century: Selected EssaysHistory and Philosophy of Logic 36 (1): 93-95. 2015.The second volume of Charles Parsons’ selected papers, dedicated to Solomon Feferman, Wilfred Sieg, and William Tait, collects eleven mainly historical essays and reviews on philosophy and philosop...
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407A subject with no object: strategies for nominalistic interpretation of mathematicsOxford University Press. 1997.Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obsc…Read more
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32Axioms for tense logic. II. Time periodsNotre Dame Journal of Formal Logic 23 (4): 375-383. 1982.
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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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