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48Book Review: Kit Fine. The Limits of Abstraction (review)Notre Dame Journal of Formal Logic 44 (4): 227-251. 2003.
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48Luca Incurvati* Conceptions of Set and the Foundations of MathematicsPhilosophia Mathematica 28 (3): 395-403. 2020.
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48On a Consistent Subsystem of Frege's GrundgesetzeNotre Dame Journal of Formal Logic 39 (2): 274-278. 1998.Parsons has given a (nonconstructive) proof that the first-order fragment of the system of Frege's Grundgesetze is consistent. Here a constructive proof of the same result is presented
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46George 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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46Review of B. Hale and A. Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology (review)Notre Dame Philosophical Reviews 2010 (10). 2010.
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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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45A Remark on Henkin Sentences and Their ContrariesNotre Dame Journal of Formal Logic 44 (3): 185-188. 2003.That the result of flipping quantifiers and negating what comes after, applied to branching-quantifier sentences, is not equivalent to the negation of the original has been known for as long as such sentences have been studied. It is here pointed out that this syntactic operation fails in the strongest possible sense to correspond to any operation on classes of models
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44Predicative Logic and Formal ArithmeticNotre Dame Journal of Formal Logic 39 (1): 1-17. 1998.After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell's Principia Mathematica with the axiom of infinity but without the axiom of reducibility
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43KripkePolity. 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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42Philosophy 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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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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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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41Kripke ModelsIn Alan Berger (ed.), Saul Kripke, Cambridge University Press. 2011.Saul Kripke has made fundamental contributions to a variety of areas of logic, and his name is attached to a corresponding variety of objects and results. 1 For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non-classical logics. What follows is an elementary introduction to Kripke’s contributions in this area, intended to prepare the reader to tackle more formal treatments elsewhere.2 2. WHAT IS …Read more
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39The completeness of intuitionistic propositional calculus for its intended interpretationNotre Dame Journal of Formal Logic 22 (1): 17-28. 1981.
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38Reconciling Anti-Nominalism and Anti-Platonism in Philosophy of MathematicsDisputatio 11 (20). 2022.The author reviews and summarizes, in as jargon-free way as he is capable of, the form of anti-platonist anti-nominalism he has previously developed in works since the 1980s, and considers what additions and amendments are called for in the light of such recently much-discussed views on the existence and nature of mathematical objects as those known as hyperintensional metaphysics, natural language ontology, and mathematical structuralism.
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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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36No 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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35The decision problem for linear temporal logicNotre Dame Journal of Formal Logic 26 (2): 115-128. 1985.
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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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33Axioms for tense logic. I. "Since" and "until"Notre Dame Journal of Formal Logic 23 (4): 367-374. 1982.
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