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111The birth of analytic philosophyIn Dermot Moran (ed.), The Routledge Companion to Twentieth Century Philosophy, Routledge. pp. 43. 2008.Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.
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127Hale on caesarPhilosophia Mathematica 5 (2): 135--52. 1997.Crispin Wright and Bob Hale have defended the strategy of defining the natural numbers contextually against the objection which led Frege himself to reject it, namely the so-called ‘Julius Caesar problem’. To do this they have formulated principles (called sortal inclusion principles) designed to ensure that numbers are distinct from any objects, such as persons, a proper grasp of which could not be afforded by the contextual definition. We discuss whether either Hale or Wright has provided inde…Read more
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1Infinite coincidences and inaccessible truthsIn Philosophy of Mathematics, Proceedings of the 15th International Wittgenstein Symposium, Hölder-pichler-tempsky. pp. 307-313. 1993.Argues, contra Dummett, that the platonist need not be any more committed than the intuitionist to the notion that there are arithmetical truths in principle inaccessible to any finite intelligence.
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Abstractionist class theory : is there any such thing?In T. J. Smiley, Jonathan Lear & Alex Oliver (eds.), The Force of Argument: Essays in Honor of Timothy Smiley, Routledge. 2010.A discussion of the philosophical prospects for basing a neo-Fregean theory of classes on a principle that attempts to articulate the limitation-of-size conception.
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114Was gödel a gödelian platonist?Philosophia Mathematica 9 (3): 331-346. 2001.del's appeal to mathematical intuition to ground our grasp of the axioms of set theory, is notorious. I extract from his writings an account of this form of intuition which distinguishes it from the metaphorical platonism of which Gödel is sometimes accused and brings out the similarities between Gödel's views and Dummett's.
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Review: Constructibility and mathematical existence by Charles S. Chihara (review)Philosophical Quarterly 41 345-348. 1991.A review.
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123Elucidating the tractatus: Wittgenstein's early philosophy of logic and language – Marie McGinn (review)Philosophical Quarterly 60 (238): 192-194. 2010.A review.
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95The logic of the TractatusIn Dov M. Gabbay & John Woods (eds.), Handbook of the History of Logic. Volume 5: From Russell to Church, North Holland. pp. 255--304. 2009.Describes some of the main features of the logic and metaphysics of Wittgenstein's Tractatus.
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117Wittgenstein's Tractatus: history and interpretation (edited book)Oxford University Press. 2013.These new studies of Wittgenstein's Tractatus represent a significant step beyond recent polemical debate.
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157Set Theory and its Philosophy: A Critical IntroductionOxford University Press. 2004.Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes th…Read more
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114Iterative set theoryPhilosophical Quarterly 44 (171): 178-193. 1994.Discusses the metaphysics of the iterative conception of set.
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71Wittgenstein's notes on logicOxford University Press. 2009.The book features the complete text of the Notesi in a critical edition, with a detailed discussion of the circumstances in which they were compiled, leading to ...
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86Reason's Nearest Kin: Philosophies of Arithmetic from Kant to CarnapOxford University Press. 2000.This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.
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IntroductionIn Michael Potter, Joan Weiner, Warren Goldfarb, Peter Sullivan, Alex Oliver & Thomas Ricketts (eds.), The Cambridge Companion to Frege, Cambridge University Press. 2012.
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1What is the problem of mathematical knowledge?In Michael Potter, Mary Leng & Alexander Paseau (eds.), Mathematical Knowledge, . 2007.Suggests that the recent emphasis on Benacerraf's access problem locates the peculiarity of mathematical knowledge in the wrong place. Instead we should focus on the sense in which mathematical concepts are or might be "armchair concepts" – concepts about which non-trivial knowledge is obtainable a priori.
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41Critical Notice: David Lewis's Parts of ClassesPhilosophical Quarterly 43 (172). 1993."Parts of Classes" tries to separate the unproblematic part of set theory (mereology) from the problematic part (singletons). In the process several things get lost: an empty set which is really empty; a satisfying account of the paradoxes; and the motivation for the iterative conception of set. Lewis' attack on the coherence of singletons makes it puzzling what he sees his book as doing. Nor is it clear that mereology is as ontologically innocent as Lewis would have us believe.
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104Classical arithmetic as part of intuitionistic arithmeticGrazer Philosophische Studien 55 (1): 127-41. 1998.Argues that classical arithmetic can be viewed as a proper part of intuitionistic arithmetic. Suggests that this largely neutralizes Dummett's argument for intuitionism in the case of arithmetic.
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Wittgenstein on mathematicsIn Marie McGinn & Oskari Kuusela (eds.), The Oxford Handbook of Wittgenstein, Oxford University Press. 2011.
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92Review of Michael Morris, Routledge Philosophy Guidebook to Wittgenstein and the Tractatus (review)Notre Dame Philosophical Reviews 2009 (8). 2009.
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67Intuition and reflection in arithmetic: Michael PotterAristotelian Society Supplementary Volume 73 (1). 1999.Classifies accounts of arithmetic into four sorts according to the resources they appeal to in constructing its subject matter.
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184What Is Wrong with Abstraction?Philosophia Mathematica 13 (2): 187-193. 2005.We correct a misunderstanding by Hale and Wright of an objection we raised earlier to their abstractionist programme for rehabilitating logicism in the foundations of mathematics
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Logic and Philosophy of Logic |
Philosophy of Mathematics |
20th Century Philosophy |