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250Mathematical Knowledge (edited book)Oxford University Press. 2007.What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions.
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210Taming the Infinite (review)British Journal for the Philosophy of Science 47 (4): 609-619. 1996.A critique of Shaughan Lavine's attempt in /Understanding the Infinite/ to reduce talk about the infinite to finitely comprehensible terms.
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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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156Set 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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126Hale 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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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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116Wittgenstein'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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113Was 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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112Iterative set theoryPhilosophical Quarterly 44 (171): 178-193. 1994.Discusses the metaphysics of the iterative conception of set.
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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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103Classical 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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97Abstraction by recarvingProceedings of the Aristotelian Society 101 (3). 2001.Explains why Bob Hale's proposed notion of weak sense cannot explain the analyticity of Hume's principle as he claims. Argues that no other notion of the sort Hale wants could do the job either.
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94The 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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91Review of Michael Morris, Routledge Philosophy Guidebook to Wittgenstein and the Tractatus (review)Notre Dame Philosophical Reviews 2009 (8). 2009.
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89The Cambridge Companion to Frege (edited book)Cambridge University Press. 2012.Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic …Read more
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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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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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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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63Paolo Mancosu. The adventure of reason: Interplay between philosophy of mathematics and mathematical logic, 1900-1940. Oxford: Oxford university press, 2010. Isbn 978-0-19-954653-4. Pp. XII + 618 (review)Philosophia Mathematica 20 (2): 256-258. 2012.
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55Recarving content: Hale's final proposalProceedings of the Aristotelian Society 102 (3). 2002.A follow-up, showing why Bob Hale's revision of his notion of weak sense is still inadequate.
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54The Rise of Analytic Philosophy, 1879-1930: From Frege to RamseyRoutledge. 2019.In this book Michael Potter offers a fresh and compelling portrait of the birth of modern analytic philosophy, viewed through the lens of a detailed study of the work of the four philosophers who contributed most to shaping it: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey. It covers the remarkable period of discovery that began with the publication of Frege's Begriffsschrift in 1879 and ended with Ramsey's death in 1930. Potter--one of the most influential scholars of t…Read more
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46Intuitive and Regressive Justifications†Philosophia Mathematica 28 (3): 385-394. 2020.In his recent book, Quine, New Foundations, and the Philosophy of Set Theory, Sean Morris attempts to rehabilitate Quine’s NF as a possible foundation for mathematics. I explain why he does not succeed.
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40Frege: The Pure Business of Being True, by Charles TravisMind. forthcoming.Travis is evidently a self-conscious prose stylist, by which I mean that he pays attention to the style of his prose, not that this style is worth emulating. On.
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40Critical 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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33Foundations Without Foundationalism: A Case for Second-Order LogicPhilosophical Quarterly 44 (174): 127-129. 1994.
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30The Philosophy of Set Theory: An Historical Introduction to Cantor's ParadisePhilosophical Books 31 (1): 63-63. 1990.
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29Wittgenstein's pre—Tractatus manuscripts: a new appraisalIn Peter M. Sullivan & Michael D. Potter (eds.), Wittgenstein's Tractatus: history and interpretation, Oxford University Press. pp. 13-39. 2013.
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Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |
20th Century Philosophy |