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19Platonism and anti-platonism in mathematics (review)Bulletin of Symbolic Logic 8 (4): 516-517. 2002.
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14Creation and Discovery in MathematicsIn John Polkinghorne (ed.), Meaning in mathematics, Oxford University Press. 2011.
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139Structuralism, Fictionalism, and Applied MathematicsIn Clark Glymour, Wei Wang & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science: Proceedings of the Thirteenth International Congress, College Publications. pp. 377-389. 2009.
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52Mathematics and RealityOxford University Press. 2010.This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best emp…Read more
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194What's wrong with indispensability?Synthese 131 (3). 2002.For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is…Read more
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72Phenomenology and mathematical practicePhilosophia Mathematica 10 (1): 3-14. 2002.A phenomenological approach to mathematical practice is sketched out, and some problems with this sort of approach are considered. The approach outlined takes mathematical practices as its data, and seeks to provide an empirically adequate philosophy of mathematics based on observation of these practices. Some observations are presented, based on two case studies of some research into the classification of C*-algebras. It is suggested that an anti-realist account of mathematics could be develope…Read more
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5Imre Lakatos and Paul Feyerabend, For and Against Method Reviewed byPhilosophy in Review 20 (2): 115-117. 2000.
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2Book reviews (review)International Studies in the Philosophy of Science 13 (2): 195-204. 1999.Naturalism in Mathematics PENELOPE MADDY, 1997 Oxford, Oxford University Press viii + 254 pp., $CAN91, ISBN 0–19–823573–9 Bohmian Mechanics and Quantum Theory: an Appraisal JAMES T. CUSHING, ARTHUR FINE & SHELDON GOLDSTEIN, 1996 Dordrecht, Kluwer viii + 403, pp., US$159.00, ISBN 0–7923–4028–0 Pragmatism as a Principle and Method of Right Thinking: the 1903 Harvard Lectures on Pragmatism CHARLES SANDERS PEIRCE, 1997 Edited and introduced, with a commentary, by PATRICIA ANN TURRISI Albany, State U…Read more
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Imre Lakatos and Paul Feyerabend, For and Against Method (review)Philosophy in Review 20 115-117. 2000.
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150Taking it Easy: A Response to ColyvanMind 121 (484): 983-995. 2012.This discussion note responds to Mark Colyvan’s claim that there is no easy road to nominalism. While Colyvan is right to note that the existence of mathematical explanations presents a more serious challenge to nominalists than is often thought, it is argued that nominalist accounts do have the resources to account for the existence of mathematical explanations whose explanatory role resides elsewhere than in their nominalistic content.