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13Platonism, Naturalism, and Mathematical KnowledgeRoutledge. 2011.This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Plato…Read more
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51Kitcher’s Mathematical NaturalismCroatian Journal of Philosophy 3 (1): 1-20. 2003.Recent years have seen a number of naturalist accounts of mathematics. Philip Kitcher’s version is one of the most important and influential. This paper includes a critical exposition of Kitcher’s views and a discussion of several issues including: mathematical epistemology, practice, history, the nature of applied mathematics. It argues that naturalism is an inadequate account and compares it with mathematical Platonism, to the advantage of the latter.
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23Who Rules in Science?: An Opinionated Guide to the WarsHarvard University Press. 2001.This eye-opening book reveals how little we've understood about the ongoing pitched battles between the sciences and the humanities--and how much may be at ...
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39Critical Notice of Roy Sorensen Thought ExperimentsCanadian Journal of Philosophy 25 (1): 135-142. 1995.This book adds to the growing literature on thought experiments. There are numerous examples drawn from the sciences and philosophy. The principle claim is that thought experiments are a limiting case of real experiments. It is a moderate empiricist view, in contrast to, e.g., the Platonism of Brown or the strict empiricism of Norton. Highly recommended
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50The philosophy of mathematical practiceInternational Journal of Philosophical Studies 18 (1). 2010.This Article does not have an abstract
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3Realism, Antirealism, and NOAIn Robert Klee (ed.), Scientific Inquiry: Readings in the Philosophy of Science, Oxford University Press. pp. 338. 1999.
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Mary Tiles, "the philosophy of set theory: An introduction to Cantor's paradise" (review)Dialogue 29 (2): 314. 1990.
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6Book reviews (review)International Studies in the Philosophy of Science 12 (1): 91-102. 1998.Time's Arrow and Archimedes’ Point: New Directions for the Physics of Time Huw PRICE, 1996 New York, Oxford University Press xiii + 306 pp. SCAN 37.00 ISBN 0–19–510095–6 Mental Reality GALEN STRAWSON, 1994 Cambridge, MA, The MIT Press xiv + 337 pp., S37.50, $17.50 ISBN 0–262–19352–3 The Rule of Reason: The Philosophy of Charles Sanders Peirce JACQUELINE BRUNNING & PAUL FORSTER, Eds, 1997 Toronto, University of Toronto Press 316 pp., $80.00, $24.95 ISBN 0–8020–0829–1, ISBN 0–8020–7819–2 Scientifi…Read more
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39Einstein's brand of verificationismInternational Studies in the Philosophy of Science 2 (1). 1987.(1987). Einstein's brand of verificationism. International Studies in the Philosophy of Science: Vol. 2, No. 1, pp. 33-54. doi: 10.1080/02698598708573301
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66Vladimir tasic. Mathematics and the roots of postmodern thoughtPhilosophia Mathematica 11 (2): 244-245. 2003.
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2The Shaky Game: Einstein, Realism, and the Quantum TheoryArthur Fine Chicaco, IL: University of Chicago Press, 1986. Pp. xi, 186. $25.00 (review)Dialogue 26 (4): 776-779. 1987.
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21Review of A. George and D. J. Velleman, Philosophies of Mathematics (review)Mind 111 (444): 860-862. 2002.
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98In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?" "This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathemat…Read more
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Models of Rationality and the History of ScienceDissertation, The University of Western Ontario (Canada). 1981.Thinkers as diverse as Kuhn and Salmon agree that should an account of scientific rationality not square with actual scientific practice, then this should be considered as a reductio ad absurdum of the proposed norms and not be taken as evidence that the history of science is in large measure irrational. While many are willing to accept the need to do justice to the history of science as a constraint on the acceptability of any candidate theory of scientific method, very few are willing to use t…Read more
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1Thought Experiments in Science, Philosophy, and the Arts (edited book)Routledge. 2012.From Lucretius throwing a spear beyond the boundary of the universe to Einstein racing against a beam of light, thought experiments stand as a fascinating challenge to the necessity of data in the empirical sciences. Are these experiments, conducted uniquely in our imagination, simply rhetorical devices or communication tools or are they an essential part of scientific practice? This volume surveys the current state of the debate and explores new avenues of research into the epistemology of thou…Read more
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22Latour’s Prosaic ScienceCanadian Journal of Philosophy 21 (2). 1991.The most embarrassing thing about ‘facts’ is the etymology of the word. The Latin facere means to make or construct. Bruno Latour, like so many other anti-realists who revel in the word’s history, thinks facts are made by us: they are a social construction. The view acquires some plausibility in Laboratory Life: The Social Construction of Scientific Facts which Latour co-authored with Steve Woolgar.1 This work, first published a decade ago, has become a classic in the sociology of science litera…Read more
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33Platonism and laws: A reply to Demetra Sfendoni‐MentzouInternational Studies in the Philosophy of Science 8 (3). 1994.his paper is a reply to Demetra Sfendoni‐Mentzou; it defends a realist—indeed a platonist—account of laws of nature.
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49Platonism, Metaphor, and MathematicsDialogue 43 (1): 47-. 2004.RésuméDans leur livre récent, George Lakoff et Rafael Núñez se livrent à une critique naturaliste soutenue du platonisme traditionnel concernant les entités mathématiques. Ils affirment que des résultats récents en sciences cognitives démontrent qu'il est faux. En particulier, ils estiment que la découverte que la cognition mathématique s'appuie pour une large part sur les métaphores conceptuelles est incompatible avec le platonisme. Nous montrons ici que tel n'est pas le cas. Nous examinons et …Read more
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33History and the Norms of SciencePSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980. 1980.Starting from the assumption that the history of science is, in some significant sense, rational and thus that historical episodes may serve as evidence in choosing between competing normative methodologies of science, the question arises: "Just what is this history-methodology evidential relation?" After examining the proposals of Laudan, a more plausible account is proposed.
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82What is applied mathematics?Foundations of Science 2 (1): 21-37. 1997.A number of issues connected with the nature of applied mathematics are discussed. Among the claims are these: mathematics "hooks onto" the world by providing models or representations, not by describing the world; classic platonism is to be preferred to structuralism; and several issues in the philosophy of science are intimately connected to the nature of applied mathematics
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172Thought Experiments in Science, Philosophy, and MathematicsCroatian Journal of Philosophy 7 (1): 3-27. 2007.Most disciplines make use of thought experiments, but physics and philosophy lead the pack with heavy dependence upon them. Often this is for conceptual clarification, but occasionally they provide real theoretical advances. In spite of their importance, however, thought experirnents have received rather little attention as a topic in their own right until recently. The situation has improved in the past few years, but a mere generation ago the entire published literature on thought experiments …Read more
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111Marco Panza and Andrea Sereni. Plato's Problem: An Introduction to Mathematical Platonism. London and New York: Palgrave Macmillan, 2013. ISBN 978-0-230-36548-3 (hbk); 978-0-230-36549-0 (pbk); 978-1-13726147-2 (e-book); 978-1-13729813-3 (pdf). Pp. xi + 306 (review)Philosophia Mathematica (1). 2013.
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University of Toronto, St. George CampusDepartment of Philosophy
Institute for the History and Philosophy of ScienceRetired faculty
Toronto, Ontario, Canada
Areas of Specialization
Science, Logic, and Mathematics |