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36Latour’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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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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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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34History 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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118Marco 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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66D avid B ostock . Philosophy of mathematics: An introductionPhilosophia Mathematica 18 (1): 127-129. 2010.(No abstract is available for this citation)
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55The rational and the socialRoutledge. 1989.THE SOCIOLOGICAL TURN The problem we are concerned with is just this: How should we understand science? Are we to account for scientific knowledge (or ...
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66Scientific Realism and the Plasticity of Mind (review)International Philosophical Quarterly 23 (2): 226-227. 1983.
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42Realism, Miracles, and the Common CausePSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982. 1982.The principle of the common cause, which gets its justification from the miracle arguments, probably constitutes the best reason for being a scientific realist. However, results in quantum mechanics steming from the work of Bell raise difficulties which anti-realists have been quick to seize. The author tries to overcome the problem and save scientific realism by reformulating the principle of the common cause so that a distinction is made between a priori and a posteriori correlations.
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31Platonic explanation: Or, what abstract entities can do for youInternational Studies in the Philosophy of Science 3 (1). 1988.(1988). Platonic explanation: Or, what abstract entities can do for you. International Studies in the Philosophy of Science: Vol. 3, No. 1, pp. 51-67. doi: 10.1080/02698598808573324
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115John D. Barrow, Pi in the Sky: Counting, Thinking, and BeingPhilosophia Mathematica 2 (3): 251-251. 1994.
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183What is a definition?Foundations of Science 3 (1): 111-132. 1998.According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further examples that suggest ma…Read more
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133Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text _The Laboratory of the Mind_, James Robert Brown continues to defend aprio…Read more
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58Review of M. Giaquinto, The Search for Certainty: A Philosophical Account of Foundations of Mathematics (review)Mind 113 (449): 177-179. 2004.
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91_Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
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1Michael Redhead, Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics Reviewed byPhilosophy in Review 8 (8): 316-320. 1988.
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24EPR As A Priori ScienceCanadian Journal of Philosophy, Supplementary Volume 18 (sup1): 253-272. 1992.Contemporary empiricism is closely allied with naturalism. Not only do empiricists hold that all our knowledge is based upon sensory experience, but they also tend to offer some sort of causal account of how this experience comes about. The causal ingredient in knowledge seems very plausible — after all, my knowing that there is a tea cup on my desk is based on sense impressions which are caused by the cup itself. Photons come from the cup to my eye; a signal is then sent down the optic nerve in…Read more
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71Siobhan Roberts. King of infinite space: Donald coxeter, the man who saved geometryPhilosophia Mathematica 15 (3): 386-388. 2007.Donald Coxeter died in 2003, at a ripe old age of 96. Though I had regularly seen him at mathematics talks in Toronto for over twenty years, I never felt rushed to seek him out. It seemed he would go on forever. His death left me regretting my missed opportunity and Siobhan Robert's excellent book makes me regret it even more. Like any good biography of an intellectual, King of Infinite Space contains personal details and mathematical achievements in some detail. Thus, we learn of the traumatic …Read more
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38Russell Marcus and Mark McEvoy, eds. An Historical Introduction to the Philosophy of Mathematics: A ReaderPhilosophia Mathematica. forthcoming.
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15Platonism, 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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52Kitcher’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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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 |