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186What 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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136Newton'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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94_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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72Siobhan 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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39Russell Marcus and Mark McEvoy, eds. An Historical Introduction to the Philosophy of Mathematics: A ReaderPhilosophia Mathematica. forthcoming.
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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 |