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61Hilbert's Program: An Essay on Mathematical Instrumentalism by Michael Detlefsen (review)Journal of Philosophy 88 (6): 331-336. 1991.
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4Teaching Elementary Arithmetic through ApplicationsIn Randall Curren (ed.), A Companion to the Philosophy of Education, Blackwell. 2003.This chapter contains sections titled: Logical Applications Empirical Applications Wittgenstein: A Social Constructivist?
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4Explaining and Explaining Away in Mathematics: The Role of “Fitness”In Carl Posy & Yemima Ben-Menahem (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner, Springer. pp. 9-22. 2023.This heretofore-unpublished lecture focusses on the phenomenon of explanation by redescription in mathematics. In such cases, the explanandum is fitted into a new mathematical framework from which it can be easily derived or even seen to be self-evident.
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15Wittgenstein on the Foundations of Mathematics (review)Journal of Symbolic Logic 49 (4): 1415-1417. 1980.
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197The application of mathematics to natural scienceJournal of Philosophy 86 (9): 449-480. 1989.The first part of the essay describes how mathematics, in particular mathematical concepts, are applicable to nature. mathematical constructs have turned out to correspond to physical reality. this correlation between the world and mathematical concepts, it is argued, is a true phenomenon. the second part of this essay argues that the applicability of mathematics to nature is mysterious, in that not only is there no known explanation for the correlation between mathematics and physical reality, …Read more
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37Shanker S. G.. Wittgenstein and the turning-point in the philosophy of mathematics. Croom Helm, Beckenham, Kent, and State University of New York Press, Albany 1987, xi + 358 pp (review)Journal of Symbolic Logic 54 (3): 1098-1100. 1989.
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22Stephan Korner. The philosophy of mathematics. An introductory essay. Hutchinson and Co., Ltd., London 1960, 198 pp. Paperbound reprint, Harper torchbooks, Harper Brothers, New York 1962, 198 pp (review)Journal of Symbolic Logic 40 (4): 588-593. 1975.
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13Wittgenstein and the Turning-Point in the Philosophy of Mathematics (review)Journal of Symbolic Logic 54 (3): 1098-1100. 1989.
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50Mathematics as a science of patterns (review)Philosophical Review 109 (1): 115-118. 2000.For the past hundred years, mathematics, for its own reasons, has been shifting away from the study of “mathematical objects” and towards the study of “structures”. One would have expected philosophers to jump onto the bandwagon, as in many other cases, to proclaim that this shift is no accident, since mathematics is “essentially” about structures, not objects. In fact, structuralism has not been a very popular philosophy of mathematics, probably because of the hostility of Frege and other influ…Read more
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Hume and Maimonides on imaginability and possibilityIn Samuel Lebens, Dani Rabinowitz & Aaron Segal (eds.), Jewish Philosophy in an Analytic Age, Oxford University Press, Usa. 2019.
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26Proof, logic and formalization, edited by Detlefsen Michael, Routledge, London and New York 1992, x + 241 pp (review)Journal of Symbolic Logic 58 (4): 1459-1462. 1993.
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Review: Michael Detlefsen, Proof, Logic and Formalization (review)Journal of Symbolic Logic 59 (4): 1459-1462. 1994.
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20Lakatos' Philosophy of Mathematics: A Historical Approach. Teun Koetsier (review)Isis 84 (3): 619-620. 1993.
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15Lakatos' Philosophy of Mathematics: A Historical Approach by Teun Koetsier (review)Isis 84 619-620. 1993.
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Getting More out of Mathematics than What We Put InIn John Polkinghorne (ed.), Meaning in mathematics, Oxford University Press. 2011.
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36Review of Mark Steiner: The Applicability of Mathematics as a Philosophical Problem (review)British Journal for the Philosophy of Science 52 (1): 181-184. 2001.
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The ontological argumentIn Paul K. Moser & Paul Copan (eds.), The Rationality of Theism, Routledge. pp. 280. 2003.
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20Penrose and platonismIn Emily Grosholz & Herbert Breger (eds.), The growth of mathematical knowledge, Kluwer Academic Publishers. pp. 133--141. 2000.