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Philosophia Mathematica Advance Access originally published online on March 26, 2007
Philosophia Mathematica 2007 15(2):257-267; doi:10.1093/philmat/nkm016
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Copyright © The Author 2007. Published by Oxford University Press.

Book Review

ROLAND OMNÈS. Converging Realities: Towards a Common Philosophy of Physics and Mathematics. Princeton and Oxford: Princeton University Press, 2005. Pp. xvii + 264. ISBN 0-691-11530-3.

Michael Liston*

* Department of Philosophy, University of Wisconsin—Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, U.S.A.

Correspondence: mnliston@uwm.edu

The first 150 words of the full text of this article appear below.

In this book physicist Roland Omnès addresses some big questions in philosophy of mathematics. Anyone who reflects on the history and practice of mathematics and the sciences, especially physics, will naturally be struck by some remarkable coincidences. First, often (especially in the seventeenth and eighteenth centuries) newly developed mathematics was not well understood. But its successful applications and its agreement with intuitive representations of reality promoted confidence in its correctness even absent clear foundations (e.g., intuitive geometrical continuity lent a naturalness to the existence of derivatives). Later, this confidence is vindicated when a proper setting for the concepts and techniques is discovered (e.g., Weierstrass's arithmetization of analysis). Second, often mathematical concepts designed for one purpose (e.g., the discovery of complex numbers as solutions of algebraic equations) later turn out to have pervasive applications (both in mathematics and in . . . [Full Text of this Article]


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