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Philosophia Mathematica Advance Access originally published online on April 13, 2006
Philosophia Mathematica 2006 14(3):394-400; doi:10.1093/philmat/nkl007
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Philosophia Mathematica (III), Vol. 14 No. 3 © The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Book Review

JOHN L. BELL. The Continuous and the Infinitesimal in Mathematics and Philosophy. Monza: Polimetrica, 2005. Pp. 349. ISBN 88-7699-015-1.

Jean-Pierre Marquis*

* Département de philosophie, Université de Montréal Montréal (Québec) H3C 3J7 Canada Jean-Pierre.Marquis@UMontreal.Ca

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

Some concepts that are now part and parcel of mathematics used to be, at least until the beginning of the twentieth century, a central preoccupation of mathematicians and philosophers. The concept of continuity, or the continuous, is one of them. Nowadays, many philosophers of mathematics take it for granted that mathematicians of the last quarter of the nineteenth century found an adequate conceptual analysis of the continuous in terms of limits and that serious philosophical thinking is no longer required, except perhaps when the question of the continuum is transferred to the arena of set theory where it takes the form of the infamous continuum hypothesis. As Philip Ehrlich has recently shown, this conviction goes back to the early writings of Russell who, in 1903 and then again in later writings, forcefully and eloquently pushed the view that mathematicians had given the final answer to immemorial conundrums arising from the . . . [Full Text of this Article]


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