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Philosophia Mathematica Advance Access originally published online on January 13, 2006
Philosophia Mathematica 2006 14(3):370-378; doi:10.1093/philmat/nkj016
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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

FRANK PIEROBON. Kant et les mathématiques: La conception kantienne des mathématiques [Kant and mathematics: The Kantian conception of mathematics]. Bibliothèque d'Histoire de la Philosophie. Paris: J. Vrin. ISBN 2-7116-1645-2. Pp. 240.

Emily Carson*

* Department of Philosophy, McGill University 855 Sherbrooke Street West, Montréal (Québec) H3A 2T7 Canada. emily.carson@mcgill.ca

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

This book is a welcome contribution to the literature on Kant's philosophy of mathematics in two particular respects. First, the author systematically traces the development of (aspects of) Kant's thought on mathematics from the very early pre-Critical writings through to the Critical philosophy. Secondly, it puts forward a challenge to contemporary Anglo-Saxon commentators on Kant's philosophy of mathematics which merits consideration.

A central theme of the book is that an adequate understanding of Kant's pronouncements on mathematics must begin with the recognition that mathematics in Kant's time was poised at the beginning of what Pierobon calls the ‘algebraic revolution’ of the nineteenth century. For Kant, Euclidean geometry, with its heavy reliance on the geometric image, was the paradigm of certainty. The algebraic revolution of the nineteenth century replaced that paradigm with an algebraic formalism, thereby freeing mathematics from any connection to the geometric image, and also severing the link to . . . [Full Text of this Article]


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