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Philosophia Mathematica Advance Access originally published online on April 16, 2008
Philosophia Mathematica 2009 17(1):35-72; doi:10.1093/philmat/nkn007
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© The Author [2008]. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.{dagger}

Sébastien Gandon *

{dagger} PHIER, Université Clermont-Ferrand II, 4 rue Ledru, 63000 Clermont-Ferrand, France. sebastien.gandon{at}univ-bpclermont.fr

Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry. The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching. The fact that such a theory of geometry was sustained by Russell compels us to question the meaning of logicism: how is it possible to reconcile Russell's global reductionist standpoint with his local defence of the specificities of geometry?

* This paper was first presented at the conference ‘Qu'est ce que la géométrie aux époques modernes et contemporaines?’ (16–20 April 2007), organized by the Universität Köln and the Archives Poincaré. I would like to thank Philippe Nabonnand for having enlightened me about the issues relative to projective geometry. I would like also to thank Nicholas Griffin, Brice Halimi, Bernard Linsky, Marco Panza, Ivahn Smadja for their helpful discussions. Many thanks also to the two anonymous referees for their useful suggestions.


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