Philosophia Mathematica 17 (1):35-72 (2009)

Abstract
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?’, 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. CiteULike Connotea Del.icio.us What's this?
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Reprint years 2008, 2009
DOI 10.1093/philmat/nkn007
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References found in this work BETA

Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
Russell’s Hidden Substitutional Theory.Gregory Landini - 1998 - Oxford, England: Oxford University Press.

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Citations of this work BETA

On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
Pasch's Empiricism as Methodological Structuralism.Dirk Schlimm - 2020 - In Erich Reck & Georg Schiemer (eds.), The Pre-History of Mathematical Structuralism. New York: Oxford University Press. pp. 80-105.

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