David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophia Mathematica 17 (1):35-72 (2009)
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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References found in this work BETA
Yehuda Rav (2007). A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices. Philosophia Mathematica 15 (3):291-320.
Patricia A. Blanchette (2007). Frege on Consistency and Conceptual Analysis. Philosophia Mathematica 15 (3):321-346.
Michael Detlefsen (1993). Poincaré Vs. Russell on the Rôle of Logic in Mathematicst. Philosophia Mathematica 1 (1):24-49.
Sébastien Gandon (2008). Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics. History and Philosophy of Logic 29 (1):1-30.
Colin Mclarty (1997). Poincaré: Mathematics & Logic & Intuition. Philosophia Mathematica 5 (2):97-115.
Citations of this work BETA
Andrew Arana & Paolo Mancosu (2012). On the Relationship Between Plane and Solid Geometry. Review of Symbolic Logic 5 (2):294-353.
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