Switch to: References

Add citations

You must login to add citations.
  1. Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics.Sébastien Gandon - 2008 - History and Philosophy of Logic 29 (1):1-30.
    This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible 'by logical principles from logical principles' does not require a preliminary reduction of all mathematics to arithmetic. In the Principles, mechanics (part VII), geometry (part VI), analysis (part IV-V) and magnitude theory (part III) are to be all directly derived from the theory of relations, without being first reduced to arithmetic (part II). The epistemological importance of this point cannot be overestimated: Russell's logicism (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.Sébastien Gandon - 2009 - Philosophia Mathematica 17 (1):35-72.
    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 (...)
    Direct download (14 more)  
     
    Export citation  
     
    Bookmark   1 citation