Chapter

Russell's Principles of Mathematics

Peter Hylton

in Russell, Idealism, and the Emergence of Analytic Philosophy

Published in print November 1992 | ISBN: 9780198240181
Published online November 2003 | e-ISBN: 9780191597763 | DOI: http://dx.doi.org/10.1093/019824018X.003.0007

Series: Clarendon Paperbacks

 Russell's Principles of Mathematics

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The focus of this chapter is on the book mentioned in its title. There, Russell combines the metaphysics of Platonic Atomism with the logic of relations, which he developed on the basis of Peano's logic and with logicism. Logicism is deployed as an argument against Idealism; in particular, it is used to defend the idea that the truths of mathematics are absolutely true, not merely relatively true as the Idealists had held. And it is also used to argue that consistent theories of space and time are available (contrary to the view Russell put forward in his 1897 book on geometry). This fact, Russell claims, undermines the Idealist claim that our ordinary knowledge is inconsistent. The chapter also raises some of the problems thrown up by Russell's view, in particular the paradox that bears his name.

Keywords: denoting; generality; logic; logicism; Russell's Paradox

Chapter.  34535 words. 

Subjects: History of Western Philosophy

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