Chapter

The Contradiction (i): The Problem

David Bostock

in Russell's Logical Atomism

Published in print April 2012 | ISBN: 9780199651443
Published online September 2012 | e-ISBN: 9780191741197 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199651443.003.0002
The Contradiction (i): The Problem

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The chapter gives some background on the mathematical achievements of Cantor and Dedekind, and describes how Russell aimed to show that all mathematics can be derived from a purely logical starting point (logicism). But it also describes Russell’s discovery of what he always called ‘the contradiction’, which we call ‘Russell’s paradox’, which presented a serious obstacle to that derivation. It gives Russell’s first reactions, namely the early theory of types sketched in 1903, the ‘zigzag’ theory, and the theory of limitation of size. The last is compared with the set theory of Zermelo-Fraenkel that is common nowadays.

Keywords: Cantor; Dedekind; mathematics; logicism; Russell’s paradox; types; zigzag theory; limitation of size; ZF set theory

Chapter.  7982 words. 

Subjects: History of Western Philosophy

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