Chapter

The Logic of Principia Mathematica

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.003.0010

Series: Clarendon Paperbacks

 The Logic of Principia Mathematica

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Here the concern is with the logic underlying Whitehead and Russell's Principia Mathematica and with the relation of that logic to Russell's underlying metaphysics. The author emphasizes the fact that work is, strictly speaking, a theory of propositional functions, not of classes; sentences containing symbols for classes are defined by means of propositional functions. It is terms of the latter sort of entity that Russell's Paradox must be solved; the theory of types is, strictly speaking, a theory of the stratification of propositional functions.

Keywords: Axiom of Infinity; Axiom of Reducibility; class; Propositional Function; Russell's Paradox; Theory of Types

Chapter.  22231 words. 

Subjects: History of Western Philosophy

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