Russell, His Paradoxes, and Cantor's Theorem: Part II

Philosophy Compass 5 (1):29-41 (2010)
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Abstract

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead.

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Kevin Klement
University of Massachusetts, Amherst

Citations of this work

In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
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The functions of Russell’s no class theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.
A Modal Account of Propositions.Andy Demfree Yu - 2017 - Dialectica 71 (4):463-488.

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References found in this work

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
The Philosophy of Logical Atomism.Bertrand Russell - 1940 - Open Court. Edited by David Pears.

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