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

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

Authors
Kevin Klement
University of Massachusetts, Amherst
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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DOI 10.1111/j.1747-9991.2009.00271.x
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References found in this work BETA

Logic, Logic and Logic.George Boolos - 1998 - Harvard University Press.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.

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Citations of this work BETA

The Functions of Russell’s No Class Theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.
Russell on Incomplete Symbols.Bryan Pickel - 2013 - Philosophy Compass 8 (10):909-923.
A Modal Account of Propositions.Andy Demfree Yu - 2017 - Dialectica 71 (4):463-488.
Walter Benjamin's Philosophy of Language.Alexei Procyshyn - 2014 - Philosophy Compass 9 (6):368-381.
Fragmented Truth.Andy Demfree Yu - 2016 - Dissertation, University of Oxford

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