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

Philosophy Compass 5 (1):16-28 (2010)

Authors
Kevin Klement
University of Massachusetts, Amherst
Abstract
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 I focuses on Cantor’s theorem, its proof, how it can be used to manufacture paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes.
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DOI 10.1111/j.1747-9991.2009.00270.x
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References found in this work BETA

Logic, Logic and Logic.George Boolos - 1998 - Harvard University Press.
The Ways of Paradox, and Other Essays.W. V. Quine - 1966 - Harvard University Press.
Principles of Mathematics.Bertrand Russell - 1903 - Cambridge University Press.

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Citations of this work BETA

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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