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

Philosophy Compass 5 (1):29-41 (2010)
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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Bryan Pickel (2013). Russell on Incomplete Symbols. Philosophy Compass 8 (10):909-923.

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