David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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References found in this work BETA
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
I. Grattan-Guinness (1977). Dear Russell, Dear Jourdain: A Commentary on Russell's Logic, Based on His Correspondence with Philip Jourdain. Columbia University Press.
Peter Hylton (2005/2008). Propositions, Functions, and Analysis: Selected Essays on Russell's Philosophy. Oxford University Press.
Kevin Klement (2004). The Origins of the Propositional Functions Version of Russell's Paradox. Russell 24 (2).
Citations of this work BETA
Kevin C. Klement (2010). The Functions of Russell's No Class Theory. Review of Symbolic Logic 3 (4):633-664.
Bryan Pickel (2013). Russell on Incomplete Symbols. Philosophy Compass 8 (10):909-923.
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