David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
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.
Similar books and articles
Kevin C. Klement (2001). Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's Response Adequate? History and Philosophy of Logic 22 (1):13-28.
Francisco A. Rodriguez Consuegra (1989). Russell's Theory of Types, 1901–1910: Its Complex Origins in the Unpublished Manuscripts. History and Philosophy of Logic 10 (2):131-164.
Kevin C. Klement (2009). A Cantorian Argument Against Frege's and Early Russell's Theories of Descriptions. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "on Denoting". Routledge.
Francesco Berto (2007). How to Sell a Contradiction. College Publications.
Kevin C. Klement, Russell-Myhill Paradox. Internet Encyclopedia of Philosophy.
Dustin Tucker & Richmond H. Thomason (2011). Paradoxes of Intensionality. Review of Symbolic Logic 4 (3):394-411.
Kevin C. Klement, Russell's Paradox. Internet Encyclopedia of Philosophy.
Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part I. Philosophy Compass 5 (1):16-28.
Added to index2009-09-08
Total downloads40 ( #43,388 of 1,102,807 )
Recent downloads (6 months)5 ( #61,871 of 1,102,807 )
How can I increase my downloads?