Russell's paradox

Internet Encyclopedia of Philosophy (2001)

Authors
Kevin Klement
University of Massachusetts, Amherst
Abstract
Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (or sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself. It is if and only if it is not. The other form is a contradiction involving properties. Some properties seem to apply to themselves, while others do not. The property of being a property is itself a property, while the property of being a cat is not itself a cat. Consider the property that something has just in case it is a property (like that of being a cat ) that does not apply to itself. Does this property apply to itself? Once again, from either assumption, the opposite follows. The paradox was named after Bertrand Russell, who discovered it in 1901.
Keywords paradox  Russell  type theory  Zermelo
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,940
External links

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

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Grelling’s Paradox.Jay Newhard - 2005 - Philosophical Studies 126 (1):1 - 27.
On Russell's Vulnerability to Russell's Paradox.James Levine - 2001 - History and Philosophy of Logic 22 (4):207-231.
The Russell Operator.L. H. Kauffman - 2012 - Constructivist Foundations 7 (2):112-115.
Russell-Myhill Paradox.Kevin C. Klement - 2003 - Internet Encyclopedia of Philosophy.

Analytics

Added to PP index
2009-01-28

Total views
75 ( #99,729 of 2,235,452 )

Recent downloads (6 months)
2 ( #751,929 of 2,235,452 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature