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By A. D. Irvine.

Extractions: MAY Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves " R ." If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics. Russell appears to have discovered his paradox in the late spring of 1901

2. Russell's Paradox [Internet Encyclopedia Of Philosophy]
Examines selfreferential linguistics used to describe properties and sets.
http://www.utm.edu/research/iep/p/par-russ.htm

Erasing russell's paradox. Home. Cantor's Theorem it is fraught with nagging inconsistencies, such as the Russell Paradox Let N denote the set of all sets which are not
http://www.geocities.com/dblowe_47/sets.htm

Extractions: The concept of set is so "naïve" and intuitive because it is directly related to the fundamental trait of human cognitive functioning to group and count in order to make sense of the constant bombardment of sensory stimuli. We group these stimuli based on common properties, and their distinctness allows us to count and relate how many items with common properties we encountered. What mathematicians have done is given this grouping concept "life" and the name of "set" and shifted focus away from the items with common properties that make up this mental grouping. Mathematicians have abstracted the concept and gone off to play with it without stopping to consider, at the most basic level, what it should and should not be. The first order of business is to establish what "exists" and what does not. Based on the general human cognitive ability to distinguish between and group "objects of thought", we can safely say that such objects of thought "exist". We generally agree upon the existence of objects since we can discuss the properties of objects among ourselves and conclude that we are discussing the same objects. And we can assume reasonably that there are many distinct objects. We can also reasonably assume that there are objects with common properties because the world would otherwise be in complete chaos. (Some might argue that the world is just that!) Philosophical questions aside, our first Axiom (1) is:

4. Russell's Paradox -- From MathWorld
Order book from Amazon. R. russell's paradox. Russell's Antinomy Eric W. Weisstein. " russell's paradox." From MathWorldA Wolfram Web Resource

russell's paradox. ©. Copyright 2000, Jim Loy. Let you tell me a famous story There was once a barber. Some say that he lived in Seville. Wherever he lived, all of the men in this town either shaved
http://www.jimloy.com/logic/russell.htm

Extractions: Go to my home page Let you tell me a famous story: There was once a barber. Some say that he lived in Seville. Wherever he lived, all of the men in this town either shaved themselves or were shaved by the barber. And the barber only shaved the men who did not shave themselves. That is a nice story. But it raises the question: Did the barber shave himself? Let's say that he did shave himself. But we see from the story that he shaved only the men in town who did not shave themselves. Therefore, he did not shave himself. But we again see in the story that every man in town either shaved himself or was shaved by the barber. So he did shave himself. We have a contradiction. What does that mean? Maybe it means that the barber lived outside of town. That would be a loophole, except that the story says that he did live in the town, maybe in Seville. Maybe it means that the barber was a woman. Another loophole, except that the story calls the barber "he." So that doesn't work. Maybe there were men who neither shaved themselves nor were shaved by the barber. Nope, the story says, "All of the men in this town either shaved themselves or were shaved by the barber." Maybe there were men who shaved themselves AND were shaved by the barber. After all, "either ... or" is a little ambiguous. But the story goes on to say, "The barber only shaved the men who did not shave themselves." So that doesn't work either. Often, when the above story is told, one of these last two loopholes is left open. So I had to be careful, when I wrote down the story.

6. The New York Review Of Books: Russell's Paradox
Volume 39, Number 14 · August 13, 1992. Review. russell's paradox. By Stuart Hampshire are indeed "the private years" of Bertrand Russell's long life, if they are compared with the
http://www.nybooks.com/articles/2834

Math puzzles. Interactive education. Logic and Paradoxes. Selfreference. russell's paradox russell's paradox. Poincaré disliked Peano's work on a formal language for mathematics, then He wrote of russell's paradox, with evident satisfaction, "Logistic has finally proved
http://www.cut-the-knot.com/selfreference/russell.html

Extractions: Oxford University Press, 1997 Sets are defined by the unique properties of their elements. One may not mention sets and elements simultaneously, but one notion has no meaning without other. The widely used Peano's notation incorporates all the pertinent attributes: a set A, a property P, elements x. But, of course, one does not always use the formal notations. For example, it's quite acceptable to talk of the set of all students at the East Brunswick High or the set of fingers I use to type this sentence. The space being limited, some sets are described on this page and some are not. Let's call russell the set of all sets described on this page. Just driving the point in: russell's elements are sets described on this page. Note that this page is where you met russell. For it's where it was defined after all. So russell has an interesting property of being its own element: russell russell.

Wikipedia Free Encyclopedia's article on 'russell's paradox' russell's paradox is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Cantor

9. KurzweilAI.net
http://www.kurzweilai.net/meme/frame.html?main=/articles/art0257.html?m=10

10. Russell's Paradox Definition Of Russell's Paradox In Computing. What Is Russell'
Computer term of Russell s paradox in the Computing Dictionary and Thesaurus. Provides search by definition of Russell s Paradox.

Extractions: Dictionaries: General Computing Medical Legal Encyclopedia Word: Word Starts with Ends with Definition (mathematics) Russell's Paradox - A logical contradiction in set theory discovered by Bertrand Russell . If R is the set of all sets which don't contain themselves, does R contain itself? If it does then it doesn't and vice versa.

11. RUSSELL'S PARADOX - Meaning And Definition Of The Word
RUSSELL S PARADOX Dictionary Entry and Meaning. Computing Dictionary. Definition A logical contradiction in set theory discovered by Bertrand Russell.

Extractions: Search Dictionary: Computing Dictionary Definition: A logical contradiction in set theory discovered by Bertrand Russell . If R is the set of all sets which don't contain themselves, does R contain itself? If it does then it doesn't and vice versa. The paradox stems from the acceptance of the following axiom : If P(x) is a property then x : P is a set. This is the Axiom of Comprehension (actually an axiom schema ). By applying it in the case where P is the property "x is not an element of x", we generate the paradox, i.e. something clearly false. Thus any theory built on this axiom must be inconsistent. In lambda-calculus Russell's Paradox can be formulated by representing each set by its characteristic function - the property which is true for members and false for non-members. The set R becomes a function r which is the negation of its argument applied to itself: If we now apply r to itself

Get the Top 10 Most Popular Sites for russell s paradox . 1 entry found for russell s paradox. russell s paradox. mathematics A

Russell s Paradox. mathematics A logical contradiction in set theory discovered by the British mathematician Bertrand Russell (18721970).

Free Online Dictionary of Computing. Russell s Paradox. mathematics A logical contradiction in set theory discovered by Bertrand Russell.

15. The DICT Development Group: Online Dictionary Query- Russell's Paradox
1 definition found From The Free Online Dictionary of Computing (15Feb98) Russell s Paradox A logical contradiction in set theory discovered by the British
http://mandrake.petra.ac.id/cgi-bin/Dict?Form=Dict2&Database=*&Query=Russell's p

16. No Match For Russell's Paradox
No match for Russell s paradox. Sorry, the term Russell s paradox is not in the dictionary. Check the spelling and try removing suffixes like ing and -s .

17. No Match For Russell's Paradox
No match for Russell s Paradox. Sorry, the term Russell s Paradox is not in the dictionary. Check the spelling and try removing suffixes like ing and -s .