A nuanced article on this paradox of naive set theory, happened upon by Russell in 1901. Includes bibliography, links to related article ... The significance of Russell's paradox can be seen once it is realized that, using classical logic, all sentences follow from a contradiction. For example, assuming both P and ~P,
plato.stanford.edu/entries/russell-paradox/ plato.stanford.edu/entries/russell-paradox/
Russell's paradox - Wikipedia, the free encyclopedia
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In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy ), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction...
en.wikipedia.org/wiki/Russell's_paradox
Barber paradox - Wikipedia, the free encyclopedia
The Barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell himself as an illustration of the paradox, though he attributes it to an unnamed person who suggested i...
en.wikipedia.org/wiki/Barber_paradox
Math puzzles. Interactive education. Logic and Paradoxes. Self-reference. Russell's Paradox ... Poincaré disliked Peano's work on a formal language for mathematics, then called "logistic." He wrote of Russell's paradox, with evident satisfaction, "Logistic has finally proved that it is not sterile. At last it has given...
www.cut-the-knot.org/selfreference/russell.shtml www.cut-the-knot.org/selfreference/russell.shtml
Examines self-referential linguistics used to describe properties and sets. ... 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.
www.utm.edu/research/iep/p/par-russ.htm
The above story about the barber is the popular version of Russell's Paradox. The story was originally told by Bertrand Russell. And of course it has a simple solution. It is inconsistent. But the story is not really that simple.
www.jimloy.com/logic/russell.htm www.jimloy.com/logic/russell.htm
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:
burks.brighton.ac.uk/burks/foldoc/59/101.htm
We found 14 dictionaries with English definitions that include the word Russell's Paradox:; Click on the first link on a line below to go directly to a page where "Russell's Paradox" is defined.; General (4 matching dictionaries);
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CiteSeerX - Document Details (Isaac Councill, Lee Giles): on this analysis, and although Oksanen quoted Russell's description of the paradox in detail, he did not show how it is explained in NFU after his resolution of the other related modal paradoxes; ... Russell's Paradox Of The Totality Of Propositions (2000)
citeseer.ist.psu.edu/cocchiarella00russells.html citeseer.ist.psu.edu/cocchiarella00russells.html
An interpretation of Russell paradox without any formal language of set theory could be stated like ``If the barber shaves all those who do not themselves shave, does he shave himself?''. If you answer himself that is false since he only shaves all those who do not themselves shave.
planetmath.org/encyclopedia/RussellsParadox.html planetmath.org/encyclopedia/RussellsParadox.html