- Russell's paradox
- The most famous of the paradoxes in the foundations of set theory, discovered by Russell in 1901. Some classes have themselves as members: the class of all abstract objects, for example, is an abstract object. Others do not: the class of donkeys is not itself a donkey. Now consider the class of all classes that are not members of themselves. Is this class a member of itself? If it is, then it is not, and if it is not, then it is.The paradox is structurally similar to easier examples, such as the paradox of the barber . But it is not so easy to say why there is no such class as the one Russell defines. It seems that there must be some restriction on the kinds of definition that are allowed to define classes, and the difficulty is that of finding a well-motivated principle behind any such restriction. See also types, theory of ; impredicative definitions.

*Philosophy dictionary.
Academic.
2011.*

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**Russell's paradox**— Part of 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.It might be assumed that, for any formal… … Wikipedia**Russell's paradox**— Math. a paradox of set theory in which an object is defined in terms of a class of objects that contains the object being defined, resulting in a logical contradiction. [1920 25; first proposed by Bertrand RUSSELL] * * * ▪ logic statement… … Universalium**russell's paradox**— ˈrəsəlz noun Usage: usually capitalized R Etymology: after Bertrand Russell : a paradox that discloses itself in forming a class of all classes that are not members of themselves and in observing that the question of whether it is true or false… … Useful english dictionary**Russell's paradox**— noun The following paradox: Let A be the set of all sets which do not contain themselves. Then does A contain itself? If it does, then by definition it does not; and if it does not, then by definition it does. See Also: Burali Forti paradox … Wiktionary**Russell**— is an English, Irish, or Scottish name derived from old French, the old French word for Red was rouse ; hence the carry over from French the English Russell, the name also derives from the animal, the fox. Its uses include:People*Arthur Russell… … Wikipedia**Russell , Bertrand Arthur William**— Russell , Bertrand Arthur William, third earl Russell (1872–1970) British philosopher and mathematician Russell, who was born at Trelleck, England, was orphaned at an early age and brought up in the home of his grandfather, the politician Lord… … Scientists**Russell, Bertrand**— ▪ British logician and philosopher in full Bertrand Arthur William Russell, 3rd Earl Russell of Kingston Russell, Viscount Amberley of Amberley and of Ardsalla born May 18, 1872, Trelleck, Monmouthshire, Wales died Feb. 2, 1970,… … Universalium**Paradox**— For other uses, see Paradox (disambiguation). Further information: List of paradoxes A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. Typically,… … Wikipedia**Russell's teapot**— part of a series on Bertrand Russell … Wikipedia**Russell, Bertrand Arthur William**— (1872–1970) English philosopher. Russell was born into the liberal and aristocratic family descended from the Prime Minister, John Russell, and educated first at home, and then from 1890 at Trinity College, Cambridge, where he read mathematics.… … Philosophy dictionary