A contradiction Bertrand Russell discovered in 1901 within naive set theory, consider the set of all sets that do not contain themselves as members: if this set contains itself, then by its own definition it must not, and if it does not contain itself, then by its own definition it must. The paradox showed that Frege's logicist foundation for mathematics, which allowed unrestricted set formation from any well-defined condition, was inconsistent, and it prompted the development of more restrictive axiomatic set theories, including Russell's own theory of types and, later, Zermelo-Fraenkel set theory, to block the offending self-referential constructions while preserving the rest of mathematics.
Facts
Origin YearRussell discovered the paradox in 1901 and communicated it to Frege in 1902, as Frege's Grundgesetze der Arithmetik was going to press. Classification
Position Kind Connections
Associated With
Source Russell's Paradox (Stanford Encyclopedia of Philosophy)
Russell communicated the paradox to Frege in 1902 as it undermined the logicist system of Frege's Grundgesetze der Arithmetik.
Source Russell's Paradox (Stanford Encyclopedia of Philosophy)
In Branch
Sources
1. Russell's Paradox (Stanford Encyclopedia of Philosophy)
Russell's Paradox
Russells paradox is a contradiction, a logical impossibility, of concern to the foundations of set theory and logical reasoning generally.
- Associated With: Bertrand Russell
- Associated With: Gottlob Frege
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