Russell's Paradox
Version 1.0.0 · Updated 2026-07-28
CORE DEFINITION
Russell's paradox, proposed by British philosopher Bertrand Russell in 1901, is a paradox concerning the intension of classes. There are more accessible descriptions of Russell's paradox, such as the barber paradox and the bibliographic paradox. However, some consider the barber paradox to be merely a description of Russell's paradox, and it cannot fully convey Russell's paradox. Russell's paradox is resolved in class theory through the axiom of comprehension.
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Russell's paradox, proposed by British philosopher Bertrand Russell in 1901, is a paradox concerning the intension of classes. There are more accessible descriptions of Russell's paradox, such as the barber paradox and the bibliographic paradox. However, some consider the barber paradox to be merely a description of Russell's paradox, and it cannot fully convey Russell's paradox. Russell's paradox is resolved in class theory through the axiom of comprehension.
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The set S contains all sets that do not contain themselves; whether S contains itself leads to a contradiction, exposing the inconsistency of naive set theory.
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- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E7%BD%97%E7%B4%A0%E6%82%96%E8%AE%BAverified
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