Last Updated：2025/11/24

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(set theory) The paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.

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Russell's paradox

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Russell's paradox

Proper noun

Japanese Meaning

（集合論）自らを含まない集合のすべてを含むように定義された集合が、自らを含むか否かについて自己矛盾に陥るというパラドックス

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Many introductory logic courses use Russell's paradox to illustrate the limits of naive set theory.

Google Translation / DeepL Translation

多くの入門的な論理学の講義では、集合自身を含まないすべての集合を含むように定義された集合に関する逆説（ラッセルの逆説）を用いて、素朴な集合論の限界を示すことが多い。

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Sense（1）

One concludes that there must be something fishy about the Axiom of Comprehension, and, over time, the replacement of the Axiom of Comprehension by the Schema of Separation was seen to resolve Russell's paradox. Indeed, one cannot apply the Schema of Separation as in Russell's paradox unless one knows in advance that the collection of all sets is itself a set.

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Russell's paradox

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Russell's paradox

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