Word.ws English Dictionary

Russell's paradox

Russell's paradox proper noun: the paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.

Proper noun

Russell's paradox

  1. The paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.
    • 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...1999, R. C. Penner, Discrete Mathematics: Proof Techniques and Mathematical Structures, World Scientific, page 109
    • The well-known theorem of Tarski that truth of sentences in any reasonably expressive language L cannot be defined in the language L itself is proved by a diagonalization argument similar to the argument involved in Russell's paradox.[…]It is usual to think that Russell's paradox excludes "large"...2001, M. Randall Holmes, “Tarski's Theorem and NFU”, in C. Anthony Anderson, Michael Zelëny, editors, Logic, Meaning and Computation: Essays in Memory of Alonzo Church, Springer (Kluwer Academic)...

Examples of Russell's paradox in a sentence

  • 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.1999, R. C. Penner, Discrete Mathematics: Proof Techniques and Mathematical Structures, World Scientific, page 109:
  • An alternate solution to Russell's paradox (and other paradoxes) was proposed by Quine (1937) in his system "New Foundations" (NF): comprehension restricted to stratified formulae.2001, M. Randall Holmes, “Tarski's Theorem and NFU”, in C. Anthony Anderson, Michael Zelëny, editors, Logic, Meaning and Computation...

Synonyms of Russell's paradox

Origin of Russell's paradox

Named after English mathematician, logician and philosopher Bertrand Russell.

Questions about Russell's paradox

What does Russell's paradox mean?
Russell's paradox means the paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.
How do you use Russell's paradox in a sentence?
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.
What part of speech is Russell's paradox?
Russell's paradox is a proper noun.

Words near Russell's paradox in the dictionary

  1. Russell County
  2. Russell Falls
  3. Russell Lea
  4. Russell Vale
  5. Russell's antinomy
  6. Russell's paradox
  7. Russell's sign
  8. Russell's syndrome
  9. Russell's teapot
  10. Russell's viper
  11. Russell's viper venom clotting time

Source and license

Adapted from Wiktionary: Russell's paradox (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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