Argument

Russell's paradox

Overview

paradox in set theory concerning the set of all sets not containing themselves

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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1. We shall later see that M. Richard has himself given with much sagacity the explanation of his paradox and that this extends, _mutatis mutandis_, to the other like paradoxes. Again, Russell cites another quite amusing paradox: _What is the least whole number which can not be defined by a phrase composed of less than a hundred English words_? This number exists; and in fact the numbers capable of being defined by a…

   Henri Poincaré, The Foundations of Science

   States what Russell's paradox is.

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2. Mr. Russell's own experience makes us hesitate. When he first adopted this definition from Frege, he was led to make the inference that the class of all possible classes might furnish a type for a greatest cardinal number.

   John Dewey, Creative Intelligence

   Close in meaning to Russell's paradox; the term itself is not named.

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3. His argument to the contrary may be supposed to appeal to the view that a finite time must consist of a finite number of instants, in which case what he says would be perfectly true on the assumption that the possibility of continued dichotomy is undeniable. If, on the other hand, we suppose the argument directed against the partisans of infinite divisibility, we must suppose it to proceed as follows:[42] "The…

   Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy

   The author is tied to Russell's paradox in the knowledge graph.

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Philosophers who discussed Russell's paradox

• George Boolos
• Bertrand Russell
• Stanisław Leśniewski
• Gottlob Frege

Related ideas

• First-order logic
• Georg Cantor
• Gödel's completeness theorem
• Skolem's paradox
• Philosophy
• Zermelo–Fraenkel set theory
• John von Neumann
• Negation
• Kurt Gödel
• Ludwig Wittgenstein
• Ernst Zermelo
• Liar paradox
• The Principles of Mathematics
• University of Göttingen
• Function (mathematics)
• Axiomatic system
• Mathematician
• Mathematical logic
• Richard Dedekind
• Power set
• Principia Mathematica
• Peano axioms
• Set (mathematics)
• Set theory

Place in the tradition

Part of Affine logic.

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