A nuanced article on this paradox of naive set theory, happened upon by Russell in 1901. Includes bibliography, links to related article Russell's paradox is the most famous of the logical or set-theoretical paradoxes. Unlike Burali-Forti's paradox, Russell's paradox does not involve either ordinals or cardinals,
plato.stanford.edu/entries/russell-paradox/ plato.stanford.edu/entries/russell-paradox/
Part of the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction.
en.wikipedia.org/wiki/Russell's_paradox en.wikipedia.org/wiki/Russell's_paradox
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Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Russell's discovery came while he was working on his Principles of Mathematics. Although Russell discovered the paradox independently,
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Russell found the paradox in 1901 and communicated it in a letter to the German mathematician-logician Gottlob Frege in 1902. Russell’s letter demonstrated an inconsistency in Frege’s axiomatic system of set theory by deriving a paradox within it. For a definition of "Russell's paradox", visit Merriam-Webster.
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Logic and Paradoxes. Self-reference. Russell's Paradox Poincaré disliked Peano's work on a formal language for mathematics, then called "logistic." He wrote of Russell's paradox, with evident satisfaction, "Logistic has finally proved that it is not sterile. At last it has given birth - to a contradiction."
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