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[[Bertrand Russell]]'s Paradox revealed a flaw in 1901 in early or naive set theory.  (It is likely others saw this flaw before Bertrand Russell.) It is a form of the [[liar's paradox]] expressed in the terms of set theory.

[[Bertrand Russell]]'s Paradox revealed a flaw in 1901 in early or naive [[set theory]].  (It is likely others saw this flaw before [[Bertrand Russell]].) It is a form of the [[liar's paradox]] expressed in the terms of [[set theory]].

The defect is as follows.  Let S be the set of all sets that do not contain  themselves as members.  In other words, set T is an element of S if, and only if, T is not an element of T:

The defect is as follows.  Let S be the set of all sets that do not contain  themselves as members.  In other words, set T is an element of S if, and only if, T is not an element of T: