Russell's paradox

a paradox of set theory in which an object is defined in terms of a class of objects that contains the object being defined, resulting in a logical contradiction.

logic the paradox discovered by Bertrand Russell in the work of Gottlob Frege, that the class of all classes that are not members of themselves is a member of itself only if it is not, and is not only if it is. This undermines the notion of an all-inclusive universal class