Category: Paradoxes of naive set theory

In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system tha

In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number. In informal terms, the paradox is that the

Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduc

In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's parad

In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. Howeve