Cantor's set theory

Some believe that Georg Cantor's set theory was not actually implicated in the set-theoretic paradoxes. One difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system.

By 1899, Cantor was aware of some of the paradoxes following from unrestricted interpretation of his theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not believe that they discredited his theory.

Cantor's paradox can actually be derived from the above (false) assumption using for P(x) "x is a cardinal number".

Frege explicitly axiomatized a theory in which a formalized version of naïve set theory can be interpreted; it was this Frege's set theory that Bertrand Russell addressed when he presented his paradox.