 At least hitherto only one solution which meets these two requirements [of avoiding the paradoxes while retaining mathematics and the theory of aggregates] has been found.…This solution consists in the theory of [simple] types.…It may seem as if another solution were afforded by the system of axioms for the theory of aggregates, as presented by Zermelo, Fraenkel and von Neumann; but it turns out that this system of axioms is nothing else but a natural generalization of the theory of types, or rather, it is what it becomes of the theory of types if certain superfluous restrictions are removed. (Gödel 1933 [1995: 45–46])