 A common criticism of Zermelo set theory is that it is an ad hoc selection of axioms chosen to avoid paradox, and we have no reason to believe that it actually achieves this end. We believe such objections to be unfounded, for two reasons. The first is that the theory of types (which is the result of a principled single modification of naive set theory) is easily shown to be precisely equivalent in consistency strength and expressive power to Z with the restriction that all quantifiers in the formulas \(\phi\) in instances of separation must be bounded in a set; this casts doubt on the idea that the choice of axioms in Z is particularly arbitrary. The fact that the von Neumann-Gödel-Bernays class theory (discussed below) turns out to be a conservative extension of ZFC suggests that full ZFC is a precise formulation of Cantor’s ideas about the Absolute Infinite (and so not arbitrary). Further, the introduction of the Foundation Axiom identifies the set theories of this class as the theories of a particular class of structures (the well-founded sets) of which the Zermelo axioms certainly seem to hold (whether Replacement holds so evidently is another matter).