One worry that emerges here is that, in the case of substantive mathematical structures (such as those invoked in set theory), knowledge of the possibility of such structures may require knowledge of substantial parts of mathematics. For instance, in order to know that the structures formulated in Zermelo set theory are possible, presumably we need to know that the theory itself is consistent. But the consistency of the theory can only be established in another theory, whose consistency, in turn, also needs to be established—and we face a regress. It would be arbitrary simply to assume the consistency of the theories in question, given that if such theories turn out to be in fact inconsistent, given classical logic, everything could be proved in them.