 On the one hand, it emerged that many of the standard definitions in mathematical analysis are impredicative. For instance, the minimal closure of an operation on a set is ordinarily defined as the intersection of all sets that are closed under applications of the operation. But the minimal closure itself is one of the sets that are closed under applications of the operation. Thus, the definition is impredicative. In this way, attention gradually shifted away from concern about the set-theoretical paradoxes to the role of impredicativity in mainstream mathematics. On the other hand, Weyl showed that it is often possible to bypass impredicative notions. It even emerged that most of mainstream nineteenth century mathematical analysis can be vindicated on a predicative basis (Feferman 1988).