 Building on work in generalized recursion theory, Solomon Feferman extended the predicativist project in the 1960s (Feferman 2005). He realized that Weyl’s strategy could be iterated into the transfinite. Also those sets of numbers that can be defined by using quantification over the sets that Weyl regarded as predicatively justified, should be counted as predicatively acceptable, and so on. This process can be propagated along an ordinal path. This ordinal path stretches as far into the transfinite as the predicative ordinals reach, where an ordinal is predicative if it measures the length of a provable well-ordering of the natural numbers. This calibration of the strength of predicative mathematics, which is due to Feferman and (independently) Schütte, is nowadays fairly generally accepted. Feferman then investigated how much of standard mathematical analysis can be carried out within a predicativist framework. The research of Feferman and others (most notably Harvey Friedman) shows that most of twentieth century analysis is acceptable from a predicativist point of view. But it is also clear that not all of contemporary mathematics that is generally accepted by the mathematical community is acceptable from a predicativist standpoint: transfinite set theory is a case in point.