Reflections on Predicativity

Charles Parsons


Solomon Feferman's classic analysis of predicative provability, together with the more or less parallel work of Schuette, brought to a sort of closure the debates about predicativity that were inaugurated at the beginning of the century by Poincare.

Some remarks will be made about the history of these debates, which included the very dramatic expressions of concern about impredicativity by Weyl and the defense of such methods on realist grounds by several writers, most decisively Gödel. It is hoped that attention can also be paid to issues left over after the work up through the 60's, impredicative specification of sets by quantification over the universe, and the claim of the author and others that the concept of natural number is impredicative.