  We reevaluate the claim that predicative reasoning (given the natural
numbers) is limited by the Feferman-Schutte ordinal Gamma_0. First we
comprehensively criticize the arguments that have been offered in support of
this position. Then we analyze predicativism from first principles and develop
a general method for accessing ordinals which is predicatively valid according
to this analysis. We find that the Veblen ordinal \phi_{\Omega^\omega}(0), and
larger ordinals, are predicatively provable.
