2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229808We 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 ϕ_{Ω^ω}(0), and larger ordinals, are predicatively provable.38 pages Some minor corrections; no major changesLogicGeneral Mathematicstext