2005/09/11 by Nik Weaver, Weaver, Nik · 1 citation
Computer Science · Psychology · #Computability, Logic, AI Algorithms #Logic, Reasoning, and Knowledge #Philosophy and Theoretical Science
paper · pdf · doi:10.48550/arxiv.math/0509244
We reevaluate the claim that predicative reasoning (given the natural numbers) is limited by the Feferman-Schutte ordinal Gamma0. 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 ϕΩω(0), and larger ordinals, are predicatively provable.