Gentzen presented a proof of the consistency of PA. This proof can be formalized in PRA (Primitive Recursive Arithmetic) + "Transfinite Induction up to $\epsilon_0$". In order to accept this proof as valid finitistically, you have to decide whether or not you accept the PRA + "$\epsilon_0$-induction" to be true. In this paper, Waxman gives an argument that this does not hold as a complete finitistic or epistemological argument for Con(PA). Are there other positions? I'm interested in reading some arguments that this is finitistic in a looser sense.
2026-03-25 21:45:57.1774475157
Arguments for Primitive Recursive Arithmetic + \epsilon_0 Induction being "True"
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