Finitism and primitive recursive arithmetic

[Lawrence Paulson]

The calculation of Ramsey numbers (for the full, finite version of Ramsey’s theorem) closely resembles Ackermann’s function. So a consideration of Ramsey’s theorem may be relevant to this discussion.

Larry Paulson

> On 12 Dec 2021, at 03:48, JOSEPH SHIPMAN <joeshipman at aol.com> wrote:
> 
> In the context of ZFC, which is a fine context for foundational discussions, it seems to me that “finitist result” ought to mean “provable without using the axiom of infinity”, which gives us, for arithmetic, the same theorems that PA does.
> 
> Did Hilbert or his collaborators ever explicitly either accept or reject the claim that Ackerman’s function was finitistic?
>