RE: Mathematicians who are finitists.
July 11, 2019 at 9:30 am
(This post was last modified: July 11, 2019 at 9:35 am by Jehanne.)
(July 11, 2019 at 2:52 am)polymath257 Wrote:(July 10, 2019 at 8:19 pm)Jehanne Wrote: Ultimately, consensus among experts. I doubt that finitism even has a chapter in any number theory, abstract alebgra or complex analysis textbook, but, I admit that I could be wrong on this one.
Well, I wouldn't expect to see much about finitism in such textbooks. I have, however, seen good discussions in introductory books on axiomatic set theory and the issues come up extensively in proof theory. Kunen's book on the Foundations of Mathemtics talks quite a bit about finitism, formalism, and Platonism in the context of introductory set theory. The point is that the meta-theory used to discuss proofs tends to be finitistic by nature.
Fact is that most professional mathematicians accept ZFC and the proofs of Cantor, which was the whole point of my OP. I don't think that it is an either/or proposition -- one can accept ZFC while having intelligent conversations about finitism; without having to reject the former while working within the confines of the latter.
