(July 10, 2019 at 8:19 pm)Jehanne Wrote:(July 10, 2019 at 8:34 am)polymath257 Wrote: Yes, precisely. So the question is *which* axioms. How do we choose the axioms? And it seems different people have different opinions on how to choose.
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.
