(July 3, 2019 at 11:51 am)Jehanne Wrote:(July 3, 2019 at 2:52 am)A Toy Windmill Wrote: I wrote:
I am not saying that intuitionistic mathematics is finitism (no need for quotes: these are the proper terms). Finitism does not permit universal quantification over infinite domains in anything other than
a schematic form. Intuitionistic mathematics does. Both, however, assume that mathematical constructions are finite, and I'm not sure what anxiety finitism alleviates that intuitionism does not.
What mathematical constructions are infinite?
All uncomputable reals, which is most of them according to classical mathematics. We might argue that such things are not "constructions", in which case, swap "mathematical object" for "mathematical construction" in my previous posts.