Mathematicians who are finitists.

[A Toy Windmill]

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.

My point is that Cantor, using a finite number of symbols, proved that some infinite sets (the Reals) are infinite and uncountable:

Wikipedia -- Cantor's diagonal argument

The rational numbers are, however, countable:

Wikipedia -- Countable set

And, so, what's the issue here?  Is finitism any different than Creationism?

Where is the proof that some sets are infinite in the first place? Cantor didn't prove the existence of such things Their existence is only granted axiomatically in set theory.

A finitist can accept Cantor's diagonal argument as a scheme to transform a finitistic function --- which the classical mathematician calls an enumeration of the reals --- into another function --- which the classical mathematician thinks gives a real not in the enumeration.