(July 3, 2019 at 10:06 pm)Jehanne Wrote:(July 3, 2019 at 1:14 pm)A Toy Windmill Wrote: 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?
For finitistic mathematics, such proofs are irrelevant because no infinite sets (like the set of positive integers or the set of reals) even exists in the system.
Yes finitism is different than creationism because it attempts to thrash out what can be known if no infinite sets are postulated to exist. This gives, for example, information about the independence of the axioms we use. It is also closely related to things like recursion theory, questions of computability, etc .
As such it is an acknowledged are of modern mathematics, even if it is a bit off the beaten track.
Creationism, however, isn't even a part of biology. It is pure superstition.
