Mathematicians who are finitists.

[Jehanne]

Polymath,

You have been such a blessing!

One last question, "Do finitists make any distinction between sets ("collections") that are countable versus uncountable?"

Thanks,

Dawn

Again, for a finitist, all sets are finite. So the issue simply doesn't arise. The definition of cardinality can be made, but it trivializes. No set is uncountable, no set is even countably infinite.

For a finitist, there *is* no set of natural numbers. There *is* no set of real numbers. ONLY finite sets exist in the finitist system.

I think you can see why most mathematicians see finitism as limiting.

I found Cantor's diagonalization proofs, as described by Rosen, to be on par with the Pythagorean theorem. Seems like the finistists are engaging in ad hoc reasoning. But, maybe they feel that there are really square circles?