Mathematicians who are finitists.

[polymath257]

For most mathematicians, though, the finitistic realm is far too constraining and the possibility to talk about infinite sets underlies a lot of calculus and thereby most of modern mathematics.

I wonder how finitists would view Turning Machines?  Or, for that matter, the Continuum Hypothesis?

Turing machines are finitistic devices and are an integral part of finitistic math.

Finitists tend to view the CH as nonsense.