Finitism is stricter than simply assuming there are no infinite sets. The finitist goes so far as to say that one cannot even quantify over the natural numbers! The most cited formal system which tries to capture what limited reasoning is left is "Primitive Recursive Arithmetic."
The finitist will accept that "n + 1 > n", but will regard this as a schema. to be filled in with particular numbers that they can muster.
The finitist will accept that "n + 1 > n", but will regard this as a schema. to be filled in with particular numbers that they can muster.
