Wiktionary
ultrafinitism
n. (context mathematics English) A form of finitism that is even more extreme in that it denies those constructs whose construction cannot be physically performed (such as a number that no human could have time to calculate).
Wikipedia
Ultrafinitism
In the philosophy of mathematics, ultrafinitism, also known as ultraintuitionism, strict-finitism, actualism, and strong-finitism is a form of finitism. There are various philosophies of mathematics that are called ultrafinitism. A major identifying property common among most of these philosophies is their objections to totality of number theoretic functions like exponentiation over natural numbers.