Existence and feasibility in arithmetic

Abstract

“From two integers k, l one passes immediately to k^l; this process leads in a few steps to numbers which are far larger than any occurring in experience, e.g., 67^(257729).Intuitionism, like ordinary mathematics, claims that this number can be represented by an arabic numeral. Could not one press further the criticism which intuitionism makes of existential assertions and raise the question: What does it mean to claim the existence of an arabic numeral for the foregoing number, since in practice we are not in a position to obtain it?