How did Aristotle distinguish potential infinity from actual infinity?
Aristotle distinguished between potential and actual infinity by rejecting the notion of an "actual" infinityâwhether spatial, temporal, or numericalâas incoherent.123
He argued that the infinite exists only in a potential sense, which he defined as the ability to continue a process without end. For example, he described magnitudes as "infinitely divisible," meaning they are "unendingly divisible" rather than composed of an infinite number of parts. No matter how many times a magnitude has been divided, it can always be divided further; thus, there is no end to the process of division.123
Similarly, he viewed counting as a potential infinity, representing the capacity to count indefinitely without ever reaching an "actual" infinite total. By maintaining this distinction, Aristotle sought to avoid the logical paradoxes he associated with the existence of an actually infinite number or a continuum composed of indivisible, infinite parts.123