The actual infinite as a day or the games

It is commonly assumed that Aristotle denies any real existence to infinity. Nothing is actually infinite. If, in order to resolve Zeno’s paradoxes, Aristotle must talk of infinity, it is only in the sense of a potentiality that can never be actualized. Aristotle’s solution has been both praised for its subtlety and blamed for entailing a limitation of mathematic. His understanding of the infinite as simply indefinite (the “bad infinite” that fails to reach its accomplishment), his conception of the cosmos and even its prime mover as finite (in the sense of autarchic/self-contained) have been contrasted with the subsequent claim of God as ens infinitum (understood as a “positive” infinity). The goal of this essay is to reexamine the major texts (notably De caelo) and to demonstrate that (1) Aristotle’s claim according to which there is no actual infinite concerns only substances, not processes. (2) That Aristotle does not deny an actual infinite as such. (3) That when considering time and God (qua eternal) Aristotle acknowledges an actual infinite.