  Now, Aristotle believes that the eternity of the world commits him only to a potential infinity. This is because saying that the world has always existed does not imply that any infinity is presently actual. Rather, it implies only that “the world has already existed for N years” will be true for any value of N. One can, so to speak, go as far as one wishes into the past, positing increasingly large (but still finite) periods of past time, just as one can divide a body as finely as one wishes. And it is far from clear that this sort of potential infinity is inapplicable to a finite magnitude. Does al-Kindi have any response to this?