  This argument seems to be a poor one. Even if Aristotle admits that nothing infinite can be predicated of a finite body, he will want to say that al-Kindi’s argument fails to take full account of the distinction between actual and merely potential infinities. An actual infinity is an infinity which is simultaneously present in its entirety – for example, an infinitely large body, or in general any set with an infinite number of members existing at the same time. A potential infinity is when a finite magnitude can be extended or multiplied indefinitely. For example, Aristotle thinks that any finite magnitude of space or time is potentially infinite, in that it can in principle be divided into as many parts as one wishes, with smaller divisions still possible. The body of the cosmos, as al-Kindi admits himself, is also potentially infinite, in the sense that there is nothing conceptually impossible about increasing its size indefinitely. Notice, though, that in either case the actual result of such a process will be finite: any determinate addition to the size of a body will still yield a body of finite size. Likewise, no matter how finely I divide a body, any particular act of division will yield a finite number of parts.