God is not a physical body, that God is not a creature continued…but not finished today. We have instead a series of nested arguments, so it will take some careful reading to keep up. Each argument contains a premise, which is proved in the next point, which itself (once or twice) has a premise proved by the next point after. This goes on at some length; indeed, we will not finish the proof this week. Plus we ranging into analysis-like subjects, which aren’t always easy to keep in mind.
Chapter 20: That God is not a body
…9 Again. No infinite power is a power residing in a magnitude. But the power of the first mover is an infinite power. Therefore it does not reside in a magnitude. And thus God, Who is the first mover, is neither a body nor a power residing in a body.i
10 The first proposition is proved as follows. If a power residing in a magnitude be infinite, this magnitude is either finite or infinite. But there is no infinite magnitude, as proved in 3 Phys. and 1 Coeli et Mundi. And it is not possible for a finite magnitude to have an infinite power. Therefore in no magnitude can there be an infinite power.ii
11 That there cannot be an infinite power in a finite magnitude is proved thus. A great power produces in less time an equal effect, which a lesser power produces in more time: of whatever kind this effect may be, whether it be one of alteration, of local movement, or of any other kind of movement. Now an infinite power surpasses every finite power. It follows therefore that it produces its effect more rapidly, by causing a more rapid movement than any finite power. Nor can this greater rapidity be one of time. Therefore it follows that the effect is produced in an indivisible point of time. And thus moving, being moved, and movement will be instantaneous: the contrary of which has been proved in 6 Phys.iii
12 That an infinite power of a finite magnitude cannot cause movement in time, is proved thus. Let A be an infinite power; and AB a part thereof. This part therefore will cause movement in more time. And yet there must be proportion between this time and the time in which the whole power causes movement, since both times are finite. Suppose then these two times to be in proportion as 1 to 10, for it does not affect this argument whether we take this or any other ratio.
Now if we increase the aforesaid finite power, we must decrease the time in proportion to the increase of the power, since a greater power causes movement in less time. If therefore we increase it tenfold, that power will cause movement in a time which will be one-tenth of the time occupied by the first part that we took of the infinite power, namely AB. And yet this power which is ten times the aforesaid power is a finite power, since it has a fixed proportion to a finite power. It follows therefore that a finite power and an infinite power cause movement in an equal time: which is impossible. Therefore an infinite power of a finite magnitude cannot cause movement in any time.iv
iThis highlights something I think sadly neglected by physicists. That to create something out of nothing, or to be the First Mover (in the Chapter 13 sense; also see this), requires infinite “power.” Just what power and how does that relate to other things we know or conjecture about the universe is very little is known. Infinity is a strange place, as we emphasize repeatedly and to say our intuitions aren’t in it is the minimum. Mathematics barely touches on it. Spheres that can fold themselves inside out without breaking? Can be split in two and be the same in size? Weird!
iiWe’re into the Land of Subtly here, where it is easy to get lost. Don’t forget our destination. That the Infinite cannot be a body. Now if God were an infinite body, that is all there would be. There would be no room for us. God would take up all the space. So God has to be something other than a body, while still being infinite. But what? That’s what the rest of this book of Summa Contra Gentiles is about: describing that what.
It seems to me that we are not at a sticking point, that the reader is willing to grant that God is not an infinite physical body. So I don’t want to take up space with minutiae; nevertheless, if you’re interested in the details, read Chapter 5 of Aristotle here.
iiiNon-locality anyone? How can entangled particles the distance of the universe apart instantaneously “decide” which states to take? Do we have an answer here, in the First Mover, or are things buried more deeply?
ivWe have a proof by contradiction. Perhaps it’s easy to miss, but St Thomas is assuming first that the infinite power causes an effect in finite time. The idea is that, by simple manipulation, if the infinite power causes an effect in any time whatsoever, we can construct a finite power that causes the effect in the same amount of time. This cannot be, thus the infinite power must operate instantaneously.
The proofs of the remaining premises aren’t in this article. We attack these next week because, I think, we’ve already reached the limit today (get it? get it? theological cum mathematical humor; plus, Yours Truly is rather in a hurry today).
 Ch. v.
 Ch. v. seqq.
 Ch. iii.