See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles.
Here’s what was proved so far: (1) that some things move and others change, and that (2) whatever is in the process of being moved or being changed is being moved or changed by another. Utterly unremarkable assertions; but both the backbone of science, even though some scientists pretend to be skeptical of causality. There is a world, nay a universe, of difference between our knowledge of a cause and of the existence of a cause. Poor Jaki spent his career reminding people of Heisenberg’s fallacy of equivocation. “Poor” because, for whatever reason, people cannot keep in mind the difference between epistemology and ontology. Once more I beg you to read the stone being moved by the stick being moved by the arm being moved by the muscles etc. example. Today we reach the end of the First Way. Next week we begin the Second way.
Chapter 13: Arguments in proof of God’s existence
…4 This argument contains two propositions that need to be proved: namely that whatever is in motion is moved by another, and that it is not possible to proceed to infinity in movers and things moved…
11 He proves the other proposition, namely that it is impossible to proceed to infinity in movers and things moved, by three arguments.i
12 The first of these is as follows. If one were to proceed to infinity in movers and things moved, all this infinite number of things would necessarily be bodies, since whatever is moved is divisible and corporeal, as is proved in 6 Phys.ii Now every body that moves through being moved is moved at the same time as it moves.iii Therefore all this infinite number of things are moved at the same time as one of them is moved. But one of them, since it is finite, is moved in a finite time. Therefore all this infinite number of things are moved in a finite time. But this is impossible. Therefore it is impossible to proceed to infinity in movers and things moved.iv
13 That it is impossible for the aforesaid infinite number of things to be moved in a finite time, he proves thus. Mover and moved must needs be simultaneous; and he proves this by induction from each species of movement. But bodies cannot be simultaneous except by continuity or contact. Wherefore since all the aforesaid movers and things moved are bodies, as proved, they must needs be as one movable thing through their continuity or contact. And thus one infinite thing would be moved in a finite time, which is shown to be impossible in 6 Phys.v
14 The second argument in proof of the same statement is as follows. In an ordinate series of movers and things moved, where namely throughout the series one is moved by the other, we must needs find that if the first mover be taken away or cease to move, none of the others will move or be moved: because the first is the cause of movement in all the others. Now if an ordinate series of movers and things moved proceed to infinity, there will be no first mover, but all will be intermediate movers as it were. Therefore it will be impossible for any of them to be moved: and thus nothing in the world will be moved.vi
15 The third argument amounts to the same, except that it proceeds in the reverse order, namely by beginning from above: and it is as follows. That which moves instrumentally, cannot move unless there be something that moves principally. But if we proceed to infinity in movers and things moved, they will all be like instrumental movers, because they will be alleged to be moved movers, and there will be nothing by way of principal mover. Therefore nothing will be moved.vii
16 We have thus clearly proved both statements which were supposed in the first process of demonstration whereby Aristotle proved the existence of a first immovable mover.viii
iIt is utterly absolutely painfully crucial that you understand what is meant by this. Aquinas means here-and-now, or at-this-very-moment causation. The stick moves the stone here-and-now, your arm moves the stick here-and-now at-this-very-moment, your muscles move your arm here-and-now at-this-very-moment, simultaneously. Your muscle and other cells here-and-now at-this-very-moment move, and so on down to something. Some first unmoved mover. It is this here-and-now at-this-very-moment chain which cannot proceed here-and-now at-this-very-moment to infinity. Update See YOS’s clarification on “instantaneous” movement/change below.
Ed Feser (who not uncoincidentally, since I’ve stolen many of my ideas from him, today wrote on a similar subject) has taken great pains in his many books and articles to teach that this per se chain of here-and-now at-this-very-moment causes exists here-and-now at-this-very-moment, that everything is happening at once. His experience has been that this teaching does not stick. Why? Who knows. But since it is so, I remind you we are not talking about accidental chains of causation, such as when one rock falls off a hill into another, and the second rock then hits a third, and so on. No no no no. We are talking about how movement or change in the here-and-now comes about. Meditate on the example until it is clear in your mind before continuing.
iiAll of Aristotle’s Chapter 6 may be found here. The stick is a body, and so is your arm, and so are your cells, the chemicals, the electrons and neutrons, the quarks, the strings (if they exist) and whatever, if anything, is “below” them. Notice that Aquinas and Aristotle use a proof by contradiction. They assume there exists an infinite here-and-now chain.
iii Here-and-now at-this-very-moment!
ivSweet, no? If there did exist an infinite chain, and because we certainly see things move or change in finite time, this entire infinite chain would have to move not only in finite time, but at this moment, here and now (have we memorized this yet?). The proof immediately follows.
vAristotle proves even more than his: his book 7 may be found here. Anyway, it is clear that if we have an infinite here-and-now chain of objects, the whole thing must itself, here-and-now at-this-moment, move. And that is not possible in finite time. Worse, this would have to be the case for everything everywhere that is in the process of being moved or changed. That’s a lot of chains and lots of infinite movements! Since it is absurd that these infinite chains can move in finite time, yet things are moved or changed in finite time, the chains must not be infinite.
viIf the here-and-now chain is finite—this is an assumption, arguendo—and the first element is removed, the later parts also cannot move, which is obvious. Now I don’t think people understand how big infinity really is. It is not just big, nor even BIG, but horrifically huge. An infinite chain would have more than a googol of elements, which is 10100; it would have more than a googoplex of elements, which is 10googol. If you were to keep doing that operation, namely taking 10 to the power of the last result, and continuing once a second for a whole day, you still would not have got close to infinity. You would still be infinitely far away. But the, to us humans anyway, unimaginably long chain would have only just got started! Just to use your arm to move a stick to push a stone.
An infinite chain is one which never stops. It goes on and on and on and always on some more. If infinite chains existed, there would not and could not be a first element. How, then, would the whole thing get started? Answer: it could not. It would be impossible—not unlikely, but impossible.
I think people believe infinity isn’t all that big because of mathematical analysis, and used in many areas of science. In analysis we regularly and somewhat glibly call on infinity. We say some function converges (perhaps) “O(n2)”, meaning as the number of elements grows, the finite function gets closer and closer to its infinite cousin. We plug in n = 20 or even n = 100 and see that the function is “settling down”, i.e. approaching some obvious value, and we think, “Ah, infinity and n = 100 aren’t that far apart.” However useful an approximation our function at some finite number of elements is, it is never the real value of the function at infinity. Taking approximations as reality and not just as approximations is a common, though not usually painful, fallacy.
It’s a killer here, though. When we are talking movement or change, we cannot have an approximation. We must needs have the whole chain. Stopping at the first (say) 100 elements just won’t do. If we remove a link, the chain cannot pull. And if we do have an infinite chain, there will be nothing to give the chain impetus. Without a first mover, nothing can happen. The chain thus cannot be infinite.
viiThe rock is being moved instrumentally by the stick, which is being moved instrumentally by the arm, and so forth. The principal unmoved mover sets off the whole shebang. I think we get it by now.
viiiLet’s review. We proved the premises in this First Way:
Whatever is in motion is moved by another: and it is clear to the sense that something, the sun for instance, is in motion. Therefore it is set in motion by something else moving it. Now that which moves it is itself either moved or not. If it be not moved, then the point is proved that we must needs postulate an immovable mover: and this we call God. If, however, it be moved, it is moved by another mover. Either, therefore, we must proceed to infinity, or we must come to an immovable mover. But it is not possible to proceed to infinity. Therefore it is necessary to postulate an immovable mover.
The premises being true, and the argument valid, the conclusion must also be true. And therefore it would irrational to deny it. But why God as the unmoved mover? Why not call the immovable mover the Higgs Field Driver or whatever? Well, we haven’t fleshed this part of the proof out yet, so our modern scientistic suspicion is natural.
As a hint—and only a hint—there cannot be more than one immovable mover, one unchangeable changer. There must be something which exists which acts to sustain everything. Stay tuned!
 7 Phys., l.c.
 7 Phys. i. ii.
 Ch. vii.
 8 Phys. v.