Aquinas's proof that everything that moves is moved by another

[Aquinas]

Hello everyone! The first thing I would like you to know: I'm new to this forum, this is my first post, so I apologize in advance if there are some technical problems with this sort of question being posted in this forum subcategory.

I am trying to grasp Thomas's proofs for the existence of God from Summa Theologiae, but I'm having trouble understanding this part of the first proof:

I q. 2 a. 3 co.:

The first and more manifest way is the argument from motion. It is certain, and evident to our senses, that in the world some things are in motion. Now whatever is in motion is put in motion by another, for nothing can be in motion except it is in potentiality to that towards which it is in motion; whereas a thing moves inasmuch as it is in act. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it. Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself.

The whole proof hinges on the bold part, and I instinctively know it to be true, but I just don't understand Aquinas's argumentation for it.

This is why I turned to his earlier explanation from the Summa Contra Gentiles I cap. 13 [4, 9], which runs thus: 

(...) In this proof, there are two propositions that need to be proved, namely, that everything that is moved is moved by another (...) In the third way, Aristotle proves the proposition as follows [VIII, 5]. The same thing cannot be at once in act and in potency with respect to the same thing. But everything that is moved is, as such, in potency. For motion is the act of something that is in potency inasmuch as it is in potency. That which moves, however, is as such in act, for nothing acts except according as it is in act. Therefore, with respect to the same motion, nothing is both mover and moved. Thus, nothing moves itself.

That didn't help much, either. So, I will now offer my understanding of Aquinas's/Aristotle's claim that everything in motion is put in motion by another.

Let us imagine a pen lying on a table. If the pen physically moves (changes location), it is either moved by something else (x) or by itself. It cannot move itself because it is actually here (A) and potentially there (B), and it cannot simultaneously be actually here (A) and actually there (B) nor potentially there (B) and potentially here (A). Does Aquinas want to say that it is impossible that this pen move itself from A to B because it would in that case have to be actually at the place B at the same time when it is actually at the place A?

And if we assume his claim "But nothing can be reduced from potentiality to actuality, except by something in a state of actuality.", how do we squirm out of the conclusion that the first mover is in motion itself? Wouldn't it have to be in a state of actuality (be moving)?

Please help me with this, I am a believer myself but I would like to be able to convince others as well.

[Geremia]

Perhaps my Philosophy StackExchange answer to the question What are the best arguments for the defense of the "principle of motion"? might help:

St. Thomas defends "quidquid movetur ab alio movetur" ("whatever is moved is moved by another") in his commentary on the beginning of Aristotle Physics book 7:

• Then at (677 [=242^a44]) he [i.e., Aristotle] proves directly that whatever is being moved is being moved by some other. This is his argument: Nothing that is being moved by itself rests from its motion on account of some other mobile's resting. (He takes this as per se evident). From this he further concludes that if a mobile rests on account of the rest of another, then the mobile is moved by another. On this ground he concludes that. necessarily whatever is being moved is being moved by some other. And that this follows from the premises, he now proves.
  
  That mobile which we have supposed as being moved by itself, i.e., ABI must be divisible, for whatever is being moved is divisible, as was proved above. Hence, because it is divisible, nothing prevents it from being divided. Therefore, let it be divided at the point C so that one part of it is PC and the other part AC. Now, if PC is part, of AB, then when the part BC rests, the entire AB must rest. But if upon the part resting, the whole does not rest, let us grant that the whole is being moved and one part is at rest. But because we have assumed that one part is resting, the whole could not be granted as being moved except by reason of the other part. Therefore, when BC (which is one part) is at rest, the other part AC is being moved. But no whole of which one part only is being moved is being moved primarily and per se. Therefore AB is not being moved primarily and per se, as we originally assumed. Therefore while BC is at rest, the entire AB must be at rest. Thus, what is being moved ceases to be moved upon the occasion of something else resting. But above we held that if something rests and ceases to be moved on the occasion of another's resting, it is being moved by that other. Therefore, AB is being moved by some other.
  
  The same argument applies to any other mobile, for whatever is being moved is divisible and, for the same reason, if the part rests the whole rests. Therefore, it is clear that whatever is moved is moved by some other.

Also, St. Thomas calls the principle of non-contradiction the "primum principium indemonstrabile" ("the first indemonstrable principle"), so it would follow that it could not be proven by the "quidquid movetur ab alio movetur" principle.
See also (from here):

• The Law of Inertia and the Principle Quidquid Movetur ab Alio Movetur by Antonio Moreno, O.P.
• The Aristotelian definition of motion and the principle of inertia, a thesis by McLaughlin, Thomas J., University of St. Thomas (Houston), author of "Nature and Inertia" in The Review of Metaphysics, Vol. 62, No. 2 (Dec., 2008), pp. 251-284

[Aquinas]

Thank you for your reply!

I personally think that the third way Aquinas proves quidquid movetur ab alio movetur in the Summa Contra Gentiles (in terms of the distinction between actuality and potentiality) is better and more universal than the first two ways on account of the fact that it takes the whole thing to the metaphysical rather than the merely physical level. I think this is why he tacitly omits the first two proofs in the later Summa Theologiae. For this reason I concentrated only on this third proof.

Based on some of the links you provided in your reply and some additional resources, I came to the conclusion that the pen in question (or any physical thing) cannot move itself from place A to place B because this would presuppose that it actually has now (when it is still at place A) what it will only have later, when it actually will be at place B. Do you agree with this conclusion?

[Geremia]

Does Aquinas want to say that it is impossible that this pen move itself from A to B because it would in that case have to be actually at the place B at the same time when it is actually at the place A?

Yes, that seems to be what he means when he says: "The same thing cannot be at once in act and in potency with respect to the same thing." (Nihil idem est simul actu et potentia respectu eiusdem.) The pen cannot both be actually and A and potentially at A at the same time and in the same way.

And if we assume his claim "But nothing can be reduced from potentiality to actuality, except by something in a state of actuality.", how do we squirm out of the conclusion that the first mover is in motion itself? Wouldn't it have to be in a state of actuality (be moving)?

Not everything in actually is moving. God is Actus Purus and immutable.