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It appears to me that the First Mover of any motion must not move only with respect to the change it is producing, but otherwise could be moved in a way unrelated to what it is changing, or moved after it has finished moving something else. How then does Aquinas identify the Unmoved Mover (or First Mover) of every possible motion as God?

The previously accepted answer to this question does not answer the question, because there could be multiple sources of different changes.

I am asking about Thomas Aquinas' First Way, a summary* of the argument he has in mind:

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. Therefore, whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God.

*(Ed Feser claims Aquinas was giving summaries in this section of the Summa Theologica.)

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  • Ultimately, there can't be multiple sources of different changes, nor ways unrelated to what is changed, because the argument subsumes every motion and every change by definition. If there are different ones then the regress has not yet reached the terminal point, which is only where the Prime Mover is inferred. It is the ultimate mover of every change whatsoever as such.
    – Conifold
    Commented Dec 30, 2020 at 23:34
  • @Conifold please elaborate into a full answer, because as it stands your conclusion does not follow. Every changed object must be changed by something else. This fact does not imply that the source of every change must be the same source: Some additional observation (fact) is needed to arrive at that conclusion. Otherwise it is easy to think that an unchanging stovetop heats things, an unchanging refrigerator cools them, etc., that changes depend on local conditions (perhaps of fundamental particles and fields) -- and hence the change ceases when those conditions cease.
    – Internet User
    Commented Dec 30, 2020 at 23:40
  • It follows because it is postulated: any collection of causes has an explanatorily unifying cause. Sometimes this is called principle of sufficient reason. It is only to the final abstraction of the all-unifying cause that the final step is applied. And this argument has been rehearsed so many times both on this site and in encyclopedias that there is no point adding one more, see e.g. SEP.
    – Conifold
    Commented Dec 30, 2020 at 23:49
  • In physics, causation is not necessarily universal. There are proposed "closed timelike curves" where the notion of causation breaks down and becomes circular. It's conceivable (though not likely) that the entire universe might be one of these curves, where our future causes our past in a loop. Alternatively it's conceivable that the universe could extend infinitely back in time, without any first cause. Or even that the universe has a mathematical structure that is not fundamentally causal. So it is not a logical necessity for there to have been any first mover.
    – causative ♦
    Commented Dec 31, 2020 at 0:00
  • @causative The principle of sufficient reason Conifold mentions leads us to ask, "How did this causation loop come to exist?" It seems nonsensical to suppose that the future could cause the past, and relies on spatial thinking to make sense of it. Mathematics -- like an equation describing a waterfall in reverse -- does not imply reality.
    – Internet User
    Commented Dec 31, 2020 at 0:11

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