One way to formulate Aristotle’s argument from motion is as follows below. An important corollary of this argument is that, given that time is just the measure of motion, the Unmoved moevr is a being that is unaffected by time. The argument and its defense go something like this:
What is moved (or changed) is moved (or changed) by something else.
But this cannot continue ad infinitum.
Therefore, there must be a first Unmoved Mover.
The major premise is just a variant of the principle of causality. But the important point to keep in mind is that motion is the actualization of a potential insofar as it is a potential. So anything that is being put in motion, is being put in motion not only by something else, but that something else itself must be actual in the relevant way to be able to actualize i.e., by setting in motion, the other thing it is moving. For example, wood is potentially burning but actually not. Fire, being itself actual, is what acts on the wood and actualizes its potentiality for burning so that it is then actually burning. Or, something that is potentially a certain color is actualized by the painter (or more specifically the paint brush) to become actually that color. All this is fairly obvious.
Proof of the minor: the series of causes of motion that this premise rules out is an essential one, not accidental one. The difference between the two is that in the latter, the motion of subsequent movers and things moved i.e., their causal activities, does not depend on the motion or, more precisely, actualizing activity, of any (presumed) first thing that imparts the movement. In other words, they contain it by virtue of themselves. For example, the causal activity of a son does not depend on that of his father once his father begets him. Once the son is begotten, he can himself beget i.e., set in motion, without the presence of (the causal activity of) his father. In the former though, this is not the case; the ability of any mover to impart motion depends the actual motion of a prior mover, and ultimately on that of the first mover of the entire series of movers. All other movers other than the first are merely instrumental in their causal activity. An example that is commonly given, following St.Thomas, is the hand that moves the stick that moves the stone which in turn moves the leaf. Suppose, for the sake of argument, that the hand is the initial first mover here (although it isn’t in reality). Now the leaf moves only insofar as it is moved by the stone, which itself moves only insofar as it is moved by the stick, and the same with the stick with respect to the hand. The actualization of the motion of each mover and moved thing is essentially dependent on the motion of the thing prior to it which moves it. I say dependent, that is, in the sense of it would not be able to move without the simultaneous movement of the thing that is moving it. This why, again, all the other movers are merely instrumental movers of the first mover i.e., they have no power to move apart from them being moved by the first member of the series i.e., the hand. Hence, why the minor rules out an actual infinite series of essential movers should be clear now; for otherwise, i.e., if there were no first mover in such a series, there would be no other movers, given that, in such a series, other movers are, as was said, only in motion to the extent that they’re moved by something else. The movement of the leaf is entirely derived from that of the stone, which is entirely derived from that of the stick, and that of the stick from the hand, which (for arguments sake) is the first mover of the series, and so does not derive its power of movement from anything else, but imparts it to others. Hence, if the hand did not move, then the other things which it sets in motion would not be in motion. But evidently, there are other things which are in motion here and now. It then follows that this sort of series cannot continue ad infinitum. And the conclusion would then be established.
So now, given that the existence of an Unmoved Mover (UM) has been established, certain other consequences follow. Of these, an important one is the fact that the UM cannot be in motion in any way whatsoever. This is because, as was said, motion is nothing but the actualization of a potentiality qua potentiality. Hence, if the UM was in motion in some way, then it would be in potency in some way, and if it were in potency in some way, then it would have to be actualized by something other than itself. And if that were the case, it would then not be the UM, but instead will just a being among one of the beings which the major premise signifies i.e., a thing that moves and is moved by something else. If this is so, then given what we’re forced to admit by the minor premise, the thing that moves the thing we thought to be the UM is would itself be the real UM. And etc . The Unmoved Mover then is Pure Act, which means there isn’t any potentiality in it, which means it does not undergo motion at all. Now if it does not undergo motion, it cannot be affected by time. The notion of time cannot be predicated of the UM because time presupposes motion; it is nothing but the measure of motion (see, Physics IV.11). And so if the UM is unaffected by motion, it is afortiori unaffected by time. In other words, it is an atemporal being.