The following is not an exposition or explanation of any argument found in the texts of Aristotle or Thomas Aquinas, but it is inspired by their work, and located within the tradition.

​Let's begin by assuming that all change must have a cause. Another word for ‘change’ in this context is ‘passion’. Let’s assume, then, that every passion has a corresponding action. On this picture, the action of the agent is the cause; the passion of the patient is the effect. Causation always involves two or more substances. Here we will also introduce a principle of proportionate causality. It is obvious, for example, that actual change or passion can only result from actual action, involving an actually existing agent and an actually possessed active power. A merely potential event cannot be the actual cause of any actual change. A merely potential agent cannot act.
 
If we were to abandon this principle of ontologically proportionate causality, we would have no explanation for the asymmetry and irreflexivity of causation. That is, we couldn’t explain why a given passion couldn’t be its own cause, promoting itself from mere potentiality to actuality. This would be tantamount to rejecting the causal principle altogether.
 
Every passion must be located in time, since time is the measure of change. What is the temporal relation (if any) between an action and its corresponding passion? There are four logical possibilities: (i) the action is earlier than the passion, (ii) the action and passion are simultaneous, (iii) the action is later than the passion, or (iv) the action is unlocated in time. I will argue that only cases (ii) and (iv) are metaphysically possible.
 
Let’s say that an entity is temporal when it has a state that is located in time. In cases (i) through (iii), the agent has a state (namely, the action) that is located in time, so the agent must be temporal. Only in case (iv) can we have an atemporal or timeless agent.
 
If an agent is temporal, then all its states are actual or potential only relative to the various moments of time (see Koons 2020, Koons forthcoming). Therefore, we cannot say that the agent’s action is actual simpliciter but only that it is actual or potential at this or that time. We must also adapt our principle of causality to incorporate this relativity: for each passion, its corresponding action must be actual at the time at which the passion occurs. Actions occurring in the past or future are, at the time of the passion, merely potential. Hence, we can rule out cases (i) and (iii).
 
Every change must have a cause. If a temporal agent A acts at time t to produce a passion in some patient, then agent A must have undergone some change that eventuated in this particular action at time t. The agent has changed from not being the agent of a particular change to being the actual agent of that change. Hence, the change in the state of the agent requires a cause.
 
If all agents were temporal, this would lead to at least one infinite causal regress at each moment of time. We could then consider the whole plurality of things undergoing change at that time and ask, What causes them to change? Since these changes are all simultaneous, nothing prevents us from aggregating them together into a single, massive event. Given the principle of causation, this simultaneous plurality of events must have a cause that is both separate from itself and actual (at t). Since the plurality includes all changes occurring at this time t, the only possible cause of the plurality of changes would be the action of an atemporal agent. An atemporal action can act at any or all times without undergoing any change itself, and so without requiring a cause.
 

I have argued that we can deduce that God is a being of pure actuality, without passive potentialities, from the fact that He is absolutely the First Cause. Joe Schmid has challenged me on this inference, rightly pointing out that the implication is not immediate. I will try here to make the connection more nearly evident.
 
To do so, I will have to introduce some technical machinery. First, I will need the concept of a logical moment. If agent A causes some effect E, then we can identify two logical moments, even if the action and the effect are temporally simultaneous. If agent A causes E, then agent A acts at one logical moment M1, and the effect is first in actuality at a posterior moment M2. The relation of priority/posteriority between logical moments is transitive and asymmetric. No logical moment is prior to itself, and no moment is prior to any moment that is prior to it.
 
We have proven that there are absolutely uncaused events. These events must belong to logical moments that are absolutely primal—i.e., logical moments that are posterior to no logical moments.
 
The second technical device that I need is the definition of a nature-constituted disjunction of properties. Let D be a (possibly infinite) disjunction of monadic properties. Then D is a nature-constituted disjunction for individual x if and only D is a minimal disjunction such that it is essential to x to have some property in D. That is, there is no disjunction D* whose disjuncts form a proper subset of the disjuncts of D and such that it is essential to x to have some property from D*.
 
Let’s say that an individual x has a full complement of properties at logical moment M just in case x has at M every property that is essential to x, and, for every nature-constituted disjunction  D of properties for x, x has a property from D at M.
 
Now I’m in a position to propose a basic principle about causality:
 

• The Completeness of Agents (COA). Necessarily, if agent x acts at logical moment M to produce some effect y, then x has a full complement of properties at M.

 
The rationale for COA is this: in order to act at a logical moment, an agent must actually exist in that moment. But an agent cannot actually exist at a moment without possessing a full complement of properties at that moment. If it didn’t possess such a full complement, it would fall short of actuality and would thereby be disqualified from acting.
 
I need one further principle:
 

• The Groundedness of Accidents (GA). Necessarily, if an individual x has property P as an intrinsic, natural property, then there is some nature-constituted disjunction D of x’s essence such that P is one of the disjuncts of D.

 
In order for a property to be an intrinsic and natural property of a thing, it must be determinate of some determinable property that is essential to that thing. A thing can’t just take on intrinsic properties willy-nilly. An intrinsic property must fulfill some essential role dictated by the thing’s nature. The requirements of a thing’s nature lay out the possibilities for a thing’s intrinsic character.
 
Let’s suppose that God is one of the agents acting at a primal moment. Suppose for contradiction that God has some intrinsic property P contingently. By GA, there must be some disjunction D such that D is a nature-constituted disjunction for God, and P is a disjunct of D. If D were a trivial disjunction (with only one disjunct), then P would be an essential property of God and so not contingent. So, D must be a non-trivial disjunction.
 
Let M be a primal moment at which God acts. By COA, we know that God possesses a full complement of properties, relative to the divine nature, at that primal moment M. So, God must possess some member of D at M. But every member of D is such that, if God possesses it at M, He must possess it contingently. Consequently, God must have some contingent intrinsic property at M. Call this property Q.
 
Now, either it is necessary that God possess Q at M, or it is contingent that He do so. Both are impossible.
 
If it is necessary that God possess Q at M, there must be some explanation of this necessity. A logical moment is not a thing in its own right, but simply a node in the causal network of the world. So, if it is necessary that God possess Q at M, this must be a result of God’s essence, and a result of God’s essence alone, since there are no prior facts to appeal to. But if God’s possessing Q is a result of God’s essence alone, then He must possess Q necessarily and not contingently.
 
There is a second reason for ruling out this first horn of the dilemma: a reason based on St. Thomas's First Way. Suppose that it is necessary for God to have Q at the primal moment M. Then, since Q is contingent, it must be possible for God to have some contrary property at some posterior logical moment. If so, this would mean that God is intrinsically changeable. But an intrinsically changeable being exists within time, not outside it. And a being that is inside time cannot be causally responsible for the propagation of time, as the Prime Mover must be.
 
If, alternatively, it is contingent that God possess Q at M, then this fact (by the PSR or principle of causality) must have a cause. But that is inconsistent with our assumption that M is a primal moment, and so no fact at M can have a cause.
 
Hence, God cannot possess any contingent intrinsic properties at any logical moment. He must be a being of pure actuality, with no passive potentiality.
 
There is a complication that is introduced by the fact of the Incarnation. The Second Person of the Trinity has two complete natures, one divine and one human. Hence, we must distinguish between the properties that God the Son has qua God and those He has qua man. Qua God, the Son cannot have any contingent intrinsic properties, for the reason given above. Qua man, the Son has many contingent intrinsic properties. In fact, having a human nature is one of those contingent properties that the Son has qua man. So, in this sense, and only in this sense, God can have contingent intrinsic properties, namely, by assuming a second nature.

Thomas Aquinas, building on arguments found in Books 7 and 8 of Aristotle's Physics, argues in The First Way (in Summa Theologiae I q2 a3, and in a parallel passage in Summa Contra Gentiles I.13) for the existence of an unmoved mover. However, there is an evident gap between such an unmoved mover and God. At the very least, Aquinas needs to show that the unmoved mover is absolutely unmovable (in all respects). If he can establish that, then he can conclude that the First Mover must exist outside of time. And, in order to exist outside of time, the First Mover must lack all passive potentiality (i.e., be a being of Pure Act).
 
Aristotle and Aquinas are both well aware of this gap, and they have a definite strategy for filling it. The argument goes something like this:
1. Assume (for contradiction) that the First Mover is changeable in some respect.
2. Necessarily, time passes if and only if change occurs.
3. All motion in fact depends on the activity of the First Mover (established by the main argument of the First Way).
4. If the First Mover were changeable in any respect, then it could be in a state in which it failed to cause any motion.
5. To be in such a state, the First Mover would have to be in that state for some period of time (since nothing can be in a state in a single instant).
6. Since all motion in fact depends on the activity of the First Mover, if the First Mover were in a state in which it failed to cause any motion, there would be no change during the period in which it is in that state.
7. If there were no change during that period, time would not pass during that period.
8. If a period has a temporal duration, time must pass during it.
9. There would be a possible state of the world during which time both does and does not pass. Contradiction.
10. So, the First Mover cannot change in any respect.
 
The crucial premises are 4, 5, and 6. Let me take 5 and 6 first.
 
Premise 5. This is based on Aristotle's resolution of Zeno's paradoxes in the Physics. Instants of time are not parts of time--they are only boundaries of such parts. Hence, nothing happens during an instant. Nothing can be in a state of activity or inactivity for only an instant. Instants can only mark the beginning or end of a period of activity or inactivity.
 
Premise 6. This depends on a kind of subtraction principle. If all change in the actual world depends on the First Mover and there is a possible state of the First Mover in which it would cause no change, then there is a possible world where no change occurs. We can simply subtract the activity of the First Mover from the actual world without being forced to add any new source of motion.
 
So, the crucial assumption is premise 4.  Suppose the First Mover is changeable in some respect. Why think that it must be changeable into a state in which it would cause no motion at all? Why couldn't it have a nature such as to cause motion in every possible internal state, while admitting of more than one such possible state?
 
There is some plausibility to the idea that the activity of a thing must depend on the thing's internal state, and that this dependence entails that there be some internal state in which no activity would result. However, this seems far from airtight to me.
 
I think there's a better strategy for defending premise 4--one that is not explicit in the texts of either Aristotle and Aquinas, but which lies quite close to their conception of time and motion.  If something is changeable in any respect, then it lies within time. If a thing lies within time, then its natural activity through time depends on the metaphysically prior passage of time. So, it is impossible for the activity of something changeable to be the ground for the passage of time itself. Yet, that is exactly what the First Mover must do. Hence, the First Mover must be absolutely unchangeable.

I've been working a lot lately on Aquinas's First Way, the argument from motion, which builds on Aristotle's arguments in Books 6, 7, and 8 of the Physics, and which Aquinas develops at length in the Summa Contra Gentiles, Book I, chapter 13. Aquinas calls it the "most manifest" way of proving God's existence, but it has not been popular with commentators or critics. Sir Anthony Kenny is thoroughly dismissive of it in his book on the Five Ways. He quotes Suarez, who wrote: "Taken by itself, this argument is shown in many ways impotent to prove there is anything immaterial in reality, let alone that there is a first and uncreated substance." (Disputationes metaphysicae XXIX, I, 7)
 
The basic argument is quite simple:
1. Some things are in motion (experience change).
2. Everything that is moved is moved by something else (no self-moving).
3. A chain of movers cannot regress to infinity.
Therefore, there must be at least one unmoved mover.
 
Almost everyone accepts premise 1, so all of the action concerns premises 2 and 3. In addition, the argument faces a serious "gap" problem: how does one get from an unmoved mover to a "first and uncreated substance" (as Suarez puts it)? By paying careful attention to the arguments, and by exercising a little imagination and creativity, we can rehabilitate the First Way into an argument that deserves consideration alongside the many other sound theistic proofs that have been crafted recently.
 
Before getting into the details, we have to consider first what Aristotelians like Aquinas assume about the nature of change and time. There are essentially only two options here: either time is fundamental, and change is definable in terms of time (Russell's at-at theory of change), or change is fundamental and time is definable in terms of change (time is the "measure" of change). There are very strong considerations in favor of the second, Aristotelian option. At-at theorists have never been able to develop a successful explanation of the direction of time or of causation. See, for example, Huw Price's Time's Arrow and Archimedes' Point, or Alex Pruss's critique of David Lewis's counterfactual-conditional account of time's arrow. In addition, at-at theorists cannot explain how we are able to measure the true duration of processes, without making the ad hoc assumption that each kind of process has a fixed velocity (like the speed of light). Aristotle's option avoids both of these defects.
 
Famously (or, infamously, depending on your point of view), Aristotle defines change in Book III of the Physics as the actuality of the potential qua potential. Aquinas does a good job of unpacking this somewhat cryptic statement in his commentary on the Physics (Lectures 2 and 3 of Book III). Potentiality is, for Aristotle, something real and irreducible. It is a feature of all natural things, a kind of "natural intentionality" as David Armstrong and George Molnar put it. When a thing has a certain potentiality, it is pointing in a specific direction to a particular, non-actual situation. Motion occurs when such a potentiality is partially but not completely actualized.
 
Take a stone that is in the process of becoming hotter. Let's say that the stone is currently lukewarm. The stone has both the potential of being colder and the potential of being hotter, but only one of these two potentialities is now partially actualized, namely, the second of the two. That is what constitutes the stone's becoming hotter. Once the stone has reached its equilibrium state, it will have fully actualized that potential and will no longer be in motion (change). At that point in time, neither of the stone's potential will be partially actualized. Both will exist only in a state of perfect potentiality.
 
All change is, therefore, inherently directional. It is always change toward some unrealized state or states. Time passes as change occurs, and time itself is therefore also directional, pointing from the terminus ab quo and toward the terminus ad quem of the process of change. Moreover, the measure of time consists in the completion of certain standard processes, like the movement of light across a fixed distance. Thus, there is no mystery about the arrow of time, nor about the fixity of the velocity of these standard processes. In addition, the Aristotelian option yields the impossibility of time travel, since this would involve making the end of a process into its beginning.
 
Time passes because change happens, and not vice versa. Once we grasp this, we see that any law of inertia is completely irrelevant to the argument from motion. A law of inertia dictates that a body will continue to move in a straight line and at a constant speed as time passes. The inertial motion of the body thus depends on the movement of time and cannot be the explanation for the passage of time. The passage of time requires the continuous occurrence of change that is independent of time, in a way that no merely inertial motion can be.
 
Thus, the First Way points us toward a crucial metaphysical question: what is the source or explanation of this time-independent change?