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.
 

Good metaphysical arguments don’t operate in a vacuum. They occur within a theoretical framework provided by a successful, time-tested research program. The oldest and most successful research program in metaphysics is that of the so-called perennial philosophy, beginning with Plato and Aristotle, extended by the Neo-Platonists, and developed in Western scholastic philosophy. At the core of this program is the distinction between two modes of being, potential and actual, along with a commitment to a strong principle of proportionate causation, that is, the principle that the greater the effect, the greater the cause must be. Many contemporary philosophers have defended this program (myself included).
 
Another important assumption of the perennial philosophy concerns the dependent nature of time. Time is not merely a static dimension within which events and states can be located. Such a Block Universe picture of time would leave us with many inexplicable data, including the irreversible direction of time and causation, the fixity of the past and the openness of the future, the basis of the Second Law of Thermodynamics and other irreversible laws, and our universal experience of the passage of time. Aristotle provides a much more satisfying account of time in Book III of his Physics: time is simply the measure of change. Change is the more fundamental phenomenon, and the distinctive characteristics of time are derivable from the nature of change.
 
This hypothesis requires that change itself not be given a real definition in terms of time. That is, we must reject Bertrand Russell’s At-At theory of change (Russell 1922, Lecture VI), according to which a thing x undergoes change just in case it has one feature at some time t1 and a contrary feature at some later time t2. Instead, we must define change as Aristotle does. A thing x is undergoing change just in case there is some feature F of such a kind that x has a potentiality for F-ness that is in some degree of partial actualization. This definition does not make any reference to moments of time or their temporal relations of earlier and later. However, it does entail that if some entity x is undergoing change with respect to F-ness, there must be earlier and later times of such a kind that x is progressively closer to F at the successively later moments of time. Partial actualization requires at least two distinct modes of being (i.e., instants of time), one in which x is (still) only potentially F, and another in which it is actually F. In fact, there must be an infinite number of such instances, each with a different degree of actuality of x’s F-ness, with the full actualization of x’s potential for F-ness occurring in exactly one of these. The direction of time is determined by the prior direction of change: if x’s potentiality for F-ness is partially actualized, and this partial actualization corresponds to a set of moments, then the later moments in that set must be ones in which x is closer to being F.
 
Now let’s add to this picture the assumption 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.

It is important to recognize that accepting this Aristotelian framework does not depend on deciding the A Theory/B Theory issue. In particular, it does not depend in any way on so radical a thesis as Presentism—the view that everything that is actual is actual at the present time. It is compatible with Aristotelianism that there be infinitely many different modes of actuality, one for each moment of time, past, present and future. All that is required  is the assumption that to effect a change that is actual in mode t, the agent must have a power that is actual in that same mode, i.e., at that same time.
 
This viewpoint would not be consistent with a non-Aristotelian version of the B Theory—one in which every event at every moment of time is actual in exactly the same way. On such a Block Universe model, there is no room for defining change as the actualization of a specific potential. Such a model, as J. M. E. McTaggart long ago noted, fails to take seriously the reality of change.
 

As Alexander Pruss has observed (Pruss 2009), the Grim Reaper paradox suggests not only that no finite time period can be divided into infinitely many sub-periods but also that it is impossible that there should exist infinitely many time periods, all of which are earlier than some event. It seems to provide grounds for thinking that time must be bounded at the beginning: that there must be a first period of time. If not, we could simply construct a new version of the Grim Placer paradox. As in the original version, we postulate the possibility of a Grim Placer, who creates a particle and places it at a designated spot, if and only if no particle is already located at a spot corresponding to any earlier Placer. In this version, Placer 1 is set to act at the first moment of 1 B.C., Placer 2 at the first moment of 2 B.C., and so on ad infinitum. Once again we can generate the contradiction: some particle must be placed within d meters of the plane, but there is no finite distance from the plane such that a particle could have been placed there.
 
Let us try to be more explicit about the premises needed to generate the paradox. First of all, we must assume that a single, isolated Grim Placer scenario is metaphysically possible:
 
P1. Possible Grim Placer (PGR). There are  numbers d and m such that for every positive integer n there is a possible world W and a region R such that R has a finite temporal duration d seconds, there is a Grim Placer wholly contained within R, and throughout R the Grim Placer has the power and disposition to create a “Fred” particle and place it at a designated position m/2^n  meters from the plane P if there is no unique particle located at m/2^i meters from P for some i >n (eliminating all other particles located within m meters of P, if there are more than one), and otherwise to maintain the unique Fred particle that is located at m/2^i meters from P in its initial position.
 
Secondly, we appeal to some version of David Lewis’s Patchwork Principles (Lewis 1983, 76-7). Much, if not most, of our knowledge of possibility is based on patchwork principles, since we have little direct access to alternative possibilities. Instead, we have to rely on our direct knowledge of the actual world, as well as the license to cut-and-paste or recombine various regions of the actual world into a new arrangement.
 
Binary Spatiotemporal Patchwork. If possible world W1 includes spatiotemporal region R1, possible world W2 includes region R2, and possible world W3 includes R3, and R1 and R2 can be mapped onto non-overlapping parts of R3 (R3.1 and R3.2) while preserving all the metrical and topological properties of the three regions, then there is a world W4 and region R4 such that R3 and R4 are isomorphic, the part of W4 within R4.1 exactly duplicates the part of W1 within R1, and the part of W4 within R4.2 exactly duplicates the part of W2 within R2.
 
Following Lewis, I will assume that ‘intrinsicality’ and ‘exact duplication’ are inter-definable:
 
Definition of Intrinsicality: a property P is intrinsic to a thing x within region R in world W if and only if x is P throughout R in W, and every counterpart of x in any region R’ of world W’ whose contents exactly duplicate the contents of R in W also has P throughout R’.
 
Binary Spatiotemporal Patchwork licenses recombining region R1 from world W1 with region R2 from world W2 in any way that respects the metrical and topological properties of the two regions, so long as there is enough “room” in spacetime as a whole to fit the two regions in non-overlapping locations (as witnessed by the two regions R3.1 and R3.2 in world W2). The Binary Patchwork principle can plausibly be generalized to the case of infinite recombinations:
 
P2. Infinite Spatiotemporal Patchwork (PInfSP). If S is a countable series of possible worlds, and T a series of regions within those worlds such that Ti is part of Wi (for each i), and f is a metric and topology structure-preserving function from T into the set of spatiotemporal regions of world W such that no two values of f overlap, then there is a possible world W* and an isomorphism f* from the spatiotemporal regions of W to the spatiotemporal regions of W* such that the part of each world Wi within the region Ri exactly resembles the part of W* within region f*(f(Ri)).
 
In order to apply the Patchwork principles to Benardete's story, we must assume that the relevant powers and dispositions are intrinsic to the things that have them when they have them. Otherwise, we cannot assume that the joint possibility of an infinite number of Grim Placer scenarios follows from the possibility of a single scenario, taken in isolation.
 
Intrinsicality of the Grim Placers’ Powers and Dispositions (PDIn). The powers and dispositions ascribed to each Grim Placer are properties intrinsic to that Placer in its corresponding region and world.
 
Our hypothesis for the reductio will be the possible existence of a world with an entity that has an infinite past:
 
HIP. Hypothesis of the Possibility of an Infinite Past. There exists a possible world W´ and a spatiotemporal region R´ in W´ such that R´ has infinitely many temporally extended parts such that these parts can be put into a sequence (ordered by the natural numbers) in which each successive part in the sequence is within the backward time cone of its predecessor, and each part is large enough to contain a Grim Placer.
 
1. Start with a possible Grim Placer in world W and region R, with finite duration d. (From PGP, the Possibility of Grim Placer)
2. Next, locate a world W' with a region R' containing a non-well-founded infinite series of non-overlapping temporal parts, each of duration d and each in the backward time cone of its predecessor. (Assumption of HPIF, for reductio)
3. Find a single possible world W* with region R* containing a non-well-founded infinite series of non-overlapping temporal parts (R1, R2, etc.), with each Ri containing a counterpart of the Grim Placer. (From 1, 2, and Infinite Spatiotemporal Patchwork)
4. Assume that, in world W*, there is after period R1 no particle located at any distance m/2^n from P, for any n > 0. (Assumption for second reductio)
5. Therefore, there is after period R2 no particle located at any distance m/2^n, for any n > 1. (From 4)
6. Grim Placer #1 in period R1 in world W* placed a Fred particle at distance m/2 from P. (From 5, and the Possibility of Grim Placer)
8. Contradiction (4 and 6). So, after R1 in W*, there is some particle located at some distance m/2^n from P, for some n > 0. 
9. Therefore, no particle is located any distance m/2^j from the plane P, for any j > n. (From 8, the Possibility of the Grim Placer)
10. Therefore, no particle is located any distance m/2^j from the plane P, for any j > n+1. (From 9)
11. Therefore, Grim Reaper n + 1 placed a particle at distance m/2^(n+1) from P. (From 10, and the Possibility of the Grim Placer).
12. Contradiction (9 and 11).
13. So, there is no possible world containing a non-well-founded infinite series of non-overlapping temporal parts, each of duration d0 and each in the backward time cone of its predecessor. (Negation of HPIF)
 
From the conclusion of this argument (step 12), we can deduce premise P3:
 
P3. Every non-eternal thing began to exist at some point in time (since the past of each non-eternal thing is finite in length).
 
If any temporal thing had an infinitely long past, then that past would include an infinite series of non-overlapping periods of length d seconds, all in the past light cone of the current state of the thing in question, in contradiction to step 12. Thus, to reach the conclusion of an eternal first cause, we need only add the assumption of causal finitism. In the next section, I will argue that the Grim Placer paradox can be generalized into an argument for causal finitism.

In Jose Benardete’s paradox, we are to suppose that there is an infinite number of Grim Reaper mechanisms, each of which is engineered to do two things: first, to check whether the victim, Fred, is still alive at the Grim Reaper’s appointed time, and, second, if he is still alive, to kill him instantaneously, and, if he is already dead at the appointed time, to do nothing. The last Grim Reaper (Reaper 1) performs this dual task at exactly one minute after noon. The next-to-last Reaper, Reaper 2, is appointed to perform the task at exactly one-half minute after noon. In general, each Reaper number n is assigned the moment 1/2^(n-1) minutes after noon. There is no first Reaper: for each Reaper n, there are infinitely many Reapers who are assigned moments of time earlier than Reaper n’s appointment.
 
It is certain that Fred does not survive the ordeal. In order to survive the whole ordeal, he must still be alive after one minute after twelve, but, we have stipulated that, if he survives until 12:01 p.m., then Reaper 1 will kill him. We can also prove that Fred will not survive until 12:01, since in order to do so, he must be alive at 30 seconds after 12, in which case Reaper 2 will have killed him.  In the same way, we can prove that Fred cannot survive until 1/2^(n-1) minutes after 12, for every n. Thus, no Grim Reaper can have the opportunity to kill Fred. Thus, it is impossible that Fred survive, and also impossible that any Reaper kill him! However, it seems also to be impossible for Fred to die with certainty and yet to do so without any cause.
 
The original Grim Reaper paradox requires some assumption about causality: that Fred cannot die unless someone or something kills him. I would like to eliminate that dependency. Consider the following variation: the Grim Placer. In place of asking whether a pre-existing victim Fred is dead or alive, we will focus instead on the question of whether or some Grim Placer has issued a death warrant. Let’s say that each Grim Placer #n can issue a death warrant by placing a particular kind of point-sized particle in a designated position, at exactly the distance of d/2^n meters from a plane P. Each Grim Placer #n checks to see if a particle is already at a distance of d/2^i  meters from plane P, for some i > n: that is, he checks to see if any earlier Placer has issued a “warrant”. If a particle has already been placed in one of the designated spots, then the Grim Placer #n does nothing, other than maintaining the status quo.
 
If there is no particle in an appropriate location, then the Grim Placer #n issues his warrant, placing a particle exactly d/2^n meters from P. We can now prove both that at 12:01 that some particle is located within d meters of the plane, and that no particle is located there. Suppose that there is no particle at any location d/2^i meters from plane P, for any i. This is impossible, since if there were no particle d/4 meters from P, then Grim Placer #1 would place a particle in the position d/2 meters from P.
 
Thus, there must at 12:01 pm be some particle in an appropriate position. Suppose that the particle is located at that time in position d/2^n meters from P, for some n. This means that every Grim Placer whose number is greater than n did nothing, contrary to our hypothesis. Thus, this option is also impossible.

​As Alexander Pruss has observed (Pruss 2009), the Grim Reaper paradox suggests not only that no finite time period can be divided into infinitely many sub-periods but also that it is impossible that there should exist infinitely many time periods, all of which are earlier than some event. It seems to provide grounds for thinking that time must be bounded at the beginning: that there must be a first period of time. If not, we could simply construct a new version of the Grim Placer paradox. As in the original version, we postulate the possibility of a Grim Placer, who creates a particle and places it at a designated spot, if and only if no particle is already located at a spot corresponding to any earlier Placer. In this version, Placer 1 is set to act at the first moment of 1 B.C., Placer 2 at the first moment of 2 B.C., and so on ad infinitum. Once again we can generate the contradiction: some particle must be placed within d meters of the plane, but there is no finite distance from the plane such that a particle could have been placed there.

Here again is my Pruss-inspired version of the Kalam argument, relying on causal finitism:

P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist (at some point in time), the event of its beginning to exist must have a cause.
P3. Every non-eternal thing began to exist at some point in time (since the past of each non-eternal thing is finite in length).
P4. If the yy cause the xx to begin to exist at t, then the yy exist at t or at some time earlier than t or eternally. 
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.

There is, however, a problem with premise P3. Causal finitism alone does not seem to give us a finite past, not even a finite history for a given thing. 

​Suppose that we have a thing x that exists in time and suppose that causal finitism is true. This means that each event in the history of x must have a finite causal history. Is this enough to entail that x must have begun to exist at some point in the past? Couldn’t the history of x begin with an event or state that is infinitely extended in the past direction? Let’s call such an initial state a simple infinitely long past state or SILPS.
 
We can refute the possibility of a SILPS by posing a dilemma: either time itself has an intrinsic measure (in which sense time can pass in the absence of change) or it does not. If time does not have an intrinsic measure, and the initial state of x is a simple state, without discrete parts, then that state cannot have any temporal duration, much less an infinite duration (since there are, ex hypothesi, no changes concurrent with this state by which time could be extrinsically measured). Hence, we must suppose that time itself has an intrinsic measure.
 
However, this is also inconsistent with a SILPS, since if time has an intrinsic measure, then any extended period of time has discrete proper parts corresponding to the measurable proper parts of that period of time. If an event or state has a duration corresponding to that extended period, then it too must have temporal parts corresponding to the proper parts of the period of time. Thus, the state is not simple or “uneventful” after all. This is a strong argument, although it will not persuade those who think that extended simples (like extended Democritean atoms) are metaphysically possible.
 
Here is a version of the argument without the assumption of a finite past (P3):
 
P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist, the event of its beginning to exist must have a cause.
P3.1. If something has existed for an infinite period of time, then it must have an infinite causal history (because a simple infinitely long past state is impossible).
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.
 
Since my argument for P3.1 is less than ironclad, I will argue in future posts both for causal finitism and for the finitude of the past of each temporal thing. This provides support for both arguments: the original argument (which depends on both causal finitism and the finite duration of the past) and the revised argument (which depends on causal finitism and the impossibility of SILPS).

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?

​My new intermediate theory of time has several advantages. First of all, it gains all the advantages possessed by the A Theory. It accords with our temporal phenomenology, including our sense of the fleetingness of the present moment. Each mode of being is associated with each moment of time only fleetingly. Second, it supports our intuition that the order of time is unique and fundamental. Time really flows from the past into the future in a uniquely directed, inexorable way. The flow of time is not a mere appearance or convention. Third, it provides an explanation for the impossibility of time travel, enabling us to explain why we cannot encounter instances of the Grandfather Paradox (a time-traveler who murders his own grandfather). Later moments in time are later by virtue of having a smaller set of potential futures. Consequently, it is logically impossible for a later moment to become earlier than an earlier one via time travel.
​
At the same time, the intermediate theory reaps many of the advantages of the B Theory (Eternalism). It is fully compatible with God's exhaustive knowledge of the future. The future is as real as the past, and so there is no bar to God's eternally knowing all moments of time in a single act of knowledge. The intermediate theory is also fully compatible with the standard interpretation of relativity: that is, the intermediate theory is compatible with the non-existence of a global, absolute relation of simultaneity between distant (space like separated) events. The flow of time is real, but flow of time at one event need not be globally synchronized with the flow of time at distant events. Every worldline (corresponding to the life of a substance or quantitative part of a substance) has its own Metaphysical Clock, and distant clocks are not absolutely synchronized. The intermediate theory also avoids the truthmaker problems that afflict Presentism.

 
I've been seeking for some time a third alternative to the A and B Theories of time. Here is my current best effort.
 
J. M. E. McTaggart introduced in 1908 a distinction between two theories of time, the A and B Theories. The A Theory can be defined in either of two ways, one entailing the other. Hence, there is actually a trichotomy of theories of time: strict A, strict B, and intermediate theories.
 
The narrow or strict definition of A Theory requires that the theory designate a single moment of time as metaphysically privileged, as the absolute Present moment. The broader definition of A Theory requires only that there be a real passage of time: that is, that there exist some metaphysically fundamental Clock whose successive states mark out the passage of time. It is clear that any strict A Theory must also be a broad A Theory, since the movement of the absolute Present would be a metaphysical Clock of the kind required. However, as we shall see, there are alternative Clocks that could be posited.
 
Similarly, strict B Theory rules out the existence of a metaphysical Clock, while broad B Theory requires only that there be no metaphysically privileged Present. Hence, there are three possible positions: strict A Theory, strict B Theory, and the Intermediate Theory (which posits a metaphysical Clock but no privileged Present).
 
I think we must embrace the thesis that the copula itself must be tensed (Johnston 1987). As I mentioned above, ‘being’ is said in many ways. There are distinct modes of present/actual being, one for each B moment. Events (including substances and their accidents) have different modes of actual being, depending on when they exist. ​Consequently, if m is the mode of being corresponding to 100 B.C. and n the mode corresponding to 100 A.D., then the death of Caesar is_m possible-in-the-future, and it is_n necessary-in-the-past. If o is the mode corresponding to the moment of Caesar’s death, then that death is_o simpliciter. In addition to such temporal modes, there is a single mode of eternal being, e. All substances and accidents are_e simpliciter, but none are_e past or future. Eternal being is the focal meaning of ‘being’.
 
There is now no contradiction in supposing that Caesar’s death is_m possible-in-the-future but is_n not possible-in-the-future, nor is_e it possible-in-the-future, since distinct modes of being are involved.
 
The various temporal modes of being are causally ordered, as mentioned above. If m is prior to n, then that things are_n as they are is causally dependent on how things are_m.
 
Suppose that the modes of being are not permanently attached to B moments of time but are in continuous motion through the B series. In other words, the mode of being m, which is the mode associated with the present moment, was once associated with 100 B. C. and will one day be associated with 2100 A.D. A function that relates modes of being to the B moments to which they belong would then constitute a metaphysical Clock, keeping track of the real passage of time without introducing a uniquely privileged Present.
 
If we relate this to the Fregean idea of direct acquaintance with the present moment, we could imagine that all of my memories and all of my anticipations of the future involve the very same mode of being. I remember when this mode, say m, was associated with the year 1980, and I look forward to when it will be associated with the year 2030. Thus, the temporal phenomenology of the fleetingness of the present and of the inexorable forward motion of time would both be vindicated, if we think of my present consciousness as borne along by the same mode of being. This degree of dynamism can be squared with a rejection of strict A Theory, since there is a future self who remembers when he was_n a child, and a past self that looks forward to being a philosopher, where n and o are modes of being associated now with future and past times, modes with which I am not now acquainted. My present mode m is not metaphysically privileged, even though it does move through the B series.

​The key to a dynamic (Aristotelian) B Theory of time is a notion of relative potentiality. Some things are potential relative to one event or point in time but no potential relative to others. So, for example, my winning the Noble prize in 2020 is potential relative to some point in my life (say 1960) but clearly it is potential relative to the present (Dec. 31, 2020). We can use relative potentiality to define relative actuality: an event E is actual relative to time t if it is absolutely actual and nothing is potential relative to t that is not also potential relative to E.
 
But what can it mean to say that one event is potential relative to a time or another event? Isn't potentiality a simple property and not a binary relation? The right B-Theoretic answer, I think, is to say that 'being' is said in many ways (as Aristotle says in Metaphysics Gamma 2). There are many ways of 'being' potential. These different modes of being correspond to different moments in time.
 
How do substances actualize potentialities? If a substance has an active power at t, and some patient has at all times prior to t the potentiality relative to those times of being changed in the appropriate way, then it is possible for t to be a time at which the agent exercises its power on the patient, actualizes the patient's potentiality. Suppose this involves the patient's becoming A (where A is some contingent accident). The patient's being A at t is absolutely or eternally actual. Nonetheless, it is actual because of the agent's exercise of its active power at t, and because of the patient's potentiality for being A in the preceding interval of time. Thus, some actual facts are causally explained by others, which corresponds to their location in time.
 
Formally, we can model this dynamic B Theory by using a series of trees. Each tree has a trunk (representing the past and present) and a set of branches, representing the potential futures. Each moment of time has its own tree, representing what is potential and what is actual relative to that time. One moment of time is later than another just in case it's tree is smaller, in the sense that the later tree will have a longer trunk and fewer branches. As time passes, branches (representing relative potentialities) fall off the tree (to use Storrs McCall's vivid image). We can then define two kinds of future tense: that which might yet happen (with reference to the present moment's future branches) and that which will actually happen (with reference to future trees).