As I mentioned in my last post, I do not think that parcels of prime matter persist for longer than an instant. How then can prime matter fulfill its traditional role (from Physics, Book II) of being the enduring substrate for substantial change: that is, being the persisting subject that is successively informed by one substantial form and then by another? In my view, it is not prime matter as such that persists, but there is a derived entity, which we can call "persisting matter" that does do so. Persisting matter is an example of what Roderick Chisholm called an 'ens successivum'. That is, a gob of persisting matter is fundamentally a series of packets of instantaneous prime matter that are tied together by a series of causal connections. These causal connections constitute what Hans Reichenbach termed a 'genidentity' relation between pairs of packets of prime matter. Two packets of prime matter count as successive versions or temporal parts of persisting matter when they are linked together by an appropriate causal relation.
 
When one substance is corrupted and another generated in its place, there is always a third entity involved: the agent of the corruption/generation. This third entity must be disjoint from the other two--neither generated nor corrupted at the moment of substantial change, but persisting through it. The agent acts upon the prime-matter packet that constitutes the corrupting substance, replacing it with a new prime-matter packet that constitutes the new, generated substance. This causal relation ties the two packets together into a single stream of "persisting matter". In the natural order, corruption and generation cannot occur unless both the old and new substance contain prime matter, and some external agent causes the replacement of the old matter by the new.
 
Let's consider a less drastic case of substantial change: substance A grows by incorporating part of substance B (which shrinks as a result). In this case, there are just two substances involved, since A can be the agent of its own growth, acting on part of the prime matter of B, causing it to be replaced by new prime matter that constitutes the new part of A. Again, this causal connection will tie together the old packet of prime matter and the new. We don't need a fundamentally persisting entity at the level of prime matter.

One of the more controversial and difficult topics in Aristotelian/Thomist philosophy of nature is that of prime matter. According to A&T, material substances are in some sense "composed" of substantial form and prime matter. Prime matter is somewhat mysterious stuff. Thomas tells us (in De Ente et Essentia) that it cannot be defined or understood in itself but only in relation to form and the composite substance. Thomists often refer to prime matter as "pure potentiality", as though it had no actuality at all. Moreover, prime matter is supposed to play some central role in individuating material substances (that is, in grounding the numerical distinctness of distinct members of the same infima species), even though prime matter is not itself an individual, and even though all the world's prime matter is in some sense numerically one. How to make sense of all this?
 
In my own view, the primary role of prime matter is that of individuation Two "packets" of prime matter are primitively, fundamentally numerically distinct. Their distinctness is not grounded in anything else. Thus, prime matter has something actual (even necessary) about it--namely, its numerical identity to itself and its numerical distinctness from all other packets of prime matter (whether actual or merely potential, past, present, or future). In addition, the mereological facts about packets of prime matter (i.e., which packets are proper parts of which, which pairs of packets overlap) are themselves necessary truths (and hence, actual truths). Prime matter is a mass of gunky bare particularity. There are no atomic bits of prime matter--each packet of prime matter is divisible into smaller bits.
 
Thomas explains, in De Ente, that it is signate matter that individuates--prime matter considered under "determinate dimensions". What can this mean? Some commentators suppose that packets of signate matter are individuated by their accidents of spatial extension (shape, size, location). However, this leads to a vicious circularity: signate matter individuated by quantitative accidents of space, accidents of space individuated by composite substances, and substances individuated by signate matter. I would propose that a packet of signate matter is simply a packet of prime matter, and that packets of signate/prime matter are primitively individual. Remember that prime matter can only be understood relationally. So, a packet of signate matter is simply some prime matter considered as the individuator of some quantitative accident of space. It is the packet of matter that individuates the accident, not vice versa. But it is in relation to that individuated accident that we are able to define and understand a particular packet of prime matter. Individuation is a metaphysical relation, while understanding is a rational or epistemic relation. The packet of prime matter is metaphysically prior to the spatial accident, but the spatial accident is prior in the order of understanding.
 
St. Thomas does not say this, but I think that the "determinate dimensions" of a packet of signate matter must include a temporal dimension as well as a spatial one. That is, I propose that all packets of prime matter exist only for a single instant. This is because substantial form is the principle of rest/motion, and so it is also the principle of persistence. Prime matter as such cannot persist.

​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.
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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).