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.