Here are four arguments in support of my “master argument” for prime matter.
- Symmetrical (Max-Black) Worlds (Steps 1-5)
Imagine a world consisting of a single perfectly spherical and continuous substance. It will have infinitely many parts – e.g., an uncountable infinity of hemispheres. Each hemisphere will instantiate the very same species of quantitative accident (i.e., size and shape). If we are Platonists or Aristotelians, there must be something that is not hemispheric in itself in the sphere that is able to receive hemisphericitiy. Alex’s modes are hemispheric in themselves, and so they would not qualify. Hence, we need prime materials (bits of prime matter) which are primitively distinct from each other but not primitively shaped or sized.
2. Another argument for persisting substrates (Step 14)
Imagine a world consisting initially of just two material substances. Let’s suppose that they engage in an act of mutual destruction at time t, producing two new substances. Let’s assume that we are relationists about external space—i.e., external space does not consist of a thing or plurality of things but only of relations among substances and their parts. Let’s also assume that the universe is spatially symmetrical around an axis separating the two substances, both before and after the destruction (so A and B are conspecific, as are C and D). Let’s call the initial two substances A and B, and their successors C and D.
Question: are there any spatial relations between A and C or D? Can we say that C is or is not located where A was located?
The laws of nature (or the causal powers, both active and passive, of A and B) ensure that two new substances are produced, and let’s say that they also guarantee that one of the new substances be located where A was and the other where B was. But what is the truthmaker for the proposition that, e.g., C is where A was? The causal relations linking C to A are exactly mirrored by relations between C and B, and between D and A. So, the causal relations are sufficient to make it true that C and D are located in time after A and B, and they suffice to ensure that either C or D is where A was, but they do not seem sufficient to make it true or false that C in particular is where A was. This doesn’t seem to be a case of indeterminism: we can’t even assign a probability to the proposition that C is where A was.
I’m assuming something like this: if the laws of nature ensure that a particular interaction causally explains the truth of an exclusive disjunction, and the laws do not assign any probability to either disjunct, then the laws must entail that the interaction causally explains one of the two disjuncts.
We can find such a truthmaker if and only if there is some residue of A that persists through the substantial change. This can’t be any accident of A, so it must be some prime material.
3. Yet another argument for Persistence of Prime Matter (Step 14)
Suppose that there is a case of substantial change in which no prime material persists. For simplicity’s sake, let’s say that agent A destroys substance B, producing new substance C, where B and C differ in species. If B’s prime materials do not survive, and if C must have a full complement of prime materials (one for every spatially circumscribed part), then the action of A on B must be causally sufficient either to create a new set of prime materials or to appropriate existing prime materials from some other substance D. The second option seems too complicated to take seriously, so let’s assume that some prime materials are generated de novo. Assuming that the interaction is deterministic, there must be some function f from prime materials to prime materials, such that A has the power to generate prime material f(x) for every x undergirding B. The simplest such function is f(x) = x, and we have no reason to introduce further complexity here. Prime materials are not ontologically dependent on any particular substance, so there is no bar to their persisting through substantial change.
4. A More Fundamental Argument for the same conclusion?
Perhaps there is a more fundamental reason why, in the Aristotelian framework, persistent prime matter is needed. All natural action in Aristotle’s scheme involves the actualizing of a pre-existing potentiality. I think Anna Marmodoro is right in thinking that the actualizing of a potentiality does not consist in producing some state or condition of the patient but simply a change in ontological status of an enduring state. The state is elevated from being merely potential to being actual. Why does that seem right? I can’t adequately explain why, at least not yet, but let’s tentatively take it on board.
Now consider the passive potentiality of a substance vis-à-vis substantial change. E.g., the potential that I have to give rise to a corpse (to over-simplify a bit).[1] Now I think it’s obvious that I don’t have the potentiality to be a corpse: once the corpse exists in actuality, I no longer do. I have the potentiality to give rise to a corpse, or to be succeeded in space and time by a corpse. But can this be a fundamental potentiality of mine? Not if Marmodoro is right, since her thesis would entail that I must have already the potentiality to be a corpse. I have the potentiality to be succeeded by a corpse by virtue of having something as a constituent (prime matter) which has the potentiality to be a corpse, when suitably informed. But this requires that my prime matter survive my demise.
Another consideration in support of this idea: Aristotle wants to reduce change and time to terms involving only actuality and potentiality (Physics II). So, we can’t understand substantial change in terms of a potential to be succeeded by a corpse, since this is to introduce time into our account of change.
Perhaps this is too quick. After all, I have the potentiality not just to be succeeded by a corpse (a non-human substance) but to be succeeded by a corpse of a very particular kind (just over 6 foot tall, and so on). And the prime matter in itself does not have (in a preferential way) this particular potentiality. It has it only by virtue of being informed by various accidents which come to it via my substantial form. So, what is it that has this more specific potentiality—to be a corpse with certain quantitative and qualitative accidents? Not me, and not my prime matter as such.
Could I say that some of the quantitative and qualitative accidents that attach to proper parts of my body (in particular, all of those accidents which would have specifically identical counterparts in my corpse) really to attach to my prime matter in such a way that they too can survive my death? I don’t think so. To say that is to abandon a core commitment of hylomorphism: the ontological priority of the whole substance over its parts and accidents.
However, I don’t think that I have to say that. I can say that prime matter has the preferential potential to be a corpse of a certain kind by virtue of being informed now by quantitative and qualitative accidents. But the potential to be a corpse of that kind is a potential possessed by the prime matter and not by the accidents. The accidents ground the fact that the prime matter has the potential, but they are not themselves the subject of the potential. Hence, all that matters is that the prime matter persist. The accidents need not.
But does my prime matter really have the potential to be a corpse? Yes and no. We have to recognize that both before and after the substantial change we have two coincident objects. After the change there is both the prime matter informed by a cadaverous substantial form and the substantial corpse itself. They are coincident objects, with distinct modal and temporal profiles, and with the former causally prior to the latter. My prime matter has the potential to be informed by different substantial forms, and so the potential to be so informed and not merely to become so informed. And that’s all that’s needed.
[1] A corpse is actually a heap of much smaller substances, but for simplicity’s sake I’ll pretend that it is just one substance.
The Analytic Thomist 