Maverick Philosopher

What is a Limit Concept? The Example of Prime Matter

In an earlier entry I suggested that the concept God is a limit concept or Grenzbegriff.  I now need to back up a few steps and clarify the concept limit concept and give some non-divine examples.  If I cannot supply any non-divine examples, then I might justifiably be accused of ad-hoc-ery.

Terminological note: The term Grenzbegriff first enters philosophy in 1781 in Kant's Critique of Pure Reason. Curiously, he uses the term only once in the works he himself published. The term surfaces a few more times in his Nachlass.  The sole passage in the published works is at A255/B311 where Kant remarks that the concept noumenon is a Grenzbegriff.

In the earlier post I distinguished between ordinary concepts and limit concepts. I said in effect that ordinary concepts 'track' essences and are more or less adequate 'captures' of the essences of things encountered in experience.  Limit concepts, I said, 'point beyond' ordinary experience. Thus the concept of God does not and cannot represent the essence of God but it can serve to conceptualize God as that which lies beyond ordinary conceptualization.  The concept of God is a limit concept that points beyond itself to something real that cannot be subsumed under ordinary concepts.

But there is an ambiguity here that I glossed over in the earlier entry. Can't there be limit concepts that simply limit without 'pointing beyond'? How do I know that the concept of God is not like this? (This is connected with the question whether the concept of God might just be a regulative ideal in Kant's sense.)

The trailhead is where the road ends. But further locomotion is possible  on foot or in some other non-motorized manner (horse, mountain bike, pogo stick . . .) The limit in this example has a this-side and an accessible far side. The limit points beyond the paved road to the unpaved trail. But let us say that I have reached the end of the road figuratively speaking: I have just died.  Assuming mortalism, my death is a limit to my life beyond which there is nothing. Some limits are such that the this-side has a far-side; others have only a far-side.

So we should distinguish between limit concepts that simply limit and limit concepts that both limit and point beyond.

Example: Prime Matter

The concept of prime matter is clearly a limit concept. For prime matter is matter at the lowest level of hylomorphic analysis.  Now does this concept point beyond itself to something real, prime matter in itself?  Or does this concept simply mark a limit to the hylomorphic analysis of the real? 

To pursue this question, a  little primer on hylomorphism is needed.

Given that thought sometimes makes contact with reality, one can ask: what must real things be like if thought is to be able to make contact with them? What must these things be like if they are to be intelligible to us? A realist answer is that these mind-independent things must be conformable to our thought, and our thought to them. There must be some sort of isomorphism between thought and thing. Since we cannot grasp anything unstructured, reality must have structure. So there have to be principles of form and organization in things. But reality is not exhausted by forms and structures; there is also that which supports form and structure. In this way matter comes into the picture.  Forms are determinations.  Matter, in a sense that embraces both primary and secondary matter, is the determinable as such.

Proximate matter can be encountered in experience, at least in typical cases. The proximate matter of a chair consists of its legs, seat, back. But this proximate matter itself has form. A leg, for example, has a shape and thus a form. (Form is not identical to shape, since there are forms that are not shapes; but shapes are forms.) Suppose the leg has the geometrical form of a cylinder. (Of course it will have other forms as well, the forms of smoothness and brownness, say.) The cylindrical form is the form of some matter. The matter of this cylindrical form is wood, say. But a piece of wood is a partite entity the parts of which have form and matter. For example, the complex carbohydrate cellulose is found in wood. It has a form and a proximate matter. But cellulose is made of beta-glucose molecules. Molecules are made of atoms, atoms of subatomic particles like electrons, and these of quarks, and so it goes.

Hylomorphic analysis is thus iterable. The iteration cannot be infinite: the material world cannot be hylomorphic compounds 'all the way down,' or 'all the way up' for that matter. The iteration has a lower limit in prime or primordial or ultimate matter (materia prima), just as it has an upper limit in pure form, and ultimately in the forma formarum, God, the purely actual being. Must hylomorphic analysis proceed all the way to prime matter, or can it coherently stop one step shy of it at the lowest level of materia secunda? I think that if one starts down the hylomorphic road one must drive to its bitter end in prime matter. (Cf. Feser's manual, p. 173 for what I read as an argument to this conclusion.) Ultimate matter, precisely because it is ultimate, has no form of its own. As John Haldane describes it, it is "stuff of no kind." (“A Return to Form in the Philosophy of Mind” in Form and Matter, ed. Oderberg, p. 50) We could say that prime matter is the wholly indeterminate determinable. As wholly indeterminate, it is wholly determinable.

The Antinomy of the Existence of Prime Matter

While it is easy to appreciate the logic that leads to the positing of prime matter, it is difficult to see that what is posited is coherently thinkable. Here is one consideration among several. Call it the Antinomy of the Existence of Prime Matter. It may be compressed into the following aporetic dyad:

1. Prime matter exists.

2. Prime matter does not exist.

Argument for limb (1). There is real substantial change and it cannot be reduced to accidental change. All change is reduction of potency to act, and all change requires an underlying substrate of change that remains self-same and secures the diachronic identity of that which changes. The substrate of a change is the matter of the change. What changes in a change are forms, whether accidental or substantial. Without the potency-act and matter-form distinctions we cannot accommodate the fact of change and avoid both the Heraclitean doctrine of radical flux and the Eleatic denial of change. Or so say the scholastics. In the case of accidental change, the subject or substrate is secondary matter (materia secunda). But substantial change is change too, and so it also requires a substrate which cannot be secondary matter and so must be prime matter. Given what we must assume to make sense of the plain fact of both accidental and substantial change, “prime matter must exist.” (Feser's manual, p. 172) It must exist in reality as the common basis of every substantial change.

So if substantial change occurs, prime matter exists!

Argument for limb (2). Prime matter is pure potency. It has to be, given the exigencies of accounting for substantial as opposed to accidental change. As pure potency, prime matter is wholly indeterminate and wholly formless. In itself, then, prime matter does not exist. It does not exist actually, as is obvious. But it also does not exist potentially: prime matter does not have potential Being. This is because the principle of the metaphysical priority of act over potency requires that every existing potency (e.g., the never actualized potency of a sugar cube to dissolve in water) be grounded in something actual (e.g., the sugar cube). The pure potency which is prime matter is not, however, grounded in anything actual. (Note that one cannot say that prime matter is a pure potency grounded in each primary substance. Prime matter is the ultimate stuff of each primary substance; it is not potency possessed by these substances.) Therefore, prime matter does not exist. It does not exist actually and it does not exist potentially. This is also evident from the first of the twenty-four Thomistic theses:

Potency and act are a complete division of being. Hence whatever is must be either pure act or a unit composed of potency and act as its primary and intrinsic principles. (Quoted by Feser, Schol. Metaph., p. 31)

If so, prime matter does not exist. For prime matter is neither pure act nor composed of potency and act. It is interesting to observe that while purely actual Being can itself be by being something actual, purely potential Being cannot itself be by being something potential (or actual). God is actual Being (Sein, esse) and an actual being (Seiendes, ens). But prime matter is neither potential nor actual. So prime matter neither is actually nor is potentially.

It thus appears that we have cogent arguments for both limbs of a contradiction. If the contradiction is real and not merely apparent, and the arguments for the dyad's limbs are cogent, then there is no prime matter, the very concept thereof being self-contradictory.  But the concept does seem to make sense.  To solve the above dyad, then, we may simply deny that prime matter exists. (And let the scholastics worry about how to account for substantial change.)  If we deny that prime matter exists, we are left with the concept, but nothing to which it 'points.'   The concept of prime matter would then be a limit concept that merely marks a limit to our hylomorphic analysis of the real, but does not refer beyond itself to anything real.

Of course, I am not maintaining that the concept of God is like this.  I am merely giving an example of a non-divine limit concept and explaining the difference between limit concepts that are 'immanent' and merely regulate our thinking activity, and those that are 'transcendent' and point beyond.

Summing Up the Dialectic

Some claim that God is inconceivable.  According to a stock objection, this is either false or meaningless. It is false if the claimant is operating with some concept of God, and meaningless if with no concept of God.  I replied to the objection by distinguishing between ordinary and limit concepts.  If the concept of God is a limit concept, then it can be true both that we have a concept of God and that God is nonetheless inconceivable in that he falls under no ordinary  concept.

What I have yet to show is the concept of God is a limit concept in the positive or transcendent sense or 'pointing' sense and a not a limit concept that merely limits us to the this-side.  The concept of prime matter is most plausibly viewed as a limit concept in the negative or immanent sense.  Why isn't the God concept like this?

 

 

Are Cats Liquid?

Meow

Thinking Meat?

Question: Is it my brain that feels and thinks when I feel and think? 

Argument A.  Meat can't think.  My brain is meat.  Therefore, what thinks in me when I think is not my brain.

A in Reverse: What thinks in me when I think is my brain.  My brain is meat. Therefore, meat can think.

The proponent of A needn't deny that we are meatheads.  Of course we are.  We are literally meat (and bone) all the way through. His point is that the res cogitans, that in us which thinks, cannot be a hunk of meat. 

Both arguments are valid, but only one is sound.  The decision comes down to the initial premises of the two arguments. Is there a rational way of deciding between these premises? 

A materialist might argue as follows.  Although we cannot at present understand how a hunk of living meat could feel and think, what is actual is possible regardless of our ability or inability to explain how it is possible.  The powers of certain configurations of matter could remain hidden for a long time from our best science, or even remain hidden forever.  What else would be doing the thinking and feeling in us if not our brains?  What else could the mind be but the living and functioning brain well-supplied with oxygen-rich blood?  The fact that we cannot understand how the brain could be a semantic engine, an engine productive of and sensitive to meanings, is not a conclusive reason for thinking that it is not a semantic engine.

It is worth noting that the reverent gushing of the neuro-scientistic types over the incredible complexity of the brain does absolutely nothing to reduce the unintelligibility of the notion that it is brains or parts of brains that are the subjects of intentional and qualitative mental states.  For it is unintelligible how ramping up complexity could trigger a metabasis eis allo genos.  Are you telling me that meat that means is just meat that is more complex than ordinary meat?  You might as well say that the leap from unmeaning meat to meaning meat is a miracle.  Some speak of 'emergence.'  But that word merely papers over the difficulty, labeling the problem without solving it.  You may as well say, as in the cartoon, "And then a miracle occurs."  But then it's Game Over for the materialist.

Our materialist would do better to insist that unintelligibility to us does not entail impossibility.  Our inability to explain how X is possible does not entail that X is not possible.

My response would be that while unintelligibility does not entail impossibility, it is excellent evidence of it.  If you tell me that a certain configuration of neurons is intrinsically object-directed, directed to an object that may or may not exist without prejudice to the object-directedness, then you are saying something unintelligible.  It is as if you said that .5 volts intrinsically represents 1 and .7 volts intrinsically represents 0.  That's nonsense.  Or it as if you said that a pile of rocks intrinsically indicates the direction of the trial.  (See The Philosophizing Hiker: The Derivative Intentionality of Trail Markers.)

No rock pile has intrinsic meaning or intrinsic representational power.   And the same goes for any material item or configuration of material items no matter how complex. No such system has intrinsic meaning; any meaning it has is derived. The meaning is derived either from an intelligent being who ascribes meaning to the material system, or from an intelligent being whose purposes are embodied in the material system, or both.

Thus I am rejecting the view that meaning could inhere in material systems apart from relations to minds that are intrinsically intentional, minds who are original Sinn-ers, if you will, original mean-ers. We are all of us Sinn-ers, every man Jack of us, original Sinn-ers,  but our Sinn-ing is not mortal or venial but vital.  Intrinsic, underived intentionality is our very lifeblood as spiritual beings.

So if the materialist says that the brain means, intends, represents, thinks, etc., then I say that makes no sense given what we understand the brain to be.  The brain is a material system and the physical, chemical, electrical, and biological properties it and its parts have  cannot be meaningfully predicated of mental states.  One cannot speak intelligibly  of a voltage drop across a mental state any more than can one speak intelligibly of the intentionality of synapses or of their point of view or of what it is like to be one.

Of course, the materialist can pin his hope on a future science that understands the brain in different terms, terms that could be sensibly attached to mental phenomena.  But this is nothing more than an empty gesturing towards a 'possibility' that cannot be described except in the vaguest terms.  It is nothing but faith, hope, and hand-waving.

There is also the dogmatism of the materialist who insists that the subject of thinking must be the functioning brain.  How does he know that?  He doesn't.  He believes it strongly is all. 

So I give the palm to Argument A: Meat can't think.  My brain is meat.  Therefore, what thinks in me when I think is not my brain.

I do not absolutely foreclose on the abstract possibility that there be thinking meat.  For I grant that unintelligibility to us is not invincible proof of impossibility.  But when I compare that vaguely described abstract possibility with the present certainty that matter as we know it cannot think due to the very unintelligibility of the idea, then the present certainty wins over the abstract possibility and over the faith and hope of the materialist. 

If you need to pin your hopes on something, pin them on the possibility that you are more than meat. 

Cf. They're Made Out of Meat 

Bare Particulars and Prime Matter: Similarities and Differences

This entry continues the discussion of prime matter begun here. That post is a prerequisite for this one.

Similarities between Bare Particulars and Prime Matter

S1. Bare particulars in themselves are property-less while prime matter in itself is formless.   The bare particular in a thing is that which exemplifies the thing's properties.  But in itself it is a pure particular and thus 'bare.'  The prime matter of a thing is the thing's ultimate matter and while supporting forms is itself formless.

S2. Bare particulars, though property-less in themselves, exemplify properties; prime matter, though formless in itself, is formed.

S3. There is nothing in the nature of a bare particular to dictate which properties it will exemplify.  This is because bare particulars do not have natures.  Correspondingly, there is nothing in the nature of prime matter to dictate which substantial forms it will take. This is because prime matter, in itself, is without form.

S4.  Bare particulars, being bare, are promiscuously combinable with any and all first-level properties. Thus any bare particular can stand in the exemplification nexus with any first-level property.  Similarly, prime matter is promiscuously receptive to any and all forms, having no form in itself.

S5.  Promiscuous combinability entails the contingency of the exemplification nexus.  Promiscuous receptivity entails the contingency of prime matter's being informed thus and so.

S6. Bare particulars are never directly encountered in sense experience.  The same holds for prime matter.  What we encounter are always propertied particulars and formed matter.

S7. A bare particular combines with properties to make an ordinary, 'thick' particular.  Prime matter combines with substantial form to make a primary (sublunary) substance.

S8. The dialectic that leads to bare particulars and prime matter respectively is similar, a form of analysis that is neither logical nor physical but ontological.  It is based on the idea that things have ontological constituents or 'principles' which, incapable of existing on their own, yet combine to from independent existents.  Hylomorphic analysis leads ultimately to prime matter, and ontological analysis in the style of Bergmann and fellow travellers leads to bare or thin particulars as ultimate substrata.

Differences Between Bare Particulars and Prime Matter

D1. There are many bare particulars each numerically different from every other one.  In themselves, bare particulars are many.  It is not the case that, in itself, prime matter is many.  It is not, in itself, parceled out into numerically distinct bits.

D2. Bare particulars are actual; prime matter is purely potential.

D3. Bare particulars account for numerical difference.  But prime matter does not account for numerical difference. (See Feser's manual, p. 199)  Prime matter is common and wholly indeterminate.  Designated matter (materia signata) is the principle of individuation, i.e., differentiation.

Related articles

Bare Particulars versus Aristotelian Substances

Van Inwagen, Properties, and Bare Particulars

Van Inwagen: No Truck with Tropes or Constituent Ontology Generally

J. P. Moreland on Constituent Ontology: Is Exemplification a Spatial Container Relation?

A Question for Trope Theorists

Reply to Ken Hochstetter on Divine Simplicity

Substantial Change, Prime Matter, and Individuation

Eric Levy wants to talk about prime matter.  I am 'primed' and my powder's dry:  Nihil philosophicum a me alienum putamus. "I consider nothing philosophical to be foreign to me."

Change, Accidental and Substantial 

There is no change without a substrate of change which, in respect of its existence and identity, does not change during the interval of the change. In a slogan: no change without unchange. No becoming other (alter-ation, Ver-aenderung) without something remaining the same. In the case of accidental change, the substrate is materia secunda, in one of its two senses, a piece of paper, say, as opposed to paper as a kind of material stuff. It is a piece of paper that becomes yellow with age, not paper as a kind of stuff. In the case of substantial change the substrate is said to be prime matter, materia prima. On the scholastic view, prime matter must exist if we are to explain substantial change. (See Edward Feser, Scholastic Metaphysics, pp. 171 ff.) Thus to the problems with substantial change already mentioned (in an earlier portion of this  text not yet 'blogged') we may add the problems that are specific to prime matter. Besides the route to prime matter via substantial change, there is the route via the very procedure of hylomorphic analysis. Traversing these routes will give us a good idea of why the positing of prime matter has seemed compelling to scholastics.

Given that thought sometimes makes contact with reality, one can ask: what must real things be like if thought is to be able to make contact with them? What must these things be like if they are to be intelligible to us? A realist answer is that these mind-independent things must be conformable to our thought, and our thought to them. There must be some sort of isomorphism between thought and thing. Since we cannot grasp anything unstructured, reality must have structure. So there have to be principles of form and organization in things. But reality is not exhausted by forms and structures; there is also that which supports form and structure. In this way matter comes into the picture.  Forms are determinations.  Matter, in a sense that embraces both primary and secondary matter, is the determinable as such.

Proximate matter can be encountered in experience, at least in typical cases. The proximate matter of a chair consists of its legs, seat, back. But this proximate matter itself has form. A leg, for example, has a shape and thus a form. (Form is not identical to shape, since there are forms that are not shapes; but shapes are forms.) Suppose the leg has the geometrical form of a cylinder. (Of course it will have other forms as well, the forms of smoothness and brownness, say.) The cylindrical form is the form of some matter. The matter of this cylindrical form is wood, say. But a piece of wood is a partite entity the parts of which have form and matter. For example, the complex carbohydrate cellulose is found in wood. It has a form and a proximate matter. But cellulose is made of beta-glucose molecules. Molecules are made of atoms, atoms of subatomic particles like electrons, and these of quarks, and so it goes.

Hylomorphic analysis is thus iterable. The iteration cannot be infinite: the material world cannot be hylomorphic compounds 'all the way down,' or 'all the way up' for that matter. The iteration has a lower limit in prime or primordial or ultimate matter (materia prima), just as it has an upper limit in pure form, and ultimately in the forma formarum, God, the purely actual being. Must hylomorphic analysis proceed all the way to prime matter, or can it coherently stop one step shy of it at the lowest level of materia secunda? I think that if one starts down the hylomorphic road one must drive to its bitter end in prime matter. (Cf. Feser's manual, p. 173 for what I read as an argument to this conclusion.) Ultimate matter, precisely because it is ultimate, has no form of its own. As John Haldane describes it, it is "stuff of no kind." (“A Return to Form in the Philosophy of Mind” in Form and Matter, ed. Oderberg, p. 50) We could say that prime matter is the wholly indeterminate determinable. As wholly indeterminate, it is wholly determinable.

(Question: if prime matter is wholly indeterminate, is it also indeterminate with respect to being either determinate or indeterminate? Presumably not.  Is there a problem lurking here?)

The Antinomy of the Existence of Prime Matter

While it is easy to appreciate the logic that leads to the positing of prime matter, it is difficult to see that what is posited is coherently thinkable. Here is one consideration among several. Call it the Antinomy of the Existence of Prime Matter. It may be compressed into the following aporetic dyad:

1. Prime matter exists.

2. Prime matter does not exist.

Argument for limb (1). There is real substantial change and it cannot be reduced to accidental change. All change is reduction of potency to act, and all change requires an underlying substrate of change that remains self-same and secures the diachronic identity of that which changes. The substrate of a change is the matter of the change. What changes in a change are forms, whether accidental or substantial. Without the potency-act and matter-form distinctions we cannot accommodate the fact of change and avoid both the Heraclitean doctrine of radical flux and the Eleatic denial of change. Or so say the scholastics. In the case of accidental change, the subject or substrate is secondary matter (materia secunda). But substantial change is change too, and so it also requires a substrate which cannot be secondary matter and so must be prime matter. Given what we must assume to make sense of the plain fact of both accidental and substantial change, “prime matter must exist.” (Feser's manual, p. 172) It must exist in reality as the common basis of every substantial change.

Argument for limb (2). Prime matter is pure potency. It has to be, given the exigencies of accounting for substantial as opposed to accidental change. As pure potency, prime matter is wholly indeterminate and wholly formless. In itself, then, prime matter does not exist. It does not exist actually, as is obvious. But it also does not exist potentially: prime matter does not have potential Being. This is because the principle of the metaphysical priority of act over potency requires that every existing potency (e.g., the never actualized potency of a sugar cube to dissolve in water) be grounded in something actual (e.g., the sugar cube). The pure potency which is prime matter is not, however, grounded in anything actual. (Note that one cannot say that prime matter is a pure potency grounded in each primary substance. Prime matter is the ultimate stuff of each primary substance; it is not potency possessed by these substances.) Therefore, prime matter does not exist. It does not exist actually and it does not exist potentially. This is also evident from the first of the twenty-four Thomistic theses:

Potency and act are a complete division of being. Hence whatever is must be either pure act or a unit composed of potency and act as its primary and intrinsic principles. (Quoted by Feser, Schol. Metaph., p. 31)

If so, prime matter does not exist. For prime matter is neither pure act nor composed of potency and act. It is interesting to observe that while purely actual Being can itself be by being something actual, purely potential Being cannot itself be by being something potential (or actual). God is actual Being (Sein, esse) and an actual being (Seiendes, ens). But prime matter is neither potential nor actual. So prime matter neither is actually nor is potentially.

It thus appears that we have cogent arguments for both limbs of a contradiction. If the contradiction is real and not merely apparent, and the arguments for the dyad's limbs are cogent, then either there is no prime matter, the very concept thereof being self-contradictory, or there is prime matter but it is is unintelligible to us. One could, I suppose, be a mysterian about prime matter: it exists but we, given our cognitive limitations, cannot understand how it could exist. (Analogy with Colin McGinn's mysterianism: consciousness is a brain process, but our cognitive limitations bar us from understanding how it could be.) But I mention mysterianism only to set it aside.

But perhaps we can avoid contradiction in the time-honored way, by drawing a distinction. A likely candidate is the distinction between prime matter in itself versus prime matter together with substantial forms. So I expect the following scholastic response to my antinomy:

Prime matter exists as a real (extramental) factor only in primary substances such as Socrates and Plato. It exists only in hylomorphic compounds of prime matter and substantial form. But it does not exist when considered in abstraction from every primary substance. So considered, it is nothing at all. It is not some formless stuff that awaits formation: it is always already formed. It is always already parcelled out among individual material substances. Once this distinction is made, the distinction between prime matter in itself and prime matter together with substantial forms, one can readily see that the 'contradiction' in the above dyad is merely apparent and rests on an equivocation on 'exist(s).' The word is being used in two different senses. In (1) 'exists' means: exists together with substantial form. In (2), 'exist' means: exist in itself. Thus the aporetic dyad reduces to the logically innocuous dyad:

1*. Prime matter exists together with substantial forms.

2*. Prime matter does not exist in itself in abstraction from substantial forms.

Unfortunately, this initially plausible response gives rise to a problem of its own. If prime matter really exists only in primary substances, then prime matter in reality is not a common stuff but is parcelled out among all the primary substances: it exists only as a manifold of designated matters, the matter of Socrates, of Plato, etc. But this conflicts with the requirement that prime matter be the substratum of substantial change. Let me explain.

If a new substance S2 comes into existence from another already existing substance S1 (parthenogenesis may be an example) then prime matter is what underlies and remains the same through this change. Now this substratum of substantial change that remains the same must be something real, but it cannot be identical to S2 or to S1 or to any other substance. For if the substratum of substantial change is identical to S1, then S1 survives, in which case S2 is not a new substance generated from S1 but a mere alteration of S1. Don't forget that substantial change cannot be reduced to an accidental change in some already existing substance or substances. In substantial change a new substance comes to be from one or more already existing substances. (I will assume that creation or 'exnihilation' does not count as substantial change.)

If, on the other hand, the substratum of change is identical to S2, then S2 exists before it comes to exist. And it seems obvious that the substratum of substantial change underlying S2's coming to be from S1 cannot be some other substance. Nor can the substratum be an accident of S2 or S1. For an accident can exist only in a substance. If the substratum is an accident of S1, then S1 must exist after it has ceased to exist. If the substratum is an accident of S2, then S2 must exist before it comes to exist.

The argumentative punchline is that prime matter cannot exist only in primary substances as a co-principle tied in every case to a substantial form. If prime matter is the substratum of substantial change, then prime matter must be a really existent, purely potential, wholly indeterminate, stuff on its own.

The Problem of the Substrate

The problem just presented, call it the Problem of the Substrate or the Problem of the Continuant, may be pressed into the mold of an aporetic tetrad:

1. Prime matter is the substrate of substantial change.

2. Prime matter does not exist in reality except as divided among individual material substances.

3. The substratum of a substantial change cannot be identified with any of the substances involved in the change, or with any other substance, or with any accident of any substance. (For example, the substratum of the substantial change which is Socrates' coming into existence from gametes G1 and G2 cannot be identified with Socrates, with G1, with G2, with any other substance, or with any accident of any substance.)

 4. There is substantial change and it requires a really existent substrate.

The tetrad is inconsistent issuing as it does in the contradiction: Prime matter does and does not exist only in individual material substances.

The obvious solution is to deny (2). But if we deny (2) to solve the Problem of the Substrate, then we reignite the Antinomy of the Existence of Prime Matter. We solved the Antinomy by making a distinction, but that distinction gave rise to the Problem of the Substrate/Continuant. We appear to be in quite a pickle. (For more on the Substrate/Continuant problem, see John D. Kronen, Sandra Menssen and Thomas D. Sullivan, “The Problem of the Continuant: Aquinas and Suárez on Prime Matter and Substantial Generation,” The Review of Metaphysics, Vol. 53, No. 4 (Jun., 2000), pp. 863-885.)

The Problem of Individuation

Finally a glance at the related ontological, not epistemological, problem of individuation. This problem is actually two problems. There is the problem of individuation proper, namely, the problem of what makes an individual substance individual as opposed to universal, and there is the connected problem of differentiation, namely, the problem of what makes numerically different individual substances numerically different. It is clear that prime matter cannot be the principle of differentiation. For one thing, prime matter is common to all material substances. For another, prime matter as pure potency is indeterminate, hence not intrinsically divided into parcels. Moreover, pace Feser, prime matter cannot “bring universals down to earth” in his phrase: it cannot be the principle of individuation, narrowly construed. (Schol. Metaph., p. 199) For what makes Socrates an individual substance rather than the substantial form he shares with Plato cannot be common, indeterminate, amorphous, matter.

Prime matter is not up to the job of individuation/differentiation. It is designated matter (materia signata quantitate) that is said to function as the ontological ground or 'principle' of individuation and numerical difference. Unfortunately, appeal to designated matter involves us in an explanatory circle. Designated matter is invoked to explain why Socrates and Plato are individual substances and why they are numerically different individual substances. But designated matter cannot be that which individuates/differentiates them since it presupposes for its individuation and differentiation the logically (not temporally) antecedent existence of individual material substances. Why are Socrates and Plato different? Because their designated matters are different. Why are their designated matters different? Because they are the matters of different substances. The explanation moves in a circle of rather short diameter.

Feser considers something like this objection but dismisses it as resting on a confusion of formal with efficient causality. But there is no such confusion in the objection as I have presented it. Efficient causality does not come into it at all. No one thinks that there is an agent who in a temporal process imposes substantial form on prime matter in the way that a potter in a temporal process imposes accidental form upon a lump of clay. I can grant Feser's point that prime matter and substantial form are related as material cause to formal cause. I can also grant that prime matter and substantial form are mutually implicative co-principles neither of which can exist without the other. Granting all this, my objection remains. Prime matter in itself is undifferentiated. It it differentiated and dimensive only in combination with substantial forms. But this is equivalent to saying that prime matter is differentiated and dimensive only as the designated matter of particular individual substances. But then designated matter cannot non-circularly explain why numerically different substances are numerically different. For the numerical difference of these matters presupposes the numerical difference of the substances.