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?

 

 

Comments

[oz the ostrich]

Is the Grenzbegriff related to the infinite/indefinite concept of the scholastics, discussed by Kant in his Logic? An ostrich is a non-man. So we have a concept 'non-man' which ostriches, lions, stones, justice fall under, to which no essence corresponds, except perhaps the essence *man*, in the negative.

I don't have the text of the Logic to hand, but will check later.

[BV]

We agree that 'non-man' does not pick out a real essence. The concept *non-man* could be called factitious in Descartes' sense. (The Frenchman distinguished among innate, adventitious, and factitious ideas, as you recall.)

But while the concept *non-man* does not pick out a real essence, it is not a Grenzbegriff because it does not mark a limit in the way the concept *materia prima* marks a limit to hylomorphic analysis.

*Hypokeimenon* in Aristotle would be a candidate Grenzbegiff. That which has properties but is not itself a property. The Absurd in Sartre; the Ding an sich in Kant; the libertarianly free noumenal agent in Kant. This would be a positive Grenzbegriff whereas the Ding an sich would be negative according to some CPR passages.

[oz the ostrich]

I read (a few times) A255/B311 and the surrounding passages, but afraid I am none the wiser.

At the moment I am looking at the relation between the scholastic conception of the categories, and Kant's reinvention of them.

If you remember, I studied Kant as a student under Stephan Körner - and then read no more. Difficult stuff.

[BV]

What's not to understand? Kant is saying that the concept of noumenon is a limit concept. Clear to me! But then I wrote my dissertation on Kant.

Here's a project for you: write something on the similarities and differences between the concepts of transcendental in the scholastics and in Kant.

[oz the ostrich]

>>What's not to understand? Kant is saying that the concept of noumenon is a limit concept. Clear to me!

Well I understand the individual words ('limit', 'concept') in their ordinary meaning but far from understanding what Kant says in that place.

>>Here's a project for you

I don't understand the concept of the transcendental in either the scholastics, or in Kant!

[BV]

Are you feigning incomprehension again, as you analytic dudes sometimes do?

Are you 'petering out'? -- I trust youcatch the allusion.

[oz the ostrich]

>>I trust youcatch the allusion

Actually, no.

[BV]

To 'peter out' is to do what Peter van Inwagen sometimes appears to do, namely, feign incomprehension. "I don't know what you mean." "I don't understand."

[BV]

See here: https://maverickphilosopher.typepad.com/maverick_philosopher/2013/09/annoying-habits-of-some-philosophers.html

8. Feigning incomprehension. Saying, 'I don't know what you are talking about,' when you have a tolerably clear idea of what I am talking about. This may be the same as Petering Out.

What is offensive here is the dismissal of an idea or an entire philosophy because it is not totally clear, when it ought to be one purpose of philosophical dialog to clarify what is not totally clear. You say you have no idea what Emmanuel Levinas is driving at in Totality and Infinity? Then I say you must be one stupid fellow or uneducated or both. Same with Heidegger and Hegel, et al. You say you don't know what Hegel is talking about what he says, at the beginning of his Science of Logic, that Being passes over into Nothing? No idea at all? Then you are dumb or inattentive or lazy or a philistine or something else it would not be good to be.

Don't feign incomprehension. If you find what I maintain unclear, explain why you think it unclear, and then ask for clarification. In that way, we may make a bit of progress.

[oz the ostrich]

OK but I am not feigning incomprehension. I read through some Kant today, to refresh myself on the idea of the 'transcendental'.

[oz the ostrich]

From the intro to the Guyer and Wood edition:

Kant's thesis that space and time are pure forms of intuition leads him to the paradoxical conclusion that although space and time are empirically real, they are transcendentally ideal, and so are the objects given in them. Although the precise meaning of this claim remains subject to debate …

So experts on Kant (not just me, who is far from an expert) cannot decide on what Kant is talking about?

[BV]

Good boy! That Giacomo Zabarella cat sounds interesting. If you can understand 'second intention' then surely Grenzbegriff and 'transcendental.'