Limit Concepts – Maverick Philosopher

How Could God be Ineffable?

The mystically inclined say that God is ineffable. The ineffable is the inexpressible, the unspeakable. Merriam-Webster:

Ineffable comes from ineffābilis, which joins the prefix in-, meaning "not," with the adjective effābilis, meaning "capable of being expressed." Effābilis comes from effārī, "to speak out," which in turn comes from ex- and fārī, meaning “to speak.”

But: "What we cannot speak about we must pass over in silence." (Wittgenstein, Tractatus Logico-Philosophicus, 7) Does it follow that there is nothing ineffable, inexpressible, unspeakable? Some will draw this conclusion; Hegel is one. Ludwig the Tractarian, however, does not draw this conclusion:

There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical. (Tractatus, 6.522)

God is the prime example of das Unaussprechliche. But if we cannot say anything about God, then we cannot say any of the following: he exists; he does not exist; he is transcendent; he is immanent; he is all-knowing; he is not all-knowing; he has attributes; he has no attributes; he is ineffable; he is not ineffable; and so on.

Is this a problem? Maybe not.

Consider any mundane thing, a rock, say. Can you put it into words? Can you capture its existence and its haecceity (its non-qualitative thisness) in concepts? You cannot. At most you can capture conceptually only its quidditative determinations, all of which are multiply exemplifiable or repeatable. But the thing itself is unrepeatable and escapes conceptual capture. The discursive intellect cannot grasp it. Es ist unbegreifbar. It cannot be 'effed' linguistically or conceptually. Individuum ineffabile est.

If you can see that the individual qua individual is conceptually ineffable, why do you balk at talk of the divine ineffability? If the haecceity of a grain of sand or a speck of dust cannot be conceptualized, then a fortiori for the super-eminent haecceity and ipseity of the super-eminent Individual who is not a mere individual among individuals but Individuality itself.

The Ineffable One cannot fall under any of our ordinary concepts. We can however, point to it by using a limit concept (Grenzbegriff). A limit concept is not an ordinary concept. Note that we do have the concept of that which is beyond all concepts. (If we did not, this discourse would be nonsense when it plainly is not, pace Wittgenstein.) That smacks of self-contradiction, but the contradiction is avoided by distinguishing between ordinary and limit concepts.

So, while remaining within the ineluctable discursivity of our discursive intellects, I am able to point beyond the sphere of the discursive intellect into the Transdiscursive. You can understand this by analogy to the transdiscursivity of a stick, a stone, a dog, a bone, a bird, a turd, or any part thereof.

How do I gain epistemic access to a mundane particular such as a stick or a stone in its unrepeatable particularity? By sensible intuition (sinnliche Anschauung in Kant's sense). We do it all the time. And so, by a second analogy, we can understand how epistemic access to the Absolute and Ineffable One is to be had: by intellectual intuition or mystical gnosis.

The Concept GOD as a Limit Concept

The concept GOD is the concept of a being that cannot be constituted in consciousness in Husserl's sense of 'constitution,' a being that cannot be a transcendence-in-immanence, but must be absolutely transcendent, transcendent in itself, not merely for us. It follows that there cannot be a phenomenology of God. At best, there can be a phenomenology of such of our experiences as purport to be of or about God.

We know that the concept GOD is the concept of something absolutely transcendent, and we know this by purely conceptual means. We have the concept GOD and we analyze it: we simply unpack its meaning. Whatever the origin of this concept, it is there in us and available for analysis. Of course, we cannot learn by conceptual analysis that God exists, but we can know something about what God cannot be like, if he does exist. We can know, for example, that God, if he exists, is not a concept. No surprise here, and nothing that distinguishes God from my chair, since my chair is not a concept either. (One cannot sit on a concept.) The difference between the concept CHAIR and the concept GOD is the difference between an ordinary concept and a limit concept (Grenzbegriff).*

This is the distinction between those concepts that can capture (mirror, represent) the essences or natures of the things of which they are the concepts, and those concepts that cannot. Call the first type ordinary concepts and the second limit concepts. Thus the concept CUBE captures the essence of every cube, which is to be a three-dimensional solid bounded by six square faces or sides with three meeting at each vertex, and it captures this essence fully. The concept HELIOTROPIC PLANT captures, partially, the essence of those plants that exhibit diurnal or seasonal motion of plant parts in response to the direction of the sun. Concepts are mental representations. Essences are extra-mental.

Now the concept GOD cannot be ordinary since this concept cannot capture the essence of God. For (i) in God essence and existence are one, and (ii) there is no ordinary concept of existence.

Ad (i). That in God essence and existence are one follows from the fact that nothing could count as the Absolute if it were a composite of essence and existence. And we know by conceptual analysis that God is the Absolute: the concept GOD is the concept of 'something' absolute. This is the case whether or not God exists.

Ad (ii). When I say that there is no ordinary concept of existence, I mean that there is no ordinary (non-limit) concept that is adequate to existence. (There are bogus concepts of existence such as Quine's.) There is no ordinary (non-limit) concept of existence because the existence of a thing, as other than its essence, cannot be conceptualized. Why not?

This is because each existing thing has its own existence. Thus the existence of Al is Al's existence, the existence of Bob is Bob's, and the existence of Carla is Carla's. For the existence of a thing is that which makes that very thing exist. Existence cannot be a property like being human, being sentient, being sunburned. These properties are multiply instantiable; existence, however, is not multiply instantiable. There are no instances of existence.

Now if each thing has its own existence, then existence is implicated in the irreducible singularity of each existing thing. Irreducible singularity, in turn, cannot be conceptualized by minds like ours which trade only in the general and multiply instantiable. It's an Aristotelian point. If Aristotle wrote in Latin it would go: individuum qua individuum ineffabile est. The individual as such, the singular as such, is ineffable and cannot be conceptualized. The Peripatetic tells us that science is never of the particular as particular but only of the particular as exhibiting general or repeatable features. The particular as such is unrepeatable. But of course there are no individuals (particulars) bare of properties. Every finite individual is a this-such. This is a law of metaphyica generalis. So, while the individual as individual cannot be conceptualized, the individual as bearer of properties can be conceptualized as an instance of those properties. If I think of Mary as an instance of lovable properties, then I abstract from the haecceity (thisness) that makes her different numerically from her indiscernible twin Sherry. So if I love Mary precisely and only as an instance of lovable properties, then it will make no difference to my so loving her whether Mary or Sherry is its object. It will, however, make a difference to Mary. "I want that you should love me for what makes me me, and not for what I have in common with her!" I explain this all in great detail in Do We Love the Person or Only Her Qualities?

The crucial point here is that when we think of an individual as an instance of properties, we abstract from (leave out of consideration) the individual's thisness and its existence. I am not saying that the existence and the thisness of a concrete individual are one and the same; I am saying that that they go together as a matter of metaphysical necessity.

Ad (i + ii). In God there is no real distinction between existence and nature. That was the first point. The second was that no ordinary (non-limit) concept captures the individuality of the thing of which it is the concept. Therefore, since God is (identically) his nature, there can be no ordinary concept of God, whence it follows frat GOD is a limit concept.

There is, then, a clear sense in which God is unconceptualizable or unbegreiflich: he cannot be grasped by the use of any ordinary concept. But it doesn't follow that we have no concept of God. We do. The concept GOD is a limit concept: it is the concept of something that cannot be grasped using ordinary concepts. Our cognitive architecture is such that we can grasp only the general, the repeatable, but never the irreducibly singular. The concept GOD, however, is the concept of 'something' absolutely and irreducibly singular. God is one without a second, one without even the possibility of a second. Any god that doesn't satisfy this metaphysical exigency just isn't worth his salt.

The concept GOD is the concept of something that lies at the outer limit of discursive intelligibility, and indeed just beyond that limit. We can argue up to this Infinite Object/Subject, but then discursive operations must cease. We cannot penetrate the divine essence since this essence is one with existence, and existence cannot be conceptually penetrated. We can however point to God, in a manner of speaking, using limit concepts. The concept GOD is the concept of an infinite, absolute and wholly transcendent reality whose realitas formalis so exceeds our powers of understanding that it cannot be taken up into the realitas objectiva of any of our ordinary concepts.

Now if you have followed that, then you are in a position to see that the following objection is a 'cheap shot' easily dismissed. "You contradict yourself. You say that God cannot be conceptualized but at the same time you operate with a concept of God as unconceptualizable." But no contradiction arises once we distinguish ordinary from limit concepts.

If the critic accuses me of inventing a distinction ad hoc to save the ineffability and transcendence of God, then my reply will be that there are numerous other examples of limit concepts. See the aptly appellated category, Limit Concepts.

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*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.

Can Kant Refer to God?

This is a re-working of an entry from 19 September 2016. It relates to present concerns about limit concepts and whether and to what extent God can be subsumed under our concepts.

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Ed Buckner raises the title question, and he wants my help with it. How can I refuse? I'll say a little now, and perhaps more later.

Kant was brought up a rationalist within the Wolffian school, but then along came David Hume who awoke him from his dogmatic slumber. This awakening began his Critical period in which he struggles mightily to find a via media between rationalism and empiricism. The result of his struggle, the Critical philosophy, is of great historical significance but it is also an unstable tissue of apparently irresolvable tensions. As a result there are competing interpretations of his doctrines.

I will propose two readings relevant to Ed's question. But first a reformulation and clarification of the question.

Can one think about God and meaningfully predicate properties of him? For example, can one meaningfully say of God that he exists, is omnipotent, and is the cause of the existence of the natural world? Or is it rather the case that such assertions are meaningless and that the category of causality, for example, has a meaningful application only within the realm of phenomena but not between the phenomenal realm as a whole and a putative transcendent causa prima? Are the bounds of sensibility (Sinnlichkeit) also the bounds of sense (Sinn), or are there senseful, meaningful assertions that transgress the bounds of sensibility?

Weak or Moderate Reading. On this reading, we can think about God and meaningfully make predications of him, but we cannot have any knowledge of God and his attributes. We cannot have knowledge of God because knowledge necessarily involves the interplay of two very different factors, conceptual interpretation via the categories of the understanding, and sensory givenness. God, however, is not given to the senses, outer or inner. In Kantian jargon, there is no intuition, keine Anschauung, of God. For intellects of our type, all intuition is sensible intuition. The Sage of Koenigsberg will not countenance any mystical intuition, any Platonic or Plotinian visio intellectualis, at least not in this life. That sort of thing he dismisses in the Enlightenment manner as Schwaermerei, 'enthusiasm' in an obsolete 18th century sense of the English term.

But while Kant denies that there is knowledge of God here below whether by pure reason or by mystical intuition, he aims to secure a 'safe space' for faith: "I have found it necessary to deny knowledge in order to make room for faith." (Preface to 2nd ed. of Kritik der reinen Vernunft, 1787, B xxx.) Now if God and the soul are objects of faith, this would imply that we can think of them and thus refer to them even if we cannot have knowledge of them.

As for the soul, it is the object of the branch of metaphysica specialis called rational psychology. Since all our intuition is sensible, there is no sensible intuition of the soul. As is well-known, Kant denies that special metaphysics in all three branches (psychology, cosmology, and theology) is possible as science, als Wissenschaft. To be science it would have to include synthetic a priori judgments, but these are possible only with respect to phenomena.

Kant's key question is: How are synthetic a priori judgments possible? He believes that they are actual in mathematics and physics, and would have to be actual in metaphysics if the latter were a science. Kant concludes that synthetic a priori judgments are possible in mathematics and physics only because the world of experience (Erfahrung) is not a world of things in themselves whose existence, nature, and law-like regularity are independent of our mental contribution, but a merely phenomenal world to whose construction (transcendental) mind makes an indispensable contribution.

The dignity and necessity of the synthetic causal principle — every event has a cause — is rescued from the jaws of Humean skepticism, but the price is high: the only world we can know is the world of phenomena. This is not a world of illusions, but a world of intersubjectively valid objects of experience. But while objective in the sense of intersubjectively valid, these objects do not exist in themselves. Things in themselves (noumena in the negative sense) are beyond our ken. Yet we must posit them since the appearances are appearances of something (obj. gen.). And it is presumably the affection of our sense organs by these things in themselves that gives rise to the sensory manifold that is then organized by a priori forms (categories and forms of sensibility) on the side of the subject. The restriction of human knowledge to phenomena secures the objectivity (intersubjective validity) of our knowledge, but by the same stroke rules out any knowledge of the objects of special metaphysics (God, the soul, the world as a whole).

On the moderate reading, then, Kant restricts the cognitive employment of the categories of the understanding to phenomena but not their thinking employment. We can think about and refer to the positive noumena, God, the soul, and the world as a whole, but we cannot have any knowledge of them. (And the same goes for the negative noumena that correspond to sensible appearances.) We can talk sense about God and the soul, and predicate properties of these entities, but we cannot come to have knowledge of them. Thus we can meaningfully speak of the soul as a simple substance which remains numerically self-same over time and through its changing states, but we cannot know that it has these properties.

The weak reading is represented by the following argument:

1) A necessary condition of knowledge is intuition (Anschauung).

2) In us, the only mode of intuition is sensible. We have no faculty of intellectual intuition.

3) The concept of God is the concept of an entity that cannot be an object of the senses.

Therefore

4) God is unknowable by us. (1, 2, 3)

Nevertheless

5) God is thinkable by us. (3)

Strong or Extreme Reading. On this reading, we cannot talk sense about positive or negative noumena: such categories as substance and causality cannot be meaningfully applied beyond the bounds of sensibility to God, the soul, angels, libertarianly free noumena agents, the world as a whole, or even things in themselves. Riffing on P. F. Strawson one could say that on the strong reading the bounds of sensibility are the bounds of sense. This reading wins the day in post-Kantian philosophy. Fichte liquidates the Ding an sich, the neo-Kantians reduce the transcendental ego to a mere concept (Rickert, e.g.), the categories which for Kant were ahistorical and fixed become historicized and relativized, and we end up with a conceptual relativism which fuels a lot of the nonsense of the present day, e.g., race and sex as social constructs, etc.

The strong reading is represented by the following argument:

1*) A necessary condition of meaningful objective reference is intuition.

2) In us, the only mode of intuition is sensible. We have no faculty of intellectual intuition.

3) The concept of God is the concept of an entity that cannot be an object of the senses.

Therefore

4*) God cannot be meaningfully referred to by us.

So my answer to Ed Buckner's title question is: It depends. It depends on whether we read Kant in the weak way or in the strong way. Read in the weak way, Kant is saying that the categories of the understanding have no cognitive employment in the absence of sensory input, but they do have an empty logical employment and objective reference/meaning. Read in the strong way, the categories are devoid of objective reference/meaning in the absence of sensory givenness. If so, the concept of God is a limit concept in the negative sense: it merely marks a limit to our understanding, but does not point beyond that limit. At best, the concept of God is a regulative Idea whose employment is purely immanent.

The Concept of the Metaphysical Self in Wittgenstein as Limit Concept

I continue my investigation of limit concepts. So far I have discussed the concepts of God, prime matter, bare particulars, and particularity. We now turn to the Tractarian Wittgenstein.

As I read him, Wittgenstein accepts Hume's famous rejection of the self as an object of experience or as a part of the world. "There is no such thing as the subject that thinks or entertains ideas." (5.631) The reason Wittgenstein gives is that, if he were to write a book called The World as I Found it in which he inventories the objects of experience, he would make mention of his body and its parts, but not of the subject of experience: "for it alone could not be mentioned in that book." (ibid.) The argument is similar to the one we find in Hume: the subject that thinks is not encountered as an object of experience.

But why not? Is it because it doesn't exist, or is it because the subject of experience, by its very nature as subject, cannot be an actual or possible object of experience? It has to be the latter for Wittgenstein since he goes on to say at 5.632 that "The subject does not belong to the world: rather, it is a limit of the world." So he is not denying that there is a subject; he is telling us what it is, namely, the limit of the world.

From the fact that the metaphysical subject is nowhere in the world, it does not follow that it does not exist. If, however, you think that this is a valid inference, then you would also have to think that from the non-appearance of one's eyes in one's visual field one could validly infer the nonexistence of one's eyes.

As 5.6331 asserts, one's eyes are not in one's visual field. If you say that they can be brought into one's visual field by the use of a mirror, I will point out that seen eyes are not the same as seeing eyes. The eyes I see in the mirror are objects of visual consciousness; they are not what do the seeing.

That is not to say that the eyes I see in my visual field, whether the eyes of another person or my own eyes seen in a mirror, are dead eyes or non-functioning eyes. They are living eyes functioning as they should, supplied with blood, properly connected via the neural pathways to the visual cortex, etc. The point is that they are not seeing eyes, subjects of visual consciousness.

If you insist that seeing eyes are indeed objects of outer perception and empirical study, then I will challenge you to show me where the seeing occurs in the eye or where in the entire visual apparatus, which includes eyeglasses, contact lenses, the neural pathways leading from the optic nerve to the visual cortex — the whole system which serves as the causal basis of vision. Where is the seeing? In the pupil? In the retina? In the optic nerve? Somewhere between the optic nerve and the brain? In the visual cortex? Where exactly? Will you say that it is in no particular place but in the whole system? But this is a very big system including as it does such instruments of vision as sunglasses and night goggles. And let's not leave out the external physical things that are causing certain wavelengths of light to impinge on the eye. And the light itself, and its source whether natural or artificial. Will you tell me that the SEEING is spread out in space over and through all of these items? But then how do you explain the unity of visual consciousness over time or at a time? And how do you explain the intentionality of visual consciousness? Does it make any sense to say that a state of the eyeball is of or about anything? If you say that the SEEING is in the eye or in the brain, then I will demand to know its electro-chemical properties.

I could go on, but perhaps you get the point: the seeing, the visual consciousness-of, is not itself seen or see-able. It is not an object of actual or possible experience. It is not in the world. It is not a part of the eye, or a state of the eye, or a property of the eye, or a relation in which the eye stands, or an activity of the eye. The same goes for the whole visual system. And yet there is seeing. There is visual consciousness, consciousness of visual objects.

Who or what does the seeing? Who or what is the subject of visual consciousness? Should we posit a self or I or ego that uses the eye as an instrument of vision, so that it is the I that sees and not the eye? No one will say that his eyeglasses do the seeing when he sees something. No one says, "My eyeglasses saw a beautiful sunset last night." We no more say that than we say, "My optic nerve registered a beautiful sunset last night," or "My visual cortex saw a beautiful sunset last night."* We say, "I saw a beautiful sunset last night."

But then who or what is this I? It is no more in the world than the seeing eye is in the visual field. Wittgenstein's little balloon above depicts the visual field. Imagine a Big Balloon that depicts the 'consciousness field,' the totality of objects of consciousness. It does not matter if we think of it as a totality of facts or a totality of things. The I is not in it any more than the eye qua seeing is in the visual field.

So far I am agreeing with Wittgenstein. There is a subject, but it is not in the world. So it is somewhat appropriate to call it a metaphysical subject, although 'transcendental subject' would be a better choice of terms, especially since Wittgenstein says that it is the limit of the world. 'Transcendental' is here being used in roughly the Kantian way. 'Transcendental' does not mean transcendent in the phenomenological sense deriving from Husserl, nor does it mean transcendent in the absolute sense of classical metaphysics as when we say that God is a transcendent being. (That is why you should never say that God is a transcendental being.)

But Wittgenstein also maintains that the transcendental subject is the limit of the world. This implies, first, that it is not nothing, and second, that it is no thing or fact in the world. "The world is all that is the case." (1) "The world is the totality of facts, not of things." (1.1) It follows that the subject is not a thing or fact outside the world. So all the self can be is the limit of the world.

We have to distinguish the world from worldly things/facts. The world is a totality of things or of facts, and a totality is distinct from its members both distributively and collectively. So we shouldn't conflate the world-as-totality with its membership (the world taken in extension). So if the metaphysical or rather transcendental subject is the limit of the world as per 5.632, then what this means is that the subject is the limit of worldly things/facts, and as such is the world-as-totality.

This is why Wittgenstein says "I am my world." (5.63)

The analogy is clear to me. Just as one's eyes are not in one's visual field, visual consciousness of objects in the world is not itself in the world. Visual consciousness, and consciousness generally, is of the world, not in it, to reverse the New Testament verse in which we are enjoined to be in the world, but not of it. (Needless to say, I am reversing the words, not the sense of the NT saying. And note that the first 'of' is a genitivus objectivus while the second is a genitivus subjectivus.)

Of course, this is not to say that there is a substantial self, a Cartesian res cogitans outside the world. "The world is all that is the case." There is nothing outside it. And of course Wittgenstein is not saying that there are soul substances or substantial selves in the world. Nor is he saying that there is a substantial self at the limit of the world. He is saying that there is a metaphysical (better: transcendental) self and that it is the limit of world. He is stretching the notion of self about as far as it can be stretched, in the direction of a radically externalist, anti-substantialist notion of consciousness, which is later developed by Sartre and Butchvarov.

What we have here is the hyper-attenuation of the Kantian transcendental ego, which is itself an attenuation of substantialist notions of the ego. The Tractarian Wittgenstein is a transcendental philosopher. He may not have read much or any Kant, but he knew the works of the Kantian, Schopenhauer, and was much influenced by them. According to P. M. S. Hacker,

Of the five main philosophical influences on Wittgenstein, Hertz, Frege, Russell, Schopenhauer, and perhaps Brouwer, at least three were deeply indebted to Kant. It is therefore not surprising that Wittgenstein's philosophy bears deepest affinities to Kant's, despite the fact he never studied Kant . . . ." (Insight and Illusion, 139)

Spot on.

So what sort of concept is the concept of the metaphysical self in Wittgenstein? It is clearly a limit concept, and indeed a negative one inasmuch as it marks a limit without pointing beyond that limit. The upshot seems to be that the metaphysical or rather transcendental self just is a concept. The neo-Kantian Heinrich Rickert maintained something similar. But how could the ultimate subject or self be a mere concept? And whose is it? Concepts are in minds. There is pressure to move in the direction of a substantial self . . .

Is the Concept of Particularity a Limit Concept?

That depends.

The term is ambiguous. 'Particularity' can be taken to refer to a category common to all particulars, whether concrete or abstract. (Tropes are abstract particulars using 'abstract' in the old, not the Quinean, way.) The concept of particularity in this sense is not a limit concept. We have no trouble conceptualizing the category of particulars. We grasp this concept by grasping the concept of unrepeatability and we grasp it in tandem with the concept of repeatability which is the mark of universals.

'Particularity' can also be used to refer to that which makes a particular particular be the very particular that it is! Socrates, for example, is a particular concrete particular, and so is Plato. Categorially, they are the same, but numerically they are different. 'Particularity' in the second sense refers, not to a categorial feature, but to a particular's haecceity (haecceitas) or thisness.

The concept of particularity in this second sense is a limit concept. This is because our minds cannot conceptualize the haecceity of a thing. We cannot form a concept that captures the Socrateity of Socrates, that 'property,' if his haecceity is a property, that he alone actually has and nothing else could possibly have. Individuum ineffabile est. That is, the particular qua particular is ineffable. It cannot be conceptually 'effed.' This why Aristotle says that there can be no science of the particular as such. A sensible particular is knowable, but only in terms of its repeatable features. It is the suchness of a this-such that is knowable, not its thisness. And of course every concrete particular is a this-such.

So the concept of particularity in the sense of haecceity is a limit concept. We have a concept of that which we cannot conceive in propria persona. So there is no incoherence in the claim that haecceity is inconceivable, just as there is no incoherence in the claim that God is inconceivable. There is no incoherence due to the distinction between limit and non-limit concepts. But is haecceity a positive or a negative limit concept?

If positive, then the concept points beyond itself to something that is real. That is, it points to something mind-independently in the thing that makes it be that very thing. If negative, then the concept merely marks a limit to our understanding. If positive, there is something we cannot understand; if negative, there is nothing there to understand.

Let us use 'ipseity' to refer to the haecceity of a person. I cannot grasp the alter ego in its otherness. The concept of ipseity, then, is a limit concept. Now suppose you said that this concept is negative. You would then be saying that there is nothing there in the other person to conceptualize as opposed to saying that there is something there that cannot be conceptualized. But surely I know that a person I love is an other mind, an other I, an other subject despite my inability to objectify this other subject as I would have to in order to conceptualize it. I know this whether or not I have any clue as to how I know it. So in this case we would have to say that the concept of ipseity is a positive limit concept. It points to an unfathomable reality in the other person that is presumably the locus of his free will, moral worth, and spirituality.

If God exists, then the concept of God is a limit concept in the positive sense. If you maintain that the concept of God is a negative limit concept, then, at best, you reduce God to a regulative Ideal in Kant's sense which is tantamount to denying the existence of God.

We will have to discuss Kant.

Bare Particular as Limit Concept

I have already shown that the concept prime matter is a limit concept. The same holds for the concept bare particular. Both are lower limits of ontological analysis. I will be using 'bare particular' in Gustav Bergmann's sense.

What is a Particular?

Particulars in the sense relevant to understanding 'bare particular' may be understood in terms of impredicability. Some things can be predicated of other things. Thus being black can be predicated of my cat, and being a property can be predicated of being black; but my cat cannot be predicated of anything. My cat is in this sense 'impredicable.' Particulars are subjects of predication but cannot themselves be predicated. Particulars, then, are ultimate subjects of predication. Thus my cat is an ultimate subject of predication unlike being black which is a subject of predication, but not an ultimate subject of predication. Particulars have properties but are not themselves properties. Properties may be characterized as predicable entities. The particulars I am referring to are of course concrete particulars. They are not those abstract particulars known in the trade as tropes. (This curious nomenclature derives from Donald C. Williams. It has nothing to do with tropes in the literary sense.) A trope is a particularized property; better: a property assayed as a particular, an unrepeatable, as opposed to a universal, a repeatable entity. Unrepeatability is the mark of particulars, whether concrete or abstract.

What is a Bare Particular?

First, what it is not. It is a complete misunderstanding to suppose that philosophers who speak of bare or thin particulars, philosophers as otherwise different in their views as Gustav Bergmann, David Armstrong, and J. P. Moreland, mean to suggest that there are particulars that have no properties and stand in no relations. There is no such monstrosity as a bare particular in this sense. What makes a bare particular bare is not its having no properties, but the way it has the properties it has.

A bare particular is a particular that lacks a nature or (real) essence. It is therefore quite unlike an Aristotelian primary substance. Every such substance has or rather is an individual nature. But while lacking a nature, a bare particular has properties, and it cannot not have them. This 'having' is understood in terms of the asymmetrical external nexus of exemplification. A bare particular is thus tied to its properties by the external nexus of exemplification. To say that the nexus that ties a to F-ness is external is to say that there is nothing in the nature of a, and nothing in the nature of F-ness to require that a exemplify F-ness. After all, a, as bare, lacks a nature, and F-ness, while it has a nature, is not such that there is anything in it to necessitate its being exemplified by a. In this sense a bare particular and its properties are external to each other. So, while it is necessary that bare particulars have properties, none of the properties a bare particular has is essential to it.

This mutual externality of property to bearer entails promiscuous combinability: any bare particular can exemplify any property, and any property can be exemplified by any bare particular.

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 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. They differ, not property-wise, but solo numero. 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.

Bare Particular as Limit Concept in the Positive Sense

It is obvious that the concept of bare particular, in the early Bergmann at least, is a limit concept. (The item-sort distinction in the later Bergmann of New Foundations of Ontology complicates matters.) But is the limit concept bare particular negative or positive? There is no prime matter in itself, which fact makes the concept of prime matter a limit concept in the negative sense: the concept does not point to anything real beyond itself but merely sets a limit to our hylomorphic analysis of the real. Should we say the same about the concept of bare particular? Not in Bergmann's constituent ontology. If an ordinary concrete particular — a round red spot to use an 'Iowa' example — is built up out of more basic constituents, then the 'building blocks' must be real.

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:

Prime matter exists.
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?