All Towards One
An Introduction to Pros Hen Equivocity
This is a general introduction to pros hen equivocity, the unification of ontology, and a brief note on a Platonic appropriation thereof. It is not meant as a scholarly essay, nor is it meant to be original, nor has it been constructed of air-tight argumentation with copious citations. But hopefully it is clear enough to convince that Aristotle is doing something very interesting in the Metaphysics, and that Platonists in particular ought to study Aristotle, for they have much to gain from his ontology.
The Possibility of Ontology
Ontology is a strange idea. It seeks to study Being qua Being, and what belongs to it in virtue of its own nature. It does not study beings insofar as they are this or that, but insofar as they are at all. Physics studies changing things, mutable things, beings insofar as they are changing and mutable; mathematics studies abstracted quantities of various types, beings insofar as they are taken to be quantity. Biology would study beings insofar as they have a bios. And so on. But ontology is to study Being qua Being, and that is a difficult notion to grasp. It does not do to gloss over this and pretend it is easy to grasp this notion of “Being qua Being”. It is not an empty and commonsense idea, nor is it a linguistic excess.
It is not at all clear that ontology is possible. A science must have a principle of unity, in virtue of which it unifies its field of objects and treats them as one. One science must treat of one sort of thing.
Some sciences achieve this unity by studying univocals, things which have the same name and the same definition. For instance, the science of mammals would study, say, dogs and squirrels and so on. A dog is mammal in the same way as is a squirrel; the definition of “mammal” applies equally and in the same way to both. Therefore we say that dogs and squirrels are mammals univocally.
Consider now the opposite case, where the objects under consideration share a name in common but not a definition, that is, wherein they are equivocals. For instance, say I propose the science of bat-ology, whereby I mean to study under the heading of one single science the “bats” which are flying mammals and the “bats” which are used in baseball. The definitions of each are of course not the same. How then could one science treat of both? You would need, it seems reasonable to suppose, two sciences. Perhaps some relation could be found between them such that each receives a place in some great hierarchy of more and less general sciences, or maybe both can be related somehow to physics, or whatever. But it is clear they are not the same science. Without unified objects of study, no unified science by which to study them.
If we are to study Being, we run into a similar problem, for, as Aristotle never tires of saying, “Being is said in many ways”.1 There are in fact four broad ways Being is said: Being according to the categories, Being as accident, Being as true, and Being as actual and potential.
Even just within the first heading, “Being according to the categories”, there are ten different ways Being is said (these are the famous “categories”, from the work of that name but also found in varying forms in other treatises): substance, quantity, quality, relative, where, when, being-in-a-position, having, doing, and being-affected.2 Being-a-dog and being-yellow and being-ten-feet-tall and being-a-Monday are all ways Being is said according to the categories. Each of these remain equivocal; there is not one definition of Being that covers them all. Being is not univocal, not a genus, nor even really a “concept” in the sense that it would comprehend these differences. Aristotle did not consider Being the broadest and most empty concept, as a universal set containing all things. Rather, Being is an equivocal.
The matter becomes even more complicated when we consider the other three major headings of how Being is said.
If Being were merely equivocal, as the flying mammal “bat” and the baseball “bat” were equivocal, then ontology would be impossible. There could be no science of Being. According to Joseph Owens, in his monumental work The Doctrine of Being in the Aristotelian Metaphysics:
The Aristotelian approach is the reverse of the Parmenidean. Parmenides sees Being as one, and asks how it could be many. Aristotle sees Beings as manifold. He asks: How could any one nature account for their differences? (p. 437)
If ontology cannot treat of Being univocally, then how can it get off the ground at all? If ontology is to be possible, there must be another, less obvious way for a science, and for its field of study, to be unified.
Unifying Ontology: Pros Hen Equivocity
In fact, Aristotle actually outlines three different ways that things can be equivocal, namely (and once again relying on Owens)…
by chance, as when the same term applies only by naming conventions
by analogy, as when “the second is related to the first as the third is related to the fourth”
by reference, as when “healthy” food gets its name because it refers to the health of the organism
Equivocity by chance is obviously no candidate for a science. Equivocity by analogy is more interesting, though it is unclear exactly how it would support a science except in an auxiliary sense. It is on equivocity by reference that Aristotle stakes his claim.
The example he uses in Met. IV is that of “health” and “healthy”, and of the medical art. “Health” refers primarily to a state of the organism, a certain harmonious order. When we say “this man is healthy”, we are referring to the state of health. In contrast, when we say “this food is healthy”, we do not mean that the food possesses the state of health; the food is not an organism, and we are not literally ascribing health to it. When we say “she has a healthy complexion”, we once again do not mean that the complexion is organized into a state of health; it is not the sort of thing that could possess the nature “health”.
Instead, what we mean when we call the food or the complexion “healthy” is that they relate in some definite way to the primary meaning of “health”, the state of an organism. Healthy food, for instance, may produce or maintain health in an organism. A healthy complexion may be a sign of health. One could produce many more such examples.
Aristotle terms this “pros hen”, meaning “towards one” or “with reference to one”. There is one primary nature, health, which bestows its name on things which do not possess that nature in its fullness but have some definite relation or reference to it. This type of equivocity, then, does unify. The primary and principal nature “health” is just one thing, one nature. And science can therefore study it.
Applying this to the study of Being qua Being is by no means totally straightfoward, and much more could be thought and said about what is to follow. In mere outline, then, this is what Aristotle does, and in what follows we shall restrict ourselves to Being according to the categories for ease of presentation.
Is there a primary meaning of Being, from which secondary meanings could be said to derive their Being-ness, as the primary meaning of health is related to various healthy implements and signs?
Aristotle answers in the affirmative. The primary meaning of Being is ousia. This has been variously translated as “substance”, “Entity”, “Thinghood”, “Being-ness”, and so on. I will follow tradition and speak of “substance”, and although there are many problems with this (and every other) translation, the translation problem will probably not cause grave misunderstandings for our purposes here. Let it be noted, however, that sometimes what is at issue is the “ousia of ousia”, and therein translations meet yet another difficulty. Ousia is, it can be said, also an equivocal.3 In any case…
If substance is the primary meaning of Being, this means that the other meanings get their name because of their definite relationship to it. And this makes good sense. Consider “The dog is furry”. What is being said is that there is a dog (substance) with the qualification or quality “being-furry”. Furriness is being predicated of or ascribed to the dog. In what sense is this furriness? Being-furry is not nothing, it’s not a privation of Being in an obvious sense. The furriness is only as a qualification of the dog, the substance. To say “the dog is furry” is to say “the dog is… and it is as being furry”. The primary nature of Being is the substance, and the furriness is by reference to that primary nature. The other categories depend, ontologically, on the category of substance, as healthy food depends on health in an organism. Just as, without the reference to an organism’s health, the food would not be healthy, so without reference to the Being of substance, the being-furry would not be at all. Substance is prior to the other categories, and they all depend on it.
A Second Unification of Ontology: Theology
Aristotle does not stop there, but proposes a second unification of ontology. The other categories all depend on substance, but does substance depend on anything? In particular, might there not be a prior substance on which sensible and mutable substance depends? In that case, a second application of pros hen reasoning would find the primary nature of Being in a particular type of substance.
To put it another way, ontology was first “horizontally” unified into ousiology, the study of substance. Now Aristotle leads us to think of a second unification, a “vertical” one, into a study of the primary substance(s). This vertical unification is controversial, and not every Aristotle scholar thinks it works, but it is clearly central to the argument of the Metaphysics. Here I will not so much defend it from alternative interpretations, including the interpretation on which it fails utterly, but will instead just present what I think Aristotle is suggesting, without getting into the technicalities of activity and potency (since so many have written at length about that).
Sensible, mutable, corruptible substances, like those we see around us, depend on supersensible substance for their Being. This is so for a variety of reasons. One reason is that supersensible substance can be said to possess more Being than sensible ones. Sensible substances are stretched between Being and non-Being, possessing not only actual Being but also potentiality, which for them always includes the potential not to exist. There is in back of this a standardly Platonic intuition that Being most of all is eternal, stable, immutable, even intelligible. If there are any substances of that sort, then they will be primary, and will be the causes and principles of Being as such.
If this is right, then supersensible substance will possess the primary nature of Being, and sensible substances will possess it only with reference to those supersensible ones. To take this further than Aristotle himself ever did, just as “the dog is furry” speaks of being-furry only in reference to the dog, so also to say “the dog is” speaks of being-a-dog, but behind this is the (admittedly strange) reference to the unmoved mover(s). The dog is only by reference to the primary nature of Being, which is not simply possessed as such by the dog, but only derivatively and in relation to the supersensible substances on which it depends.
An adequate account of activity, particularly of the pure activity sans potentiality possessed by the supersensible substances, would be required to make this more intelligible. In Aristotle, this immediately gets into murky territory (if it is not already far too murky!). So here we turn to a Platonic reading of the pros hen hierarchy, since Platonism is of course our interest in the matter.
The Platonic Pros Hen Hierarchy
We can understand the Platonic ontological hierarchy, with all its many levels of images and archetypes, as a generalization of the Aristotelian pros hen structure. Platonists have frequently dealt with the problem of how, say, great things and the Form of Greatness could be related such that both are “great”, but in different ways. The Form of Greatness cannot be great like a great mountain, but neither can it have no relation whatsoever to greatness. The cause or paradigm must be both the same as and different than the effect. Clearly the effect gets its name with reference to the archetype or Form which is its cause. The Form of Greatness makes a great thing great.
What Aristotle did for the nature of Being, Platonists do for each and every nature. Great things are called great pros hen, with reference to one nature, namely the primary possessor of greatness, the Form of Greatness.
The role of supersensible substance is taken over primarily by Intellect. Intellect possesses all the natures primarily by cognitive identity, in eternally thinking all the Forms. The tree outside my window is called a tree because it bears some definite relation to the intelligible nature of Tree present in and to the Divine Mind. This definite relation is not, as in the healthy food, because it brings about or maintains the intelligible Tree; rather, the relation is one of image and archetype. The image possesses the nature in a deficient mode (as we see with regard to the equal sticks in the Phaedo).
With the intelligible natures present in Intellect, and the image-archetype relation, it makes a bit more sense how the Being of the tree can be said only with reference to supersensible substance. As in Aristotle, everything is referred back to substance, including qualities and quantities and so on, but now the substance under consideration is a Form. We still have the primary meaning of Being as substance, but this is, for lack of a better word, “intelligized”; it is a generalization of the Aristotelian project, to some degree.
In Platonism it is a commonplace that at each level of the hierarchy, a unification takes place. Higher things are more unified, lower things less so. One way to conceive this is to see how all things point back or strive towards a single nature prior to them, something that is more primary, which possesses Being to a higher degree. Many trees point to one. Many principles point to one. The pros hen or “towards one” ultimately culminates in a single One. Everything is with reference to this.
The rigor with which Platonism thinks the simultaneous identity and difference of the cause and the effect (as in the doctrine of emanation), remains to be specified. But in this at least, Platonism has adopted Aristotelian tools and insights for its own purposes.
Aristotle, Met. IV, 2.
Aristotle, Cat. 4. See also a slightly different but substantially identical listing at Met. V, 7.
Indeed, as we see, equivocals are themselves equivocal. In fact, they may be pros hen equivocals, and pros hen equivocity may be the primary meaning. But that can be set aside.