6. Let us now consider relation. Let us see whether, in relative matters, there be something common that constitutes a kind, or which is a point of union in any other manner. Let us, before everything else, examine whether relation (as, for example, left and right, double and half, and so forth) be a kind of “hypostasis,” or substantial act, or an habituation; or, whether it be a kind of hypostatic existence in certain things, while in others it is not so; or whether it be this under no circumstances. What is there indeed that is particular in relations such as double and half; surpasser and surpassed; in possession, and in disposition; lying down, standing, sitting; in the relation of father and son; of master and slave; in the like and different; the equal and unequal; the active and passive; measurer and measured; sensation and knowledge? Knowledge, for instance, relates to the object which can be known, and sensation to sense-object; for the relation of knowledge to the object which can be known has a kind of hypostatic existence in the actualization relative to the form of the object which can be known; likewise with the relation of sensation to the sense-object. The same may be said about the relation of the “active” to the “passive,” which results in a single actualization, as well as about the relation between the measure and the measured object, from which results mensuration. But what results from the relation of the similar to the similar? If in this relation there be nothing begotten, one can at least discover there something which is its foundation, namely, the identity of quality; nevertheless, neither of these two terms would then have anything beside their proper quality. The same may be said of equal things, because the identity of quantity precedes the manner of being of both things; this manner of being has no foundation other than our judgment, when we say, This one or that one are of the same size; this one has begotten that one, this one surpasses that one. What are standing and sitting outside of him who stands or sits? As to the possession, if it apply to him who possesses, it rather signifies the fact of possession; if it apply to what is possessed, it is a quality. As much can be said of disposition. What then exists outside of the two relative terms, but the comparison established by our judgment? In the relation of the thing which surpasses the thing which is surpassed, the first is some one size, and the second is some other size; those are two independent things, while as to the comparison, it does not exist in them, except in our judgment. The relation of left to right and that of the former to the latter consist in the different positions. It is we who have imagined the distinction of right to left; there is nothing in the objects themselves that answers thereto. The former and the latter are two relations of time, but it is we who have established that distinction.
WHETHER THESE RELATIONS ARE SUBJECTIVE OR OBJECTIVE.
7. If, when we speak of things, we utter nothing true, then there is nothing real in the relation, and this kind of being has no foundation. But if, when we compare two moments, we say, This one is anterior, and that one is posterior, we speak truly, then we conceive that the anterior and the posterior are something independent of the subjects in which they exist. Likewise with the left and the right, as well as with sizes; we admit that in these, besides the quantity which is suitable to them, there is a certain habituation, as far as the one surpasses and the other is surpassed. If, without our enunciating or conceiving anything, it be real that such a thing is the double of another; if the one possess while the other is possessed, even if we had known nothing about it; if the objects had been equal before we had noticed them; if they be likewise identical in respect of quality; finally if, in all relative things, there be a habituation which is independent of the subjects in which it is found; and if we limit ourselves to noticing its existence (without creating it); if the same circumstances obtain in the relation of knowledge to what can be known, a relation which evidently constitutes a real habituation; if it be so, there is nothing left to do but to ask whether this habituation (named a relation) be something real. We shall have to grant, however, that this habituation subsists in certain subjects as long as these subjects remain such as they were, and even if they were separate; while, in other subjects, this habituation is born only when they are brought together. We shall also have to grant that, in the very subjects that remain, there are “some in which this habituation is annihilated or altered (such as, for example, the left direction, or proximity). This has led people to believe that in all these relations there is nothing real. This point having been granted, we shall have to seek what common element there is in all these relations, and to examine whether what is common to them all constitutes a kind, or an accident; and last, we shall have to consider how far that which we have discovered corresponds to reality.
RELATIONS ARE SIMULTANEOUS EXISTENCES.
We should call relative not what is said absolutely of another thing, such as, for instance, the habits of the soul and the body; nor what belongs to such a thing, nor what is in such a thing (as for instance the soul is said to be the soul of such an individual, or to be in such a subject), but what wholly derives its existence from this habit (called relation). By “hypostatic existence” I here mean not the existence which is proper to subjects, but the existence which is called relative; as, for instance, the double causes the (correlative) existence of the half; while it does not cause the existence of the two foot object, nor of two in general, nor the one foot object, nor one in general. The manner of existence of these objects consists in that this one is two, and that one one. As a result of this, when these objects exist, the first is called double, and is such in reality; and the second is half. These two objects have therefore simultaneously and spontaneously effected that the one was double, and the other half. They have been correlatively begotten. Their only existence lies in their correlation, so that the existence of the double lies in its surpassing the half, and the half derives its existence from its being surpassed by the double. Consequently these two objects are not, the one anterior, and the other posterior, but simultaneous. We might also examine whether or not other things do w not also possess this simultaneity of existence, as happens with father and son, and other similar cases. The son continues to exist, indeed, even after the death of the father; brother also survives brother, since we often say that some one person resembles some other deceased person.
DISTINCTION BETWEEN ACTIVE HABITUATION IMMEDIATE AND REMOTE.
8. The above digression gives us the opportunity of investigating why there should be a difference between these relations, and those of which we spoke above. However, we should be glad to have the Aristotelians first state what community of existence obtains in this correlation. It would be impossible to claim that this community was anything corporeal. If then it be corporeal, it must exist either within the very subjects, or without them. If such a habituation be identical among all, it is a synonym. If it be a habituation which differs according to the subjects in which it exists, it is a homonym; for the mere name of “habituation” (in different things) does not always correspond to the existence of any genuine similarity. Should we then divide the habituations into two classes, recognizing that certain objects have an inert and inactive habituation, implying simultaneity of existence, and that other objects have a habituation always implying “potentiality” and “actualization,” so that before “actualizing” the “potentiality” be already ready to exert itself, and to pass from “potentiality” to “actualization” in the approximation of relative conditions? Must we assert that in general certain things actualize, while others limit themselves to existing? Must we also assert that that which limits itself to existence only gives its correlative a name, while that which actualizes gives it existence? Of this latter kind of things are the father and son, the “active” and “passive,” for such things exert a kind of life and action. Must we then divide habituation in several kinds, not as possessing something similar and common in the differences, but as having a nature different in each member of the division, and thus constituting a “homonym” (or, mere verbal label) ? In this case, we would apply to the active habituation the names of “doing” and “suffering,” because both imply an identical action. Further, we will have to posit another “habituation” which, without itself actualizing, implies something which acts in two relative terms. For example, there is equality; which equates two objects ; for it is equality which renders things equal, just as identity makes them identical; just as the names “great” and “small” are derived one from the presence of greatness, and the other from that of smallness. But if we should consider greatness and smallness in the individuals which participate therein, it must be acknowledged that such individual is greater by the act of greatness which manifests in him, and that another is smaller because of the inherent act of littleness.
HABITUATIONS ARE REASONS THAT PARTICIPATE IN FORMS.
9. It must therefore be granted that in the things of which we first spoke, such as knowing and doing (active being), there is an actualization, an habituation, and an actualizing reason; while in the other things there is a participation in form and reason. For indeed, if the bodies were the only essences, the relative habituations would bear no reality. If, on the contrary, we assign the first rank in existence to incorporeal things, and to the reasons, and if we define the habituations as reasons that participate in the forms, we should say that what is double has the double for its cause, and what is half, has the half as its cause; and that other things are what they are named because of the presence of the same, or of the contrary form. Now either two things simultaneously receive one the double, and the other the half, and one greatness, and the other smallness; or contraries such as resemblance and dissimilarity are to be found in each thing, as well as identity and difference; and everything finds itself simultaneously similar and dissimilar, identical and different. It might be objected that if one object were ugly, and another uglier still, they are such because they participate in a form. Not so; for if these two objects be equally ugly, they are equal in the absence of the form. If they be unequally ugly, the least ugly is such because it participates in a form which does not sufficiently subdue matter, and the uglier is such because it participates in a form which does so still less. They could, besides, be judged from the standpoint of deprivation, comparing them to each other as if they contained some form. The sensation is a form that results from two things (of that which feels, and that which is felt); so also with knowledge. In respect to the thing possessed, possession is an act which contains, which has a kind of efficacity. As to mensuration, which is an actualization of measure, in respect of the measured object, it consists in a reason.
WHILE SOME ARISTOTELIAN CATEGORIES ARE LOGICALLY POSSIBLE. THE OBJECTS SUBSUMED ARE IMPOSSIBLE.
If then, considering the constitution of the relative relations as a generic form, it be admitted that it constitutes an unity, it forms a classification; consequently it constitutes an existence and a form in all things. But if the reasons (or, relations) be opposed to each other, if the above-mentioned differences obtain among them, they do not constitute a class, and everything must be reduced to a resemblance, or category. Now, even if we admit that the things of which we have spoken can be reduced to a unity, it does not follow that all the things gathered under the same category by the Aristotelians, could be reduced to a single sort. Indeed, they lump together into the same classification, both objects and mere statements of their absence, as well as the objects which derive their appellation from them; as, for instance, doubleness itself, and the double object. Now how is it possible to reduce to the same classification both a thing and the mere lack of it, as, for instance, doubleness and the non-double, the relative and the non-relative? This is as absurd as it would be to gather into the same classification the living “being,” and the non-living “being.” Worse yet, how could one assort together duplication and the double object, whiteness and the white object? Such things could not possibly be identical.