QUANTITY AS EQUAL AND UNEQUAL DOES NOT REFER TO THE OBJECTS.
As to (Aristotle's) assertion that the property of quantity is to be both equal and unequal,[257] this property belongs to quantity itself, and not to the objects which participate in quantity, unless it be by accident, so far as one does not consider these objects in themselves. A three foot object, for instance, is a quantity so far as it is taken in its totality; but it does not form a kind with quantity itself; only, along with it, it is traced back to a kind of unity, a common category.
RELATION.[258]
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.