INFINITE IS CONCEIVED BY THE THOUGHT'S MAKING ABSTRACTION OF THE FORM.
How then can we conceive the infinite? By making abstraction of form by thought. How will it be conceived? We may conceive of the infinite as simultaneously being the contraries, and not being them. It will have to be conceived as being simultaneously great and small; for the infinite becomes both of these.[6] It may also be conceived as both being moved, and being stable[7]; for the infinite becomes these two things also. But before the infinite becomes these two contraries, it is neither of them in any determinate manner; otherwise, you would have determined it. By virtue of its nature, the infinite is these things therefore in an indeterminate and infinite manner; only on this condition will it appear to be these contrary things. If, by applying your thought to the infinite, you do not entice it into a determination, as into a net, you will see the infinite escaping you, and you will not find anything in it that would be a unity; otherwise, you would have determined it. If you represented to yourself the infinite as a unity, it would seem to you manifold; if you say that it is manifold, it will again make game of you; for, all things do not form a manifold where no one thing is one. From still another standpoint, the nature of the infinite is movement, and according to another nature, stability; for its property of being invisible by itself constitutes a movement which distinguishes it from intelligence[8]; its property of not being able to escape, of being exteriorly embraced, of being circumscribed within an unescapable circle constitutes a sort of stability. Movement therefore cannot be predicated of infinity, without also attributing stability to it.
HOW OTHER NUMBERS FORM PART OF THE INTELLIGIBLE WORLD.
4. Let us now examine how the numbers form part of the intelligible world. Are they inherent in the other forms? Or are they, since all eternity, the consequences of the existence of these forms? In the latter case, as the very essence possessed primary existence, we would first conceive the monad; then, as movement and stability emanated from it, we would have the triad; and each one of the remaining intelligible entities would lead to the conception of some of the other numbers. If it were not so, if a unity were inherent in each intelligible entity, the unity inherent in the first Essence would be the monad; the unity inherent in what followed it, if there be an order in the intelligible entities, would be the "pair"; last, the unity inhering in some other intelligible entity, such as, for instance, in ten, would be the decad. Nevertheless this could not yet be so, each number being conceived as existing in itself. In this case, will we be compelled to admit that number is anterior to the other intelligible entities, or posterior thereto? On this subject Plato[9] says that men have arrived to the notion of number by the succession of days and nights, and he thus refers the conception of number to the diversity of (objective) things. He therefore seems to teach that it is first the numbered objects that by their diversity produce numbers, that number results from movement of the soul, which passes from one object to another, and that it is thus begotten when the soul enumerates; that is, when she says to herself, Here is one object, and there is another; while, so long as she thinks of one and the same object, she affirms nothing but unity. But when Plato says that being is in the veritable number, and that the number is in the being,[10] he intends to teach that by itself number possesses a hypostatic substantial existence, that it is not begotten in the soul which enumerates, but that the variety of sense-objects merely recalls to the soul the notion of number.
PYTHAGOREAN INTELLIGIBLE NUMBERS DISCUSSED.
5. What then is the nature of number? Is it a consequence, and partially an aspect of each being, like man and one-man, essence and one-essence? Can the same be said for all the intelligibles, and is that the origin of all numbers? If so, how is it that on high (in the intelligible world) the pair and triad exist? How are all things considered within unity, and how will it be possible to reduce number to unity, since it has a similar nature? There would thus be a multitude of unities, but no other number would be reduced to unity, except the absolute One. It might be objected that a pair is the thing, or rather the aspect of the thing which possesses two powers joined together, such as is a composite reduced to unity, or such as the Pythagoreans conceived the numbers,[11] which they seem to have predicated of other objects, by analogy. For instance, they referred to justice as the (Tetrad, or) group-of-four,[12] and likewise for everything else. Thus a number, as for instance a group-of-ten, would be considered as a single (group of) unity, and would be connected with the manifold contained in the single object. This, however, is an inadequate account of our conception of "ten"; we speak of the objects after gathering (ten) separate objects. Later, indeed, if these ten objects constitute a new unity, we call the group a "decad." The same state of affairs must obtain with intelligible Numbers. If such were the state of affairs (answers Plotinos), if number were considered only within objects, would it possess hypostatic existence? It might be objected, What then would hinder that, though we consider white within things, that nevertheless the White should (besides) have a hypostatic substantial existence? For movement is indeed considered within essence, and yet (it is agreed that) movement possesses a "hypostatic" substantial existence within essence. The case of number, however, is not similar to that of movement; for we have demonstrated that movement thus considered in itself is something unitary.[13] Moreover, if no more than such a hypostatic substantial existence be predicated of number, it ceases to be a being, and becomes an accident, though it would not even then be a pure accident; for what is an accident must be something before becoming the accident (of some substance). Though being inseparable therefrom, it must possess its own individual nature in itself, like whiteness; and before being predicated of something else, it already is what it is posited. Consequently, if one be in every (being), one man is not identical with man; if "one" be something different from "man"[14] and from every other (being), if it be something common to all (beings), one must be anterior to all men and to all other (beings), so that man and all other beings may be one. The one is therefore anterior to movement, since movement is one, and likewise anterior to essence, to allow for essence also being one. This of course does not refer to the absolute Unity that is recognized as superior to essence, but of the unity which is predicated of every intelligible form. Likewise, above that of which the decad is predicated subsists the "Decad in itself," for that in which the decad is recognized could not be the Decad in itself.
THE INTELLIGIBLE UNITY AND DECAD EXIST BEFORE ALL NUMBERS ONE OR TEN.
Does unity therefore inhere in essences, and does it subsist with them? If it inhere in essences, or if it be an accident, as health is an accident of man, it must be something individual (like health). If unity be an element of the composite, it will first have to exist (individually), and be an unity in itself, so as to be able to unify itself to something else; then, being blended with this other thing that it has unified, it will not longer remain really one, and will thereby even become double. Besides, how would that apply to the decad? What need of the (intelligible) Decad has that which is already a decad, by virtue of the power it possesses? Will it receive its form from that Decad? If it be its matter, if it be ten and decad only because of the presence of the Decad, the Decad will have first to exist in itself, in the pure and simple state of (being a) Decad.