13. To begin with, it is unreasonable to insist that the notion of the subject one comes to us from the subject itself (which is one), from the visible man, for instance, or from some other animal, or even some stone. Evidently the visible man and the One are things entirely different, which could not be identified[28]; otherwise, our judgment would not be able (as it is) to predicate unity of the non-man. Besides, as the judgment does not operate on emptiness for the right side, and other such things, seeing a difference of position when it tells us that an object is here, or there; likewise, it also sees something when it says that an object is one; for it does not experience there an affection that is vain, and it does not affirm unity without some foundation. It cannot be believed that the judgment says that an object is one because it sees that it is alone, and that there is no other; for, while saying that there is no other, the judgment implicitly asserts that the other is one. Further, the notions of "other" and "different" are notions posterior to that of unity; if the judgment did not rise to unity, it would not assert either the "other" nor the "different"; when it affirms that an object is alone, it says, "there is one only object"; and therefore predicates unity before "only." Besides, the judgment which affirms is itself a substantial (being) before affirming unity of some other (being); and the (being) of which it speaks is one likewise before the judgment either asserts or conceives anything about it. Thus (being) must be one or many; if it be many, the one is necessarily anterior, since, when the judgment asserts that plurality is present, it evidently asserts that there is more than one; likewise, when it says that an army is a multitude, it conceives of the soldiers as arranged in one single corps. By this last example, it is plain that the judgment (in saying one body), does not let the multitude remain multitude, and that it thus reveals the existence of unity; for, whether by giving to the multitude a unity which it does not possess, or by rapidly revealing unity in the arrangement (which makes the body of the multitude), the judgment reduces multitude to unity. It does not err here about unity, any more than when it says of a building formed by a multitude of stones that it is a unity; for, besides, a building is more unified than an army.[29] If, further, unity inhere in a still higher degree in that which is continuous, and in a degree still higher in what is not divisible,[30] evidently that occurs only because the unity has a real nature, and possesses existence; for there is no greater or less in that which does not exist.
UNITY, THOUGH BY PARTICIPATION EXISTING IN SENSE-OBJECTS, IS INTELLIGIBLE.
Just as we predicate being of every sense-thing, as well as of every intelligible thing, we predicate it in a higher degree of intelligible things, attributing a higher degree (of substantiality) to the (beings that are veritable than to sense-objects), and to sense-objects than to other genera (of physical objects); likewise, clearly seeing unity in sense-objects in a degree higher than in the intelligible (essences), we recognize the existence of unity in all its modes, and we refer them all to Unity in itself. Besides, just as "being and essence"[31] are nothing sensual, though sense-objects participate therein, so unity, though by participation it inhere in sense-objects, is not any the less an intelligible Unity. Judgment grasps it by an intellectual conception; by seeing one thing (which is sensual) it also conceives another which it does not see (because it is intelligible); it therefore knew this thing in advance; and if judgment knew it in advance, judgment was this thing, and was identical with that whose existence it asserted. When it says, "a certain" object, it asserts the unity, as, when it speaks of "certain" objects, it says that they are two or more. If then one cannot conceive of any object whatever without "one," "two," or some other number, it becomes possible to insist that the thing without which nothing can be asserted or conceived, does not at all exist. We cannot indeed deny existence to the thing without whose existence we could not assert or conceive anything. Now that which is everywhere necessary to speak and to conceive must be anterior to speech and conception, so as to contribute to their production. If, besides, this thing be necessary to the hypostatic existence of every essence—for there is no essence that lacks unity—it must be anterior to being, and being must be begotten by it. That is why we say "an essence" instead of first positing "essence," and "a" only thereafter, for there must be "one" in essence, to make "several" possible; but (the converse is not true; for) unity does not contain essence, unless unity itself produce it by applying itself to the begetting of it. Likewise, the word "that" (when employed to designate an object) is not meaningless; for instead of naming the object, it proclaims its existence, its presence, its "being," or some other of its kinds of "essence." The word "that" does not therefore express something without reality, it does not proclaim an empty conception, but it designates an object as definitely as some proper name.
UNITY ONLY AN ACCIDENT IN SENSE-THINGS, BUT SOMETHING IN ITSELF IN THE INTELLIGIBLE.
14. As to those who consider unity as relative, they might be told that unity could not lose its proper nature merely as a result of the affection experienced by some other being without itself being affected. It cannot cease being one without experiencing the privation of unity by division into two or three. If, on being divided, a mass become double without being destroyed in respect to its being a mass, evidently, besides the subject, there existed unity; and the mass lost it because the unity was destroyed by the division. So this same thing which now is present, and now disappears, should be classified among essences wherever it be found; and we must recognize that, though it may be an accident of other objects, it nevertheless exists by itself, whether it manifest in sense-objects, or whether it be present in intelligent entities; it is only an accident in posterior (beings, namely, the sense-objects); but it exists in itself in the intelligible entities, especially in the first Essence, which is One primarily, and only secondarily essence.
TWO IS NOT AN ADDITION TO ONE, BUT A CHANGE (REFUTATION OF ARISTOTLE).
The objection that unity, without itself experiencing anything, by the mere addition of something else, is no longer one, but becomes double, is a mistake.[32] The one has not become two, and is not that which has been added to it, nor that to which something has been added. Each of them remains one, such as it was; but two can be asserted of their totality, and one of each of them separately. Two therefore, not any more than "pair," is by nature a relation. If the pair consisted in the union (of two objects), and if "being united" were identical with "to duplicate," in this case the union, as well as the pair, would constitute two. Now a "pair" appears likewise in a state contrary (to that of the reunion of two objects); for two may be produced by the division of a single object. Two, therefore, is neither reunion nor division, as it would have to be in order to constitute a relation.
OBJECTS PARTICIPATE IN NUMBERS JUST AS THEY PARTICIPATE IN ALL INTELLIGIBLE ENTITIES.
What then is the principal cause (by virtue of which objects participate in numbers)? A being is one by the presence of one; double, because of the presence of the pair; just as it is white because of the presence of whiteness; beautiful, because of the presence of beauty; and just by that of justice. If that be not admitted, we shall be reduced to asserting that whiteness, beauty and justice are nothing real, and that their only causes are simple relations; that justice consists in some particular relation with some particular being; that beauty has no foundation other than the affection that we feel; that the object which seems beautiful possesses nothing capable of exciting this affection either by nature, or by acquirement. When you see an object that is one, and that you call single, it is simultaneously great, beautiful, and susceptible of receiving a number of other qualifications. Now why should unity not inhere in the object as well as greatness and magnitude, sweetness and bitterness, and other qualities? We have no right to admit that quality, whatever it be, forms part of the number of beings, whilst quantity is excluded; nor to limit quantity to continuous quantity, while discrete quantity is excluded from the conception of quantity; and that so much the less as continuous quantity is measured by discrete quantity. Thus, just as an object is great because of the presence of magnitude, as it is one by the presence of unity; so is it double because of the presence of being a pair, and so forth.[33]