Part 2

9. It remains for us to discover whether it were "Being," in the process of division, that begat number, or whether it be the number that divided "Being." (This is the alternative:) either "being," movement, stability, difference and identity produced number, or it is number that produced all these (categories, or) genera. Our discussion must start thus. Is it possible that number should exist in itself, or must we contemplate two in two objects, three in three objects, and so forth? The same question arises about unity as considered within numbers; for if number can exist in itself independently of numbered things,[19] it can also exist previously to the essences. Can number therefore exist before the essences? It might be well preliminarily to assert that number is posterior to the Essence, and proceeds therefrom. But then if essence be one essence, and if two essences be two essences, one will precede essence, and the other numbers will precede the essences. (Would number then precede the essences) only in thought and conception, or also in the hypostatic existence? We should think as follows. When you think of a man as being one, or the beautiful as being one, the one that is thus conceived in both (beings) is something that is thought only afterward. Likewise, when you simultaneously consider a dog and a horse, here also two is evidently something posterior. But if you beget the man, if you beget the horse or the dog, or if you produce them outside when they already exist in you, without begetting them, nor producing them by mere chance (of seeing them), you will say, "We should go towards one (being), then pass to another, and thus get two; then make one more being, by adding my person." Likewise, (beings) were not numbered after they were created, but before they were created, when (the creator) decided how many should be created.

NUMBER SPLIT THE UNITY INTO PLURALITY; PYTHAGOREAN IDENTIFICATION OF IDEAS AND NUMBERS.

The universal Number therefore existed before the essences (were created); consequently, Number was not the essences. Doubtless, Number was in Essence; but it was not yet the number of Essence; for Essence still was one. But the power of Number, hypostatically existing within it, divided it, and made it beget the manifold. Number is either the being or actualization (of Essence); the very Organism and Intelligence are number. Essence is therefore the unified number, while the essences are developed number; Intelligence is the number which moves itself, and the Organism is the number that contains. Since therefore Essence was born from Unity, Essence, as it existed within Unity, must be Number. That is why (the Pythagoreans[20]) called the ideas unities and numbers.

TWO KINDS OF NUMBER: ESSENTIAL AND UNITARY.

Such then is "essential" Number (number that is "Being"). The other kind of number, which is called a number composed of digits, or "unities," is only an image of the former. The essential Number is contemplated in the intelligible forms, and assists in producing them; on the other hand, it exists primitively in essence, with essence, and before the essences. The latter find therein their foundation, source, root and principle.[21] Indeed, Number is the principle of Essence, and rests in it, otherwise it would split up. On the contrary, the One does not rest upon essence; otherwise essence would be one before participating in the One; likewise, what participates in the decad would be the decad already before participating in the decad.

ESSENCE IS A LOCATION FOR THE THINGS YET TO BE PRODUCED.

10. Subsisting therefore in the manifold, Essence therefore became Number when it was aroused to multiplicity, because it already contained within itself a sort of preformation or representation of the essences which it was ready to produce, offering the essences, as it were, a locality for the things whose foundation they were to be. When we say, "so much gold," or, "so many other objects," gold is one, and one does not thereby intend to make gold out of the number, but to make a number out of the gold; it is because one already possesses the number that one seeks to apply it to gold, so as to determine its quality. If essences were anterior to Number, and if Number were contemplated in them when the enumerating power enumerates the objects, the number of the (beings), whatever it is, would be accidental, instead of being determined in advance. If this be not the case, then must number, preceding (the beings) determine how many of them must exist; which means that, by the mere fact of the primitive existence of the Number, the (beings) which are produced undergo the condition of being so many, and each of them participates in unity whenever they are one. Now every essence comes from Essence because essence, by itself, is Essence; likewise, the One is one by itself. If every (being) be one, and if the multitude of (beings) taken together form the unity that is in them, they are one as the triad is one, and all beings also are one; not as is the Monad (or Unity), but as is a thousand, or any other number. He who, while enumerating, produced things, proclaims that there are a thousand of them, claims to do no more than to tell out what he learns from the things, as if he was indicating their colors, while really he is only expressing a condition of his reason; without which, he would not know how much of a multitude was present there. Why then does he speak so? Because he knows how to enumerate; which indeed he knows if he know the number, and this he can know only if the number exist. But not to know what is the number, at least under the respect of quantity, would be ridiculous, and even impossible.

AN OBJECT'S EXISTENCE IMPLIES A PREVIOUS MODEL IN ITSELF.

When one speaks of good things, one either designates objects which are such by themselves, or asserts that the good is their attribute. If one designate the goods of the first order,[22] one is speaking of the first Hypostasis, or rank of existence; if one designate the things of which the good is the attribute, this implies the existence of a nature of the good which has been attributed to them, or which produces this characteristic within them, or which is the Good in itself, or which, producing the good, nevertheless dwells in its own nature. Likewise, when, in connection with (beings), we speak of a decad, (or, group of ten), one is either referring to the Decad in itself, or, referring to the things of which the decad is an attribute, one is forced to recognize the existence of a Decad in itself, whose being is that of a decad. Consequently, the conferring of the name "decad" implies either that these (beings) are the Decad in itself, or above them in another Decad whose being is that of being a Decad in itself.

UNITY AND NUMBER PRECEDE THE ONE AND THE MANY BEINGS.

In general, everything which is predicated of an object either comes to it from without, or is its actualization. Unless by nature it be inconstant, being present now, and absent then, if it be always present, it is a being when the object is a being. If it be denied that its nature were that of a being, it will surely be granted that it is a part of the essences, and that it is an essence. Now, if the object can be conceived without the thing which is its actualization, this thing nevertheless exists contemporaneously with it, even though in thought it be conceived posteriorily. If the object cannot be conceived without this thing, as man cannot be conceived of without one, in this case one is not posterior to man, but is simultaneous, or even anterior, since the man's subsistence is entirely dependent thereon. As to us, we recognize that Unity and Number precede (Essence and the essences).

UNITY MUST EXIST IN THE INTELLIGIBLE BEFORE BEING APPLIED TO MULTIPLE BEINGS.

11. It may be objected that the decad is nothing else than ten unities. If the existence of the One be granted, why should we not also grant the existence of ten unities? Since the supreme Unity (the unity of the first Essence), possesses hypostatic existence, why should the case not be the same with the other unities (the complex unities contained within each of the essences)? It must not be supposed that the supreme Unity is bound up with a single essence; for in this case each of the other (beings) would no longer be one. If each of the other (beings) must be one, then unity is common to all the (beings); that is that single nature which may be predicated of the multiple (beings), and which must, as we have explained it, subsist in itself (in the primary essence) before the unity which resides in the multiple (beings).

THE SUPREME UNITY ADJUSTS ALL LOWER GROUP UNITIES.

As unity is seen in some one (being), and then in some other, if the second unity possess hypostatic existence also, then the supreme Unity (of the first Essence) will not alone possess hypostatic existence, and there will be thus a multitude of unities (as there is a multitude of beings). If the hypostatic existence of the first Unity be alone acknowledged, this will exist either in the Essence in itself, or in the One in itself. If it exist in the Essence in itself, the other unities (which exist in the other beings) will then be such merely by figure of speech, and will no longer be subordinated to the primary unity; or number will be composed of dissimilar unities, and the unities will differ from each other in so far as they are unities. If the primary unity exist already in the Unity in itself, what need would that Unity in itself have of that unity to be one? If all that be impossible, we shall have to recognize the existence of the One which is purely and simply one, which, by its "being" is entirely independent of all the other beings, which is named the chief Unity, and is conceived of as such. If unity exist on high (in the intelligible world) without any object that may be called one, why might not another One (the one of the first Being) subsist on high also? Why would not all the (beings), each being a separate unity, not constitute a multitude of unities, which might be the "multiple unity"? As the nature (of the first Being) begets, or rather, as it has begotten (from all eternity); or at least, as it has not limited itself to one of the things it has begotten, thus rendering the unity (of the first Being) somewhat continuous; if it circumscribe (what it produces) and promptly ceases in its procession, it begets small numbers; if it advance further, moving alone not in foreign matters, but in itself, it begets large numbers. It thus harmonizes every plurality and every being with every number, knowing well that, if each of the (beings) were not in harmony with some number, either they would not exist, or they would bear neither proportion, measure, nor reason.

ONE AND UNITY ARE WITHIN US; INDEPENDENTLY OF THE ONE OUTSIDE.

12. (Aristotle[23]) objects that "One" and "Unity" have no hypostatic (or, genuine) existence. Everywhere the One is something that is one. That is nothing but a simple modification experienced in our soul in presence of each essence. We might as easily affirm that when we assert "essence," this is but a simple modification of our soul, Essence (in itself) being absolutely nothing. If it be insisted that Essence exists because it excites and strikes our soul, which then represents it to herself, we see that the soul is equally impressed by the One, and represents Him to herself. Besides, we should ask (Aristotle) if this modification or conception of our soul do not bear to us the aspect of unity or the manifold? So much the more, we often say that an object is not one; evidently we then are not deriving the notion of unity from the object, because we are affirming that there is no unity in it. Unity therefore dwells within us, and it is in us without the object of which we predicate that it is some one thing.

THERE IS INDEED A UNITARY MODE OF EXISTENCE IN OUTSIDE OBJECTS.

It may be objected that having this unity in our soul depends on receiving from the exterior object a notion and an image, which is a conception furnished by this object. As the philosophers who profess this opinion do not differentiate the species of one and of number, and as they allow them no other hypostatic existence (than to be conceived by our soul), if they (practically do) allow them any sort of hypostatic existence, it will be very interesting to scrutinize the opinions of these.[24] They then say that the notion or conception that we have of the one or of the number derives from the objects themselves, is a notion as much "a posteriori" as those of "that,"[25] "something," "crowd," "festival," "army," or of "multitude"; for, just as the manifold is nothing without the multiple objects, nor a festival without the men gathered to celebrate the religious ceremony, thus "the One" is nothing without the one object, when we posit the one, conceiving it alone, having made an abstraction of everything else. The partisans of this opinion will cite many examples of the same kind, as the "right hand side," "the upper part," and their contraries. What reality indeed (to speak as they do), can the "right hand side" possess outside of a person who stands or sits here or there[26]? The case is similar with "the upper side," which refers to a certain part of the universe, and the "lower side" to another.[27] Our first answer to this argument is that we will allow that there is a certain kind of existence in the things themselves of which we have just spoken; but that this mode of existence is not identical in all things, considered either in respect to each other, or each in respect to the One which is in all. Further, we intend to refute one by one these arguments that have been opposed to us.

THE NOTION OF THE SUBJECT ONE DOES NOT COME FROM THE SUBJECT ITSELF.

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]

THE VERITABLE NUMBERS ARE INTELLIGIBLE ENTITIES.

Should we be asked to describe the operation of the participation of objects in unity and in numbers, we shall answer that this question connects with the more general problem of the participation of objects in intelligible forms. Besides, we shall have to admit that the decad presents itself under different aspects, according as it is considered to exist either in discrete quantities, or in continuous quantities, or in the reduction of many great forces to unity, or, last, into the intelligible entities to which we are later raised. It is among them, indeed, that are found the veritable Numbers (spoken of by Plato,[10]) which, instead of being considered as discovered in other (beings), exist within themselves; such is the Decad-in-itself, which exists by itself, instead of simply being a decad[34] composed of some intelligible entities.

NUMBER EXISTS BEFORE EVERY ANIMAL, AND THE UNIVERSAL ANIMAL.