(186) The number nine is divine, receives its completion from three triads, and attains the summits of theology, according to the Chaldaic philosophy as Porphyry informeth us.

(5) What then is the veritable nature of Number?

Is it an accompaniment upon each substance, something seen in the things as in a man we see one man, in a being one being and in the total of presentations the total of number?

But how explain the dyad and triad? How comes the total to be unitary and any particular number to be brought under unity? The theory offers a multiplicity of units, and no number is reducible to unity but the simple "one." It might be suggested that a dyad is that thing- or rather what is observed upon that thing- which has two powers combined, a compound thing related to a unity: or numbers might be what the Pythagoreans seem to hold them in their symbolic system in which Justice, for example, is a Tetrad: but this is rather to add the number, a number of manifold unity like the decad, to the multiplicity of the thing which yet is one thing. Now it is not so that we treat the ten things; we bring them together and apply the figure ten to the several items. Or rather in that case we say ten, but when the several items form a unity we say decad. This would apply in the Intellectual as in the sensible.

But how then can number, observed upon things, rank among Real Beings?

One answer might be that whiteness is similarly observed upon things and yet is real, just as movement is observed upon things and there is still a real existence of movement. But movement is not on a par with number: it is because movement is an entity that unity can be observed upon it. Besides, the kind of real existence thus implied annuls the reality of number, making it no more than an attribute; but that cannot be since an attribute must exist before it can be attributed; it may be inseparable from the subject but still must in itself be something, some entity as whiteness is; to be a predicate it must be that which is to be predicated. Thus if unity is observed in every subject, and "one man" says more than "man's oneness being different from the manness and common to all things- then this oneness must be something prior to man and to all the rest: only so can the unity come to apply to each and to all: it must therefore be prior also to even movement, prior to Being, since without unity these could not be each one thing: of course what is here meant is not the unity postulated as transcending Being but the unity predicable of the Ideas which constitute each several thing. So too there is a decad prior to the subject in which we affirm it; this prior would be the decad absolute, for certainly the thing in which the decad is observed is not that absolute.

Is this unity, then, connate and coexistent to the Beings? Suppose it coexistent merely as an accidental, like health in man, it still must exist of itself; suppose it present as an element in a compound, there must first exist unity and the unity absolute that can thus enter into composition; moreover if it were compounded with an object brought into being by its agency it would make that object only spuriously a unity; its entry would produce a duality.

But what of the decad? Where lies the need of decad to a thing which, by totalling to that power, is decad already?

The need may be like that of Form to Matter; ten and decad may exist by its virtue; and, once more, the decad must previously exist of its own existence, decad unattached.

(3) And out of the triad one stands apart; and in the heptad there are two triads, and one standing apart. The dodecad symbolizes war, the triad of amity, the triad of enmity, three which are life-giving, three which are death-dealing, and God, the faithful king, rules over all from the throne of his sanctity. One above three, three above seven, and seven above twelve, and all are linked together, and one with another.

(11) It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real existence why not the rest? We are certainly not compelled to attach that one henad to some one thing and so deprive all the rest of the means to unity: since every existent must be one thing, the unity is obviously common to all. This means one principle applying to many, the principle whose existence within itself we affirmed to be presupposed by its manifestation outside.

But if a henad exists in some given object and further is observed in something else, then that first henad being real, there cannot be only one henad in existence; there must be a multiplicity of henads.

Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads . If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity.

Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well?

Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously- or rather has produced once for all- not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent- not in the sense of moving from point to point but in its inner changes- it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason.

(3) The ten numbers formed from nothing are the Decad: these are seen in the fingers of the hands, five on one, five on the other, and over them is the Covenant by voice spiritual, and the rite of Circumcision, corporeal (as of Abraham).

(4) On another principle, 120 is a triangular number, and consists of the equality of the number 64, [which consists of eight of the odd numbers beginning with unity], the addition of which (1, 3, 5, 7, 9, 11, 13, 15) in succession generate squares; and of the inequality of the number 56, consisting of seven of the even numbers beginning with 2 (2, 4, 6, 8, 10, 12, 14), which produce the numbers that are not squares Again, according to another way of indicating. the number 120 consists of four numbers - of one triangle, 15; of another, a square, 25; of a third, a pentagon, 35; and of a fourth, a hexagon, 45. The 5 is taken according to the same ratio in each mode. For in triangular numbers, from the unity 5 comes 15; and in squares, 25; and of those in succession, proportionally. Now 25, which is the number 5 from unity, is said to be the symbol of the Levitical tribe. And the number 35 depends also on the arithmetic, geometric, and harmonic scale of doubles - 6, 8, 9, 12; the addition of which makes 35. In these days, the Jews say that seven months' children are formed. And the number 45 depends on the scale of triples - 6, 9, 12, 18 - the addition of which makes 45; and similarly, in these days they say that nine months' children are formed.

(4) From two letters, or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty; from seven, five thousand and forty; and from thence their numbers increase in a manner beyond counting; and are incomprehensible. These seven are Planets of the Universe, the Sun, Venus, Mercury, Moon, Saturn, Jupiter, and Mars; the seven days are the days of creation; and these an the seven gateways of a man, two eyes, two ears, two nostrils and a mouth, through which he perceives by his senses.

(16) But here we may be questioned about these numbers which we describe as the primal and authentic:

"Where do you place these numbers, in what genus among Beings? To everyone they seem to come under Quantity and you have certainly brought Quantity in, where you say that discrete Quantity equally with the continuous holds place among Beings; but you go on to say that there are the numbers belonging to the Firsts and then talk of other numbers quite distinct, those of reckoning; tell us how you arrange all this, for there is difficulty here. And then, the unity in sense-things- is that a quantity or is quantity here just so many units brought together, the unity being the starting-point of quantity but not quantity itself? And, if the starting-point, is it a kindred thing or of another genus? All this you owe it to us to make clear."

Be it so; we begin by pointing out a distinction:

You take one thing with another- for we must first deal with objects of sense- a dog and a man, or two men; or you take a group and affirm ten, a decad of men: in this case the number affirmed is not a Reality, even as Reality goes in the sphere of sense, but is purely Quantity: similarly when you resolve into units, breaking up the decad, those units are your principle of Quantity since the single individual is not a unity absolute.

But the case is different when you consider one man in himself and affirm a certain number, duality, for example, in that he is at once living and reasoning.

By this analysis and totalling, you get quantity; but there are two objects under consideration and each of these is one; each of the unities contributes to the complete being and the oneness is inherent in each; this is another kind of number; number essential; even the duality so formed is no posterior; it does not signify a quantity apart from the thing but the quantity in the essence which holds the thing together. The number here is no mere result of your detailing; the things exist of themselves and are not brought together by your reckoning, but what has it to do with essential reality that you count one man in with another? There is here no resultant unity such as that of a choir- the decad is real only to you who count the ten; in the ten of your reckoning there cannot be a decad without a unitary basis; it is you that make the ten by your counting, by fixing that tenness down to quantity; in choir and army there is something more than that, something not of your placing.

But how do you come to have a number to place?

The Number inherent apart from any enumeration has its own manner of being, but the other, that resulting upon the appearance of an external to be appraised by the Number within yourself, is either an Act of these inherent numbers or an Act in accordance with them; in counting we produce number and so bring quantity into being just as in walking we bring a certain movement into being.

But what of that "Number within us having its own manner of being"?

It is the Number of our essence. "Our essence" we read "partakes of Number and harmony and, also, is Number and harmony." "Neither body nor magnitude," someone says: soul, then, is Number since it is essence. The number belonging to body is an essence of the order of body; the number belonging to soul constitutes the essences of souls.

In the Intellectuals, all, if the Absolute Living-Form, there is a multiple- a triad, let us say- that Triad of the Living-Form is of the nature of essence: and the Triad prior to any living thing, Triad in the realm of Being, is a principle of essence.

When you enumerate two things- say, animal and beauty- each of these remains one thing; the number is your production; it lay within yourself; it is you that elaborate quantity, here the dyad. But when you declare virtue to be a Tetrad, you are affirming a Tetrad which does actually exist; the parts, so to speak, make one thing; you are taking as the object of your act a Unity- Tetrad to which you accommodate the Tetrad within yourself.