(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.

(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.

(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.

(9) It remains then to consider whether Being by its distinction produced Number or Number produced that distinction. It is certain that either Number was the cause of Being, movement, rest, identity and difference, or these the cause of Number.

The first question is whether Number can exist in and of itself or is dependent upon things- Two being something observed in two things, Three in three; and so of the arithmetical One, for if this could exist apart from numbered objects it could exist also before the divisions of Being.

But could it precede Being itself?

For the present we must take it that Being precedes Number, is its source. But if One means one being and the duality two beings, then unity precedes Being, and Number precedes the Beings.

Mentally, to our approach? Yes: and in reality of existence as well.

Let us consider: When we think of the existence and the fine appearance of a man as forming one thing, that unity is certainly thought of as subsequent to a precedent duality; when we group a horse with a dog, the duality is obviously the subsequent. But think of that which brings man or horse or dog into being or produces them, with full intention, from where they lie latent within itself: the producer must say "I begin with a first, I pass on to a second; that makes two; counting myself there are three." Of course there was no such numbering even of Beings for their production, since the due number was known from the very beginning; but this consideration serves to show that all Number precedes the very Beings themselves.

But if Number thus preceded the Beings, then it is not included among them?

The truth is that it existed within the Authentic Being but not as applying to it, for Being was still unparted; the potentiality of Number existed and so produced the division within Being, put in travail with multiplicity; Number must be either the substance of Being or its Activity; the Life-Form as such and the Intellectual-Principle must be Number. Clearly Being is to be, thought of as Number Collective, while the Beings are Number unfolded: the Intellectual-Principle is Number moving within itself, while the Living-Form is Number container of the universe. Even Being is the outcome of the Unity, and, since the prior is unity, the secondary must be Number.

Hence it is that the Forms have been described as Henads and Numbers. This is the authentic Number; the other, the "monadic" is its image. The Authentic is that made manifest in the Forms and helping to bring them to be; primally it is the Number in the Authentic Being, inherent to it and preceding the Beings, serving to them as root, fount, first principle.

For the Unity is source to Being; Being's Being is stayed upon the Unity as its safeguard from dissolution; the Unity cannot rest upon Being which at that would be a unity before possessing unity; and so with the decad before possessing decadhood.

(14) To the argument touching relation we have an answer surely legitimate:

The Unity is not of a nature to lose its own manner of being only because something else stands in a state which it does not itself share; to stray from its unity it must itself suffer division into duality or the still wider plurality.

If by division the one identical mass can become a duality without loss of quantity, clearly the unity it possessed and by this destructive division lost was something distinct. What may be alternatively present and absent to the same subject must be classed among Real-Beings, regardless of position; an accidental elsewhere, it must have reality in itself whether it be manifested in things of sense or in the Intellectual- an accidental in the Laters but self-existent in the higher, especially in the First in its aspect of Unity developing into Being. We may be told that Unity may lose that character without change in itself, becoming duality by association with something else; but this is not true; unity does not become two things; neither the added nor what takes the addition becomes two; each remains the one thing it was; the duality is predicable of the group only, the unity remaining unchanged in each of those unchanged constituents.

Two and the Dyad are not essentially relative: if the only condition to the construction of duality were meeting and association such a relation might perhaps constitute Twoness and Duality; but in fact we see Duality produced by the very opposite process, by the splitting apart of a unity. This shows that duality- or any other such numerical form- is no relation produced either by scission or association. If one configuration produces a certain thing it is impossible that the opposite should produce the same so that the thing may be identified with the relation.

What then is the actual cause?

Unity is due to the presence of Unity; duality to that of Duality; it is precisely as things are white by Whiteness, just by Justice, beautiful by Beauty. Otherwise we must reject these universals and call in relation here also: justice would arise from a certain attitude in a given situation, Beauty from a certain pattern of the person with nothing present able to produce the beauty, nothing coming from without to effect that agreeable appearance.

You see something which you pronounce to be a unity; that thing possesses also size, form, and a host of other characteristics you might name; size, bulk, sweetness, bitterness and other Ideas are actually present in the thing; it surely cannot be thought that, while every conceivable quality has Real-Being, quantity has not and that while continuous quantity exists, discrete quantity does not and this though continuous quantity is measured by the discrete. No: as size by the presence of Magnitude, and Oneness by the presence of Unity, so with Duality and all the other numerical modes.

As to the How of participation, the enquiry is that of all participation in Ideal Forms; we must note, however, that the presence of the Decad in the looser totals is different from its presence in the continuous; there is difference again in its presence within many powers where multiplicity is concentred in unity; arrived at the Intellectuals, there too we discover Number, the Authentic Number, no longer entering the alien, Decad-Absolute not Decad of some particular Intellectual group.

(4) We have said that all must be brought back to a unity: this must be an authentic unity, not belonging to the order in which multiplicity is unified by participation in what is truly a One; we need a unity independent of participation, not a combination in which multiplicity holds an equal place: we have exhibited, also, the Intellectual Realm and the Intellectual-Principle as more closely a unity than the rest of things, so that there is nothing closer to The One. Yet even this is not The purely One.

This purely One, essentially a unity untouched by the multiple, this we now desire to penetrate if in any way we may.

Only by a leap can we reach to this One which is to be pure of all else, halting sharp in fear of slipping ever so little aside and impinging on the dual: for if we fail of the centre, we are in a duality which does not even include The authentic One but belongs on both sides, to the later order. The One does not bear to be numbered in with anything else, with a one or a two or any such quantity; it refuses to take number because it is measure and not the measured; it is no peer of other entities to be found among them; for thus, it and they alike would be included in some container and this would be its prior, the prior it cannot have. Not even essential number can belong to The One and certainly not the still later number applying to quantities; for essential number first appears as providing duration to the divine Intellection, while quantitative number is that which furnishes the Quantity found in conjunction with other things or which provides for Quantity independent of things, if this is to be thought of as number at all. The Principle which in objects having quantitative number looks to the unity from which they spring is a copy of the Principle which in the earlier order of number looks to the veritable One; and it attains its existence without in the least degree dissipating or shattering that prior unity: the dyad has come into being, but the precedent monad still stands; and this monad is quite distinct within the dyad from either of the two constituent unities, since there is nothing to make it one rather than the other: being neither, but simply that thing apart, it is present without being inherent.

But how are the two unities distinct and how is the dyad a unity, and is this unity the same as the unity by which each of the constituents is one thing?

Our answer must be that the unity is that of a participation in the primal unity with the participants remaining distinct from that in which they partake; the dyad, in so far as it is one thing, has this participation, but in a certain degree only; the unity of an army is not that of a single building; the dyad, as a thing of extension, is not strictly a unit either quantitatively or in manner of being.

Are we then to take it that the monads in the pentad and decad differ while the unity in the pentad is the same as that in the decad?

Yes, in the sense in which, big and little, ship is one with ship, army with army, city with city; otherwise, no. But certain difficulties in this matter will be dealt with later.

(10) When it takes lot with multiplicity, Being becomes Number by the fact of awakening to manifoldness;- before, it was a preparation, so to speak, of the Beings, their fore-promise, a total of henads offering a stay for what was to be based upon them.

Here with us a man will say "I wish I had such and such a quantity of gold"- or "such and such a number of houses." Gold is one thing: the wish is not to bring the numerical quantity into gold but to bring the gold to quantity; the quantity, already present in the mind, is to be passed on to the gold so that it acquire that numerical value.

If the Beings preceded the number and this were discerned upon them at the stirring, to such and such a total, of the numbering principle, then the actual number of the Beings would be a chance not a choice; since that total is not a matter of chance, Number is a causing principle preceding that determined total.

Number then pre-exists and is the cause by which produced things participate in quantity.

The single thing derives its unity by participation in Unity-Absolute; its being it derives from Being-Absolute, which holds its Being from itself alone; a unity is a unity in virtue of Being; the particular unity- where the unity is a multiple unity- is one thing only as the Triad is; the collective Being is a unity of this kind, the unity not of the monad but of the myriad or any such collective number.

Take a man affirming the presence of ten thousand things; it is he that produces the number; he does not tell us that the ten thousand have uttered it; they merely exhibit their several forms; the enumerator's mind supplies the total which would never be known if the mind kept still.

How does the mind pronounce?

By being able to enumerate; that is by knowing Number: but in order to this, Number must be in existence, and that that Principle should not know its own total content is absurd, impossible.

It is with Number as with Good. When we pronounce things to be good either we mean that they are in their own nature so or we affirm goodness as an accidental in them. Dealing with the primals, the goodness we have in mind is that First Hypostasis; where the goodness is an accidental we imply the existence of a Principle of Good as a necessary condition of the accidental presence; there must be some source of that good which is observed elsewhere, whether this source be an Absolute Good or something that of its own nature produces the good. Similarly with number; in attributing the decad to things we affirm either the truly existent decad or, where the decadhood is accidental, we necessarily posit the self-subsistent decad, decad not associated; if things are to be described as forming a decad, then either they must be of themselves the decad or be preceded by that which has no other being than that of decadhood.

It must be urged as a general truth that anything affirmed of a subject not itself either found its way in from outside or is the characteristic Act of that subject; and supposing the predicated attribute to show no variation of presence and absence but to be always present, then, if the subject is a Real Being so also is the accidental in an equal degree; or, failing Real Being, it at least belongs to the existents, it exists. In the case when the subject can be thought of as remaining without its Act, yet that Act is inbound with it even though to our minds it appears as a later; when on the contrary the subject cannot be conceived without the attribute-man, for example, without unity- then the attribute is either not later but concomitant or, being essential to the existence, is precedent. In our view, Unity and Number are precedent.

(4) We have to enquire into the existence of the Numbers in the Intellectual. Are they Ideas added to the other Ideas? Or are they no more than necessary concomitants to the Ideas?

In the latter case, Being, as the first would give us the conception of the Monad; then since Being produces motion and rest, Three exists; and so on for all the other members of the realm of Being. Or perhaps there is one monad for each member, or a monad for the first, with a dyad for its next, since there exists a series, and a corresponding number for every successive total, decad for ten, and so on.

If, on the contrary, Number is a direct production of the Intellectual-Principle , there is the question whether it preceded or followed the other Ideas.

Plato, where he says that men arrived at the conception of Number by way of the changes of day and night- thus making the concept depend upon variation among things- seems to hold that the things numerable precede and by their differences produce number: Number then would consist in a process within the human mind passing onwards from thing to thing; it results by the fact that the mind takes count, that is when the mind traverses things and reports their differences; observing pure identity unbroken by difference, it says One. But there is the passage where he tells us that the veritable Number has Being, is a Being; this is the opposed view that Number is no product of the reckoning mind but a reality in itself, the concept of which is reawakened in the mind by changes in things of sense.

(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.

(21) And as marriage generates from male and female, so six is generated from the odd number three, which is called the masculine number, and the even number two, which is considered the feminine. For twice three are six.

(15) We must repeat: The Collective Being, the Authentic, There, is at once Being and Intellectual-Principle and the Complete Living Form; thus it includes the total of living things; the Unity There is reproduced by the unity of this living universe in the degree possible to it- for the sense-nature as such cannot compass that transcendental unity- thus that Living-All is inevitably Number-Entire: if the Number were not complete, the All would be deficient to the extent of some number, and if every number applicable to living things were not contained in it, it would not be the all-comprehending Life-Form. Therefore, Number exists before every living thing, before the collective Life-Form.

Again: Man exists in the Intellectual and with him all other living things, both by possession of Real-Being and because that is the Life-Form Complete. Even the man of this sphere is a member of the Intellectual since that is the Life-Form Complete; every living thing by virtue of having life, is There, There in the Life-form, and man is There also, in the Intellectual, in so far as he is intellect, for all intelligences are severally members of That. Now all this means Number There. Yet even in Intellect Number is not present primally; its presence There is the reckoning of the Acts of Intellectual-Principle; it tallies with the justice in Intellectual-Principle, its moral wisdom, its virtues, its knowledge, all whose possession makes That Principle what it is.

But knowledge- must not this imply presence to the alien? No; knowledge, known and knower are an identity; so with all the rest; every member of Intellectual-Principle is therefore present to it primally; justice, for example, is not accidental to it as to soul in its character as soul, where these virtues are mainly potential becoming actual by the intention towards Intellectual-Principle and association with it.

Next we come to Being, fully realized, and this is the seat of Number; by Number, Being brings forth the Beings; its movement is planned to Number; it establishes the numbers of its offspring before bringing them to be, in the same way as it establishes its own unity by linking pure Being to the First: the numbers do not link the lower to the First; it suffices that Being is so linked; for Being, in taking form as Number, binds its members to itself. As a unity, it suffers no division, remaining self-constant; as a thing of division, containing its chosen total of members, it knows that total and so brings forth Number, a phase therefore of its content: its development of part is ruled by the powers of Number, and the Beings it produces sum to that Number. Thus Number, the primal and true, is Principle and source of actuality to the Beings.

Hence it is that in our sphere, also, Number accompanies the coming to be of particular things and to suppose another number than the actual is to suppose the production of something else or of nothing.

These then are the primal numbers; they are numerable; the numbers of the other order are of a double character; as derived from the first numbers they are themselves numerable but as acting for those first they are measures of the rest of things, numbering numbers and numerables. For how could they declare a Decad save in the light of numbers within themselves?

(524) Most true. This was what I meant when I spoke of impressions which invited the intellect, or the reverse—those which are simultaneous with opposite impressions, invite thought; those which are not simultaneous do not. I understand, he said, and agree with you. And to which class do unity and number belong? I do not know, he replied. Think a little and you will see that what has preceded will supply the answer; for if simple unity could be adequately perceived by the sight or by any other sense, then, as we were saying in the case of the finger, there would be nothing to attract towards being; but when there is some contradiction always present, and one is the reverse of one and involves the conception of plurality, then thought begins to be aroused within us, and the soul perplexed and wanting to arrive at a decision asks ‘What is absolute unity?’ This is the way in which the study of the one has a power of drawing and converting the mind to the contemplation of true being. And surely, he said, this occurs notably in the case of one; for we see the same thing to be both one and infinite in multitude? Yes, I said; and this being true of one must be equally true of all number? Certainly. And all arithmetic and calculation have to do with number? Yes.

(2) It may be suggested that, while in the unities of the partial order the essence and the unity are distinct, yet in collective existence, in Real Being, they are identical, so that when we have grasped Being we hold unity; Real Being would coincide with Unity. Thus, taking the Intellectual-Principle as Essential Being, that principle and the Unity Absolute would be at once Primal Being and Pure Unity, purveying, accordingly, to the rest of things something of Being and something, in proportion, of the unity which is itself.

There is nothing with which the unity would be more plausibly identified than with Being; either it is Being as a given man is man or it will correspond to the Number which rules in the realm of the particular; it will be a number applying to a certain unique thing as the number two applies to others.

Now if Number is a thing among things, then clearly so this unity must be; we would have to discover what thing of things it is. If Number is not a thing but an operation of the mind moving out to reckon, then the unity will not be a thing.

We found that anything losing unity loses its being; we are therefore obliged to enquire whether the unity in particulars is identical with the being, and unity absolute identical with collective being.

Now the being of the particular is a manifold; unity cannot be a manifold; there must therefore be a distinction between Being and Unity. Thus a man is at once a reasoning living being and a total of parts; his variety is held together by his unity; man therefore and unity are different- man a thing of parts against unity partless. Much more must Collective Being, as container of all existence, be a manifold and therefore distinct from the unity in which it is but participant.

Again, Collective Being contains life and intelligence- it is no dead thing- and so, once more, is a manifold.

If Being is identical with Intellectual-Principle, even at that it is a manifold; all the more so when count is taken of the Ideal Forms in it; for the Idea, particular or collective, is, after all, a numerable agglomeration whose unity is that of a kosmos.

Above all, unity is The First: but Intellectual-Principle, Ideas and Being, cannot be so; for any member of the realm of Forms is an aggregation, a compound, and therefore- since components must precede their compound- is a later.

Other considerations also go to show that the Intellectual-Principle cannot be the First. Intellect must be above the Intellectual Act: at least in its higher phase, that not concerned with the outer universe, it must be intent upon its Prior; its introversion is a conversion upon the Principle.

Considered as at once Thinker and Object of its Thought, it is dual, not simplex, not The Unity: considered as looking beyond itself, it must look to a better, to a prior: looking simultaneously upon itself and upon its Transcendent, it is, once more, not a First.

There is no other way of stating Intellectual-Principle than as that which, holding itself in the presence of The Good and First and looking towards That, is self-present also, self-knowing and Knowing itself as All-Being: thus manifold, it is far from being The Unity.

In sum: The Unity cannot be the total of beings, for so its oneness is annulled; it cannot be the Intellectual-Principle, for so it would be that total which the Intellectual-Principle is; nor is it Being, for Being is the manifold of things.

(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.

(5) As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the divine, unless by a deliberate apostasy.

Bringing itself close to the divine Intellect, becoming, as it were, one with this, it seeks still further: What Being, now, has engendered this God, what is the Simplex preceding this multiple; what the cause at once of its existence and of its existing as a manifold; what the source of this Number, this Quantity?

Number, Quantity, is not primal: obviously before even duality, there must stand the unity.

The Dyad is a secondary; deriving from unity, it finds in unity the determinant needed by its native indetermination: once there is any determination, there is Number, in the sense, of course, of the real Number. And the soul is such a number or quantity. For the Primals are not masses or magnitudes; all of that gross order is later, real only to the sense-thought; even in seed the effective reality is not the moist substance but the unseen- that is to say Number and the Reason-Principle .

Thus by what we call the Number and the Dyad of that higher realm, we mean Reason Principles and the Intellectual-Principle: but while the Dyad is, as regards that sphere, undetermined- representing, as it were, the underly of The One- the later Number - that which rises from the Dyad and The One- is not Matter to the later existents but is their forming-Idea, for all of them take shape, so to speak, from the ideas rising within this. The determination of the Dyad is brought about partly from its object- The One- and partly from itself, as is the case with all vision in the act of sight: intellection is vision occupied upon The One.