(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.

(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.

(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.

(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.

(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 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.

(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.

(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.

(13) It cannot reasonably be thought that the notion of unity is derived from the object since this is physical- man, animal, even stone, a presentation of that order is something very different from unity ; if that presentation were unity, the mind could never affirm unity unless of that given thing, man, for example.

Then again, just as in the case of "On the right" or other such affirmation of relation, the mind does not affirm in some caprice but from observation of contrasted position, so here it affirms unity in virtue of perceiving something real; assuredly the assertion of unity is not a bare attitude towards something non-existent. It is not enough that a thing be alone and be itself and not something else: and that very "something else" tells of another unity. Besides Otherness and Difference are later; unless the mind has first rested upon unity it cannot affirm Otherness or Difference; when it affirms Aloneness it affirms unity-with-aloneness; thus unity is presupposed in Aloneness.

Besides, that in us which asserts unity of some object is first a unity, itself; and the object is a unity before any outside affirmation or conception.

A thing must be either one thing or more than one, manifold: and if there is to be a manifold there must be a precedent unity. To talk of a manifold is to talk of what has something added to unity; to think of an army is to think of a multitude under arms and brought to unity. In refusing to allow the manifold to remain manifold, the mind makes the truth clear; it draws a separate many into one, either supplying a unity not present or keen to perceive the unity brought about by the ordering of the parts; in an army, even, the unity is not a fiction but as real as that of a building erected from many stones, though of course the unity of the house is more compact.

If, then, unity is more pronounced in the continuous, and more again where there is no separation by part, this is clearly because there exists, in real existence, something which is a Nature or Principle of Unity. There cannot be a greater and less in the non-existent: as we predicate Substance of everything in sense, but predicate it also of the Intellectual order and more strictly there- since we hold that the greater and more sovereign substantiality belongs to the Real Beings and that Being is more marked in Substance, even sensible Substance, than in the other Kinds- so, finding unity to exhibit degree of more and less, differing in sense-things as well as in the Intellectual, we must similarly admit that Unity exists under all forms though still by reference, only, to that primal Unity.

As Substance and Real Being, despite the participation of the sensible, are still of the Intellectual and not the sensible order, so too the unity observed present in things of sense by participation remains still an Intellectual and to be grasped by an Intellectual Act. The mind, from a thing present to it, comes to knowledge of something else, a thing not presented; that is, it has a prior knowledge. By this prior knowledge it recognises Being in a particular being; similarly when a thing is one it can affirm unity as it can affirm also duality and multiplicity.

It is impossible to name or conceive anything not making one or two or some number; equally impossible that the thing should not exist without which nothing can possibly be named or conceived; impossible to deny the reality of that whose existence is a necessary condition of naming or affirming anything; what is a first need, universally, to the formation of every concept and every proposition must exist before reasoning and thinking; only as an existent can it be cited to account for the stirring of thought. If Unity is necessary to the substantial existence of all that really is- and nothing exists which is not one- Unity must precede Reality and be its author. It is therefore, an existent Unity, not an existent that develops Unity; considered as Being-with-Unity it would be a manifold, whereas in the pure Unity there is no Being save in so far as Unity attends to producing it. As regards the word "This," it is nat a bare word; it affirms an indicated existence without using the name, it tells of a certain presence, whether a substance or some other existent; any This must be significant; it is no attitude of the mind applying itself to a non-existent; the This shows a thing present, as much as if we used the strict name of the object.

(11) We are bound however to enquire under what mode unity is contained in Being. How is what is termed the "dividing" effected- especially the dividing of the genera Being and unity? Is it the same division, or is it different in the two cases?

First then: In what sense, precisely, is any given particular called and known to be a unity? Secondly: Does unity as used of Being carry the same connotation as in reference to the Absolute?

Unity is not identical in all things; it has a different significance according as it is applied to the Sensible and the Intellectual realms- Being too, of course, comports such a difference- and there is a difference in the unity affirmed among sensible things as compared with each other; the unity is not the same in the cases of chorus, camp, ship, house; there is a difference again as between such discrete things and the continuous. Nevertheless, all are representations of the one exemplar, some quite remote, others more effective: the truer likeness is in the Intellectual; Soul is a unity, and still more is Intellect a unity and Being a unity.

When we predicate Being of a particular, do we thereby predicate of it unity, and does the degree of its unity tally with that of its being? Such correspondence is accidental: unity is not proportionate to Being; less unity need not mean less Being. An army or a choir has no less Being than a house, though less unity.

It would appear, then, that the unity of a particular is related not so much to Being as to a standard of perfection: in so far as the particular attains perfection, so far it is a unity; and the degree of unity depends on this attainment. The particular aspires not simply to Being, but to Being-in-perfection: it is in this strain towards their perfection that such beings as do not possess unity strive their utmost to achieve it.

Things of nature tend by their very nature to coalesce with each other and also to unify each within itself; their movement is not away from but towards each other and inwards upon themselves. Souls, moreover, seem to desire always to pass into a unity over and above the unity of their own substance. Unity in fact confronts them on two sides: their origin and their goal alike are unity; from unity they have arisen, and towards unity they strive. Unity is thus identical with Goodness ; for no being ever came into existence without possessing, from that very moment, an irresistible tendency towards unity.

From natural things we turn to the artificial. Every art in all its operation aims at whatsoever unity its capacity and its models permit, though Being most achieves unity since it is closer at the start.

That is why in speaking of other entities we assert the name only, for example man; when we say "one man," we have in mind more than one; and if we affirm unity of him in any other connection, we regard it as supplementary : but when we speak of Being as a whole we say it is one Being without presuming that it is anything but a unity; we thereby show its close association with Goodness.

Thus for Being, as for the others, unity turns out to be, in some sense, Principle and Term, not however in the same sense as for things of the physical order- a discrepancy leading us to infer that even in unity there are degrees of priority.

How, then, do we characterize the unity in Being? Are we to think of it as a common property seen alike in all its parts? In the first place, the point is common to lines and yet is not their genus, and this unity we are considering may also be common to numbers and not be their genus- though, we need hardly say, the unity of Unity-Absolute is not that of the numbers, one, two and the rest. Secondly, in Being there is nothing to prevent the existence of prior and posterior, simple and composite: but unity, even if it be identical in all the manifestations of Being, having no differentiae can produce no species; but producing no species it cannot be a genus.

(17) But what of the Infinite Number we hear of; does not all this reasoning set it under limit?

And rightly so if the thing is to be a number; limitlessness and number are in contradiction.

How, then, do we come to use the term? Is it that we think of Number as we think of an infinite line, not with the idea that any such lire exists but that even the very greatest- that of the universe, for example- may be thought of as still greater? So it might be with number; let it be fixed, yet we still are free to think of its double, though not of course to produce the doubled quantity since it is impossible to join to the actual what is no more than a conception, a phantasm, private to ourselves.

It is our view that there does exist an infinite line, among the Intellectual Beings: for There a line would not be quantitative and being without quantity could be numerically infinite. This however would be in another mode than that of limitless extension. In what mode then? In that the conception of the Absolute Line does not include the conception of limit.

But what sort of thing is the Line in the Intellectual and what place does it hold?

It is later than Number since unity is observed in it; it rises at one point and traverses one course and simply lacks the quantity that would be the measure of the distance.

But where does this thing lie? Is it existent only in the defining thought, so to speak?

No; it is also a thing, though a thing of the Intellectual. All that belongs to that order is at once an Intellectual and in some degree the concrete thing. There is a position, as well as a manner of being, for all configurations, for surface, for solid. And certainly the configurations are not of our devising; for example, the configurations of the universe are obviously antecedent to ourselves; so it must be with all the configurations of the things of nature; before the bodily reproductions all must exist There, without configuration, primal configurations. For these primals are not shapes in something; self-belonging, they are perfect without extension; only the extended needs the external. In the sphere of Real-Being the configuration is always a unity; it becomes discrete either in the Living-Form or immediately before: I say "becomes discrete" not in the sense that it takes magnitude There but that it is broken apart for the purpose of the Living-Form and is allotted to the bodies within that Form- for instance, to Fire There, the Intellectual Pyramid. And because the Ideal-Form is There, the fire of this sphere seeks to produce that configuration against the check of Matter: and so of all the rest as we read in the account of the realm of sense.

But does the Life-Form contain the configurations by the mere fact of its life?

They are in the Intellectual-Principle previously but they also exist in the Living-Form; if this be considered as including the Intellectual-Principle, then they are primally in the Life-Form, but if that Principle comes first then they are previously in that. And if the Life-Form entire contains also souls, it must certainly be subsequent to the Intellectual-Principle.

No doubt there is the passage "Whatever Intellect sees in the entire Life-Form"; thus seeing, must not the Intellectual-Principle be the later?

No; the seeing may imply merely that the reality comes into being by the fact of that seeing; the Intellectual-Principle is not external to the Life-Form; all is one; the Act of the Intellectual-Principle possesses itself of bare sphere, while the Life-Form holds the sphere as sphere of a living total.

(12) But why, after all, should it not be such a manifold as long as it remains one substantial existence, having the multiplicity not of a compound being but of a unity with a variety of activities?

Now, no doubt, if these various activities are not themselves substantial existences- but merely manifestations of latent potentiality- there is no compound; but, on the other hand, it remains incomplete until its substantial existence be expressed in act. If its substantial existence consists in its Act, and this Act constitutes multiplicity, then its substantial existence will be strictly proportioned to the extent of the multiplicity.

We allow this to be true for the Intellectual-Principle to which we have allotted self-knowing; but for the first principle of all, never. Before the manifold, there must be The One, that from which the manifold rises: in all numerical series, the unit is the first.

But- we will be answered- for number, well and good, since the suite makes a compound; but in the real beings why must there be a unit from which the multiplicity of entities shall proceed?

Because the multiplicity would consist of disjointed items, each starting at its own distinct place and moving accidentally to serve to a total.

But, they will tell us, the Activities in question do proceed from a unity, from the Intellectual-Principle, a simplex.

By that they admit the existence of a simplex prior to the Activities; and they make the Activities perdurable and class them as substantial existences ; but as Hypostases they will be distinct from their source, which will remain simplex; while its product will in its own nature be manifold and dependent upon it.

Now if these activities arise from some unexplained first activity in that principle, then it too contains the manifold: if, on the contrary, they are the very earliest activities and the source and cause of any multiple product and the means by which that Principle is able, before any activity occurs, to remain self-centred, then they are allocated to the product of which they are the cause; for this principle is one thing, the activities going forth from it are another, since it is not, itself, in act. If this be not so, the first act cannot be the Intellectual-Principle: the One does not provide for the existence of an Intellectual-Principle which thereupon appears; that provision would be something intervening between the One and the Intellectual-Principle, its offspring. There could, in fact, be no such providing in The One, for it was never incomplete; and such provision could name nothing that ought to be provided. It cannot be thought to possess only some part of its content, and not the whole; nor did anything exist to which it could turn in desire. Clearly anything that comes into being after it, arises without shaking to its permanence in its own habit. It is essential to the existence of any new entity that the First remain in self-gathered repose throughout: otherwise, it moved before there was motion and had intellectual act before any intellection- unless, indeed, that first act was incomplete, nothing more than a tendency. And what can we imagine it lights upon to become the object of such a tendency?

The only reasonable explanation of act flowing from it lies in the analogy of light from a sun. The entire intellectual order may be figured as a kind of light with the One in repose at its summit as its King: but this manifestation is not cast out from it: we may think, rather, of the One as a light before the light, an eternal irradiation resting upon the Intellectual Realm; this, not identical with its source, is yet not severed from it nor of so remote a nature as to be less than Real-Being; it is no blind thing, but is seeing and knowing, the primal knower.

The One, as transcending Intellect, transcends knowing: above all need, it is above the need of the knowing which pertains solely to the Secondary Nature. Knowing is a unitary thing, but defined: the first is One, but undefined: a defined One would not be the One-absolute: the absolute is prior to the definite.

(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.

(12) We may be told that unity and monad have no real existence, that the only unity is some definite object that is one thing, so that all comes to an attitude of the mind towards things considered singly.

But, to begin with, why at this should not the affirmation of Being pass equally as an attitude of mind so that Being too must disappear? No doubt Being strikes and stings and gives the impression of reality; but we find ourselves just as vividly struck and impressed in the presence of unity. Besides, is this attitude, this concept itself, a unity or a manifold? When we deny the unity of an object, clearly the unity mentioned is not supplied by the object, since we are saying it has none; the unity therefore is within ourselves, something latent in our minds independently of any concrete one thing.

"But the unity we thus possess comes by our acceptance of a certain idea or impression from things external; it is a notion derived from an object. Those that take the notion of numbers and of unity to be but one species of the notions held to be inherent in the mind must allow to numbers and to unity the reality they ascribe to any of the others, and upon occasion they must be met; but no such real existence can be posited when the concept is taken to be an attitude or notion rising in us as a by-product of the objects; this happens when we say "This," "What," and still more obviously in the affirmations "Crowd," "Festival," "Army," "Multiplicity." As multiplicity is nothing apart from certain constituent items and the festival nothing apart from the people gathered happily at the rites, so when we affirm unity we are not thinking of some Oneness self-standing, unrelated. And there are many other such cases; for instance "on the right," "Above" and their opposites; what is there of reality about this "On-the-right-ness" but the fact that two different positions are occupied? So with "Above": "Above" and "Below" are a mere matter of position and have no significance outside of this sphere.

Now in answer to this series of objections our first remark is that there does exist an actuality implicit in each one of the relations cited; though this is not the same for all or the same for correlatives or the same for every reference to unity.

But these objections must be taken singly.

(12) Enough upon that side of the question. But how does the perfection of numbers, lifeless things, depend upon their particular unity? Just as all other inanimates find their perfection in their unity.

If it should be objected that numbers are simply non-existent, we should point out that our discussion is concerned with beings considered from the aspect of their unity.

We may again be asked how the point- supposing its independent existence granted- participates in perfection. If the point is chosen as an inanimate object, the question applies to all such objects: but perfection does exist in such things, for example in a circle: the perfection of the circle will be perfection for the point; it will aspire to this perfection and strive to attain it, as far as it can, through the circle.

But how are the five genera to be regarded? Do they form particulars by being broken up into parts? No; the genus exists as a whole in each of the things whose genus it is.

But how, at that, can it remain a unity? The unity of a genus must be considered as a whole-in-many.

Does it exist then only in the things participating in it? No; it has an independent existence of its own as well. But this will, no doubt, become clearer as we proceed.

(3) We may be told that nothing prevents an identity being thus multiple. But there must be a unity underlying the aggregate: a manifold is impossible without a unity for its source or ground, or at least, failing some unity, related or unrelated. This unity must be numbered as first before all and can be apprehended only as solitary and self-existent.

When we recognize it, resident among the mass of things, our business is to see it for what it is- present to the items but essentially distinguished from them- and, while not denying it there, to seek this underly of all no longer as it appears in those other things but as it stands in its pure identity by itself. The identity resident in the rest of things is no doubt close to authentic identity but cannot be it; and, if the identity of unity is to be displayed beyond itself, it must also exist within itself alone.

It may be suggested that its existence takes substantial form only by its being resident among outside things: but, at this, it is itself no longer simplex nor could any coherence of manifolds occur. On the one hand things could take substantial existence only if they were in their own virtue simplex. On the other hand, failing a simplex, the aggregate of multiples is itself impossible: for the simplex individual thing could not exist if there were no simplex unity independent of the individual, and, not existing, much less could it enter into composition with any other such: it becomes impossible then for the compound universe, the aggregate of all, to exist; it would be the coming together of things that are not, things not merely lacking an identity of their own but utterly non-existent.

Once there is any manifold, there must be a precedent unity: since any intellection implies multiplicity in the intellective subject, the non-multiple must be without intellection; that non-multiple will be the First: intellection and the Intellectual-Principle must be characteristic of beings coming later.

(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?

(9) Anaxagoras, again, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision.

Heraclitus, with his sense of bodily forms as things of ceaseless process and passage, knows the One as eternal and intellectual.

In Empedocles, similarly, we have a dividing principle, "Strife," set against "Friendship"- which is The One and is to him bodiless, while the elements represent Matter.

Later there is Aristotle; he begins by making the First transcendent and intellective but cancels that primacy by supposing it to have self-intellection. Further he affirms a multitude of other intellective beings- as many indeed as there are orbs in the heavens; one such principle as in- over to every orb- and thus his account of the Intellectual Realm differs from Plato's and, failing reason, he brings in necessity; though whatever reasons he had alleged there would always have been the objection that it would be more reasonable that all the spheres, as contributory to one system, should look to a unity, to the First.

We are obliged also to ask whether to Aristotle's mind all Intellectual Beings spring from one, and that one their First; or whether the Principles in the Intellectual are many.

If from one, then clearly the Intellectual system will be analogous to that of the universe of sense-sphere encircling sphere, with one, the outermost, dominating all- the First will envelop the entire scheme and will be an Intellectual Kosmos; and as in our universe the spheres are not empty but the first sphere is thick with stars and none without them, so, in the Intellectual Kosmos, those principles of Movement will envelop a multitude of Beings, and that world will be the realm of the greater reality.

If on the contrary each is a principle, then the effective powers become a matter of chance; under what compulsion are they to hold together and act with one mind towards that work of unity, the harmony of the entire heavenly system? Again what can make it necessary that the material bodies of the heavenly system be equal in number to the Intellectual moving principles, and how can these incorporeal Beings be numerically many when there is no Matter to serve as the basis of difference?

For these reasons the ancient philosophers that ranged themselves most closely to the school of Pythagoras and of his later followers and to that of Pherekudes, have insisted upon this Nature, some developing the subject in their writings while others treated of it merely in unwritten discourses, some no doubt ignoring it entirely.

(1) It is in virtue of unity that beings are beings.

This is equally true of things whose existence is primal and of all that are in any degree to be numbered among beings. What could exist at all except as one thing? Deprived of unity, a thing ceases to be what it is called: no army unless as a unity: a chorus, a flock, must be one thing. Even house and ship demand unity, one house, one ship; unity gone, neither remains thus even continuous magnitudes could not exist without an inherent unity; break them apart and their very being is altered in the measure of the breach of unity.

Take plant and animal; the material form stands a unity; fallen from that into a litter of fragments, the things have lost their being; what was is no longer there; it is replaced by quite other things- as many others, precisely, as possess unity.

Health, similarly, is the condition of a body acting as a co-ordinate unity. Beauty appears when limbs and features are controlled by this principle, unity. Moral excellence is of a soul acting as a concordant total, brought to unity.

Come thus to soul- which brings all to unity, making, moulding, shaping, ranging to order- there is a temptation to say "Soul is the bestower of unity; soul therefore is the unity." But soul bestows other characteristics upon material things and yet remains distinct from its gift: shape, Ideal-Form and the rest are all distinct from the giving soul; so, clearly, with this gift of unity; soul to make things unities looks out upon the unity just as it makes man by looking upon Man, realizing in the man the unity belonging to Man.

Anything that can be described as a unity is so in the precise degree in which it holds a characteristic being; the less or more the degree of the being, the less or more the unity. Soul, while distinct from unity's very self, is a thing of the greater unity in proportion as it is of the greater, the authentic, being. Absolute unity it is not: it is soul and one soul, the unity in some sense a concomitant; there are two things, soul and soul's unity as there is body with body's unity. The looser aggregates, such as a choir, are furthest from unity, the more compact are the nearer; soul is nearer yet but still a participant.

Is soul to be identified with unity on the ground that unless it were one thing it could not be soul? No; unity is equally necessary to every other thing, yet unity stands distinct from them; body and unity are not identical; body, too; is still a participant.

Besides, the soul, even the collective soul for all its absence of part, is a manifold: it has diverse powers- reasoning, desiring, perceiving- all held together by this chain of unity. Itself a unity, soul confers unity, but also accepts it.

(6) In what sense, then, do we assert this Unity, and how is it to be adjusted to our mental processes?

Its oneness must not be entitled to that of monad and point: for these the mind abstracts extension and numerical quantity and rests upon the very minutest possible, ending no doubt in the partless but still in something that began as a partible and is always lodged in something other than itself. The Unity was never in any other and never belonged to the partible: nor is its impartibility that of extreme minuteness; on the contrary it is great beyond anything, great not in extension but in power, sizeless by its very greatness as even its immediate sequents are impartible not in mass but in might. We must therefore take the Unity as infinite not in measureless extension or numerable quantity but in fathomless depths of power.

Think of The One as Mind or as God, you think too meanly; use all the resources of understanding to conceive this Unity and, again, it is more authentically one than God, even though you reach for God's unity beyond the unity the most perfect you can conceive. For This is utterly a self-existent, with no concomitant whatever. This self-sufficing is the essence of its unity. Something there must be supremely adequate, autonomous, all-transcending, most utterly without need.

Any manifold, anything beneath The Unity, is dependent; combined from various constituents, its essential nature goes in need of unity; but unity cannot need itself; it stands unity accomplished. Again, a manifold depends upon all its factors; and furthermore each of those factors in turn- as necessarily inbound with the rest and not self-standing- sets up a similar need both to its associates and to the total so constituted.

The sovranly self-sufficing principle will be Unity-Absolute, for only in this Unity is there a nature above all need, whether within itself or in regard to the rest of things. Unity seeks nothing towards its being or its well-being or its safehold upon existence; cause to all, how can it acquire its character outside of itself or know any good outside? The good of its being can be no borrowing: This is The Good. Nor has it station; it needs no standing ground as if inadequate to its own sustaining; what calls for such underpropping is the soulless, some material mass that must be based or fall. This is base to all, cause of universal existence and of ordered station. All that demands place is in need; a First cannot go in need of its sequents: all need is effort towards a first principle; the First, principle to all, must be utterly without need. If the Unity be seeking, it must inevitably be seeking to be something other than itself; it is seeking its own destroyer. Whatever may be said to be in need of a good is needing a preserver; nothing can be a good to The Unity, therefore.

Neither can it have will to anything; it is a Beyond-Good, not even to itself a good but to such beings only as may be of quality to have part with it. Nor has it Intellection; that would comport diversity: nor Movement; it is prior to Movement as to Intellection.

To what could its Intellection be directed? To itself? But that would imply a previous ignorance; it would be dependent upon that Intellection in order to knowledge of itself; but it is the self-sufficing. Yet this absence of self-knowing does not comport ignorance; ignorance is of something outside- a knower ignorant of a knowable- but in the Solitary there is neither knowing nor anything unknown. Unity, self-present, it has no need of self-intellection: indeed this "self-presence" were better left out, the more surely to preserve the unity; we must eliminate all knowing and all association, all intellection whether internal or external. It is not to be though of as having but as being Intellection; Intellection does not itself perform the intellective act but is the cause of the act in something else, and cause is not to be identified with caused: most assuredly the cause of all is not a thing within that all.

This Principle is not, therefore, to be identified with the good of which it is the source; it is good in the unique mode of being The Good above all that is good.