(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.

(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.

(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.

(17) You are One, you are One, as one might tell you, you are One.

(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.

(2) But One, because He is uniquely all, as beseems an excess of unique Oneness, and is Cause of all without departing from the One. For there is no single existing being, which does not participate in the one, but as every number participates in an unit, and one dual and one decade is spoken of, and one half, and one third and tenth, so everything, and part of everything participates in the one, and by the fact that the One is, all existing things are. And the Cause of all is not One, as one of many, but before every one and multitude, and determinative of every one and multitude. For there is no multitude which does not partake in some way or other of the one. Yea, that which is many by parts, is one in the whole; and the many by the accidents, is one by the subject; and the many by the number or the powers, is one by the species, and the many by the species, is one by the genus; and the many by the progressions, is one by the source. And there is no single thing which does not participate in some way in the one, which uniformly pre-held in the uniqueness throughout all, all and whole, all, even the things opposed. And indeed, without the one there will not be a multitude, but without the multitude there will be the one, even as the unit previous to every multiplied number; and, if any one should suppose, that all things are united to all, the All will be one in the whole.

(6) All this, however, we may leave to individual judgement: to proceed:

This produced reality is an Ideal form- for certainly nothing springing from the Supreme can be less- and it is not a particular form but the form of all, beside which there is no other; it follows that The First must be without form, and, if without form, then it is no Being; Being must have some definition and therefore be limited; but the First cannot be thought of as having definition and limit, for thus it would be not the Source but the particular item indicated by the definition assigned to it. If all things belong to the produced, which of them can be thought of as the Supreme? Not included among them, this can be described only as transcending them: but they are Being and the Beings; it therefore transcends Being.

Note that the phrase transcending Being assigns no character, makes no assertion, allots no name, carries only the denial of particular being; and in this there is no attempt to circumscribe it: to seek to throw a line about that illimitable Nature would be folly, and anyone thinking to do so cuts himself off from any slightest and most momentary approach to its least vestige.

As one wishing to contemplate the Intellectual Nature will lay aside all the representations of sense and so may see what transcends the sense-realm, in the same way one wishing to contemplate what transcends the Intellectual attains by putting away all that is of the intellect, taught by the intellect, no doubt, that the Transcendent exists but never seeking to define it.

Its definition, in fact, could be only "the indefinable": what is not a thing is not some definite thing. We are in agony for a true expression; we are talking of the untellable; we name, only to indicate for our own use as best we may. And this name, The One, contains really no more than the negation of plurality: under the same pressure the Pythagoreans found their indication in the symbol "Apollo" with its repudiation of the multiple. If we are led to think positively of The One, name and thing, there would be more truth in silence: the designation, a mere aid to enquiry, was never intended for more than a preliminary affirmation of absolute simplicity to be followed by the rejection of even that statement: it was the best that offered, but remains inadequate to express the Nature indicated. For this is a principle not to be conveyed by any sound; it cannot be known on any hearing but, if at all, by vision; and to hope in that vision to see a form is to fail of even that.

(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.

(13) Thus The One is in truth beyond all statement: any affirmation is of a thing; but the all-transcending, resting above even the most august divine Mind, possesses alone of all true being, and is not a thing among things; we can give it no name because that would imply predication: we can but try to indicate, in our own feeble way, something concerning it: when in our perplexity we object, "Then it is without self-perception, without self-consciousness, ignorant of itself"; we must remember that we have been considering it only in its opposites.

If we make it knowable, an object of affirmation, we make it a manifold; and if we allow intellection in it we make it at that point indigent: supposing that in fact intellection accompanies it, intellection by it must be superfluous.

Self-intellection- which is the truest- implies the entire perception of a total self formed from a variety converging into an integral; but the Transcendent knows neither separation of part nor any such enquiry; if its intellectual act were directed upon something outside, then, the Transcendent would be deficient and the intellection faulty.

The wholly simplex and veritable self-sufficing can be lacking at no point: self-intellection begins in that principle which, secondarily self-sufficing, yet needs itself and therefore needs to know itself: this principle, by its self-presence, achieves its sufficiency in virtue of its entire content : it becomes thus competent from the total of its being, in the act of living towards itself and looking upon itself.

Consciousness, as the very word indicates, is a conperception, an act exercised upon a manifold: and even intellection, earlier though it is, implies that the agent turns back upon itself, upon a manifold, then. If that agent says no more than "I am a being," it speaks as a discoverer of the extern; and rightly so, for being is a manifold; when it faces towards the unmanifold and says, "I am that being," it misses both itself and the being : if it is truth it cannot indicate by "being" something like a stone; in the one phrase multiplicity is asserted; for the being thus affirmed- the veritable, as distinguished from such a mere container of some trace of being as ought not to be called a being since it stands merely as image to archetype- even this must possess multiplicity.

But will not each item in that multiplicity be an object of intellection to us?

Taken bare and single, no: but Being itself is manifold within itself, and whatever else you may name has Being.

This accepted, it follows that anything that is to be thought of as the most utterly simplex of all cannot have self-intellection; to have that would mean being multiple. The Transcendent, thus, neither knows itself nor is known in itself.

(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.

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

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

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

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

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

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

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

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

(3) An old woman offered Bu All a piece of gold saying: 'Accept this from me.' He replied: 'I can accept things only from God.' The old woman retorted: 'Where did you learn to see double? You are not a man of power to bind and unbind. If you were not squint-eyed would you see several things at once?'

There is neither Ka'aba nor Pagoda. Learn from my mouth the true doctrine - the eternal existence of Being. We

must not see anyone other than Him. We are in Him, by Him, and with Him. We may also be outside these states. Whoever is not immersed in the Ocean of Unity is not worthy of the race of men.

The day will come when the Sun will draw' aside the veil which covers it. So long as you are separate, good and evil will arise in you, but when you lose yourself in the sun of the divine essence they will be transcended by love. While you loiter on the road you will be held back by faults and weaknesses. Have you not yet realized that in your body there are conceit, vanity, self-pride, selflove and other dirty things! Though the serpent and the scorpion may seem to be dead within you they are only asleep; and if something touches them they will wake up with the strength of a hundred dragons. In each of us is a Hell of serpents. If you make yourself secure against these unclean creatures you may remain tranquil; if not, they will sting you even in the dust of the tomb until the day of reckoning.

And now, O Attar, leave your metaphorical discourses and return to the description of the mysterious Valley of Unity.

The Hoopoe continued: 'When the spiritual traveller enters this valley he will disappear and be lost to sight because the Unique Being will manifest himself; he will be silent because this Being wiU speak.

'The part will become the whole, or rather, there will be neither part nor whole. In the School of the Secret you will see thousands of men with intellectual knowledge, their lips parted in silence. What is intellectual knowledge here? It stops on the threshold of the door like a blind child. He who discovers something of this secret turns his face from the kingdom of the tuo worlds. The Being I speak of does not exist separately; everyone is this Being, existence and nonexistence is this Being. '

(5) We return to our statement that The First remains intact even when other entities spring from it.

In the case of numbers, the unit remains intact while something else produces, and thus number arises in dependence on the unit: much more then does the unit, The One, remain intact in the principle which is before all beings; especially since the entities produced in its likeness, while it thus remains intact, owe their existence to no other, but to its own all-sufficient power.

And just as there is, primarily or secondarily, some form or idea from the monad in each of the successive numbers- the later still participating, though unequally, in the unit- so the series of Beings following upon The First bear, each, some form or idea derived from that source. In Number the participation establishes Quantity; in the realm of Being, the trace of The One establishes reality: existence is a trace of The One- our word for entity may probably be connected with that for unity.

What we know as Being, the first sequent upon The One, advanced a little outward, so to speak, then chose to go no further, turned inward again and comes to rest and is now the reality and hearth of the universe. Pressing on the word for Being we have the word "hen" , an indication that in our very form of speech we tell, as far as may be, that Being is that which proceeds from The One. Thus both the thing that comes to be and Being itself are carriers of a copy, since they are outflows from the power of The primal One: this power sees and in its emotion tries to represent what it sees and breaks into speech "On"; "einai"; "ousia," "hestia" , sounds which labour to express the essential nature of the universe produced by the travail of the utterer and so to represent, as far as sounds may, the origin of reality.

(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.

(5) 'Twas not to know the number in which are The motors here above, or if 'necesse' With a contingent e'er 'necesse' make, 'Non si est dare primum motum esse,' Or if in semicircle can be made Triangle so that it have no right angle. Whence, if thou notest this and what I said, A regal prudence is that peerless seeing In which the shaft of my intention strikes. And if on 'rose' thou turnest thy clear eyes, Thou'lt see that it has reference alone To kings who're many, and the good are rare. With this distinction take thou what I said, And thus it can consist with thy belief Of the first father and of our Delight. And lead shall this be always to thy feet, To make thee, like a weary man, move slowly Both to the Yes and No thou seest not; For very low among the fools is he Who affirms without distinction, or denies, As well in one as in the other case; Because it happens that full often bends Current opinion in the false direction, And then the feelings bind the intellect.

(76) There are two orders of number: odd and even. Because unity, or 1, always remains indivisible, the odd number cannot be divided equally. Thus, 9 is 4+1+4, the unity in the center being indivisible. Furthermore, if any odd number be divided into two parts, one part will always be odd and the other even. Thus, 9 may be 5+4, 3+6, 7+2, or 8+1. The Pythagoreans considered the odd number--of which the monad was the prototype--to be definite and masculine. They were not all agreed, however, as to the nature of unity, or 1. Some declared it to be positive, because if added to an even (negative) number, it produces an odd (positive) number. Others demonstrated that if unity be added to an odd number, the latter becomes even, thereby making the masculine to be feminine. Unity, or 1, therefore, was considered an androgynous number, partaking of both the masculine and the feminine attributes; consequently both odd and even. For this reason the Pythagoreans called it evenly-odd. It was customary for the Pythagoreans to offer sacrifices of an uneven number of objects to the superior gods, while to the goddesses and subterranean spirits an even number was offered.

(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.

(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.

(11) Now all that is engendered is imperfect, it is divisible, to increase subject and to decrease; but with the Perfect [One] none of these things doth hold. Now that which is increasable increases from the Oneness, but succumbs through its own feebleness when it no longer can contain the One. And now, O Tat, God's Image hath been sketched for thee, as far as it can be; and if thou wilt attentively dwell on it and observe it with thine heart's eyes, believe me, son, thou'lt find the Path that leads above; nay, that Image shall become thy Guide itself, because the Sight [Divine] hath this peculiar [charm], it holdeth fast and draweth unto it those who succeed in opening their eyes, just as, they say, the magnet [draweth] iron.

(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.