Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Western Esoteric
Secret Teachings of All Ages
Pythagorean Mathematics (73)
The monad signifies (a) the all-including ONE. The Pythagoreans called the monad the "noble number, Sire of Gods and men." The monad also signifies (b) the sum of any combination of numbers considered as a whole. Thus, the universe is considered as a monad, but the individual parts of the universe (such as the planets and elements) are monads in relation to the parts of which they themselves are composed, though they, in turn, are parts of the greater monad formed of their sum. The monad may also be likened (c) to the seed of a tree which, when it has grown, has many branches (the numbers). In other words, the numbers are to the monad what the branches of the tree are to the seed of the tree. From the study of the mysterious Pythagorean monad, Leibnitz evolved his magnificent theory of the world atoms--a theory in perfect accord with the ancient teachings of the Mysteries, for Leibnitz himself was an initiate of a secret school. By some Pythagoreans the monad is also considered (d) synonymous with the one.
The self-existent Super-goodness then, as projecting the first gift of self-existent being, is celebrated by the elder and first of the...
(6) The self-existent Super-goodness then, as projecting the first gift of self-existent being, is celebrated by the elder and first of the participations; and being itself is from It, and in It; as also the sources of things being, and all the things that be, and the things howsoever sustained by being, and that irresistibly, and comprehensively and uniformly. For even in a monad, every number preexists in the form of a unit, and the monad holds every number in itself singly. And every number is united in the monad, but so far as it advances from the monad, so far it is distributed and multiplied. And in a centre, all the lines of the circle coexist within one union, and the point holds all the straight lines in itself, uniformly united, both to each other, and to the one source from which they proceeded, and in the centre itself they are completely united; but standing slightly distant from it, they are slightly separated; but when more apart, more so. And in one word, the nearer they are to the centre, the more they are united to it and to each other? and the more they stand apart from it, the more they stand apart from each other.
That the Intellectual Beings Are Not Outside the Intellectual-principle: and on the Nature of the Good (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...
(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.
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...
(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.
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...
(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.
As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule...
(15) As I said earlier, among the things that were created the monad is first, the dyad follows it, and the triad, up to the tenths. Now the tenths rule the hundredths; the hundredths rule the thousandths; the thousands rule the ten thousands. This is the pattern immortals. First Man is like this: His monad [...].
It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real...
(11) It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real existence why not the rest? We are certainly not compelled to attach that one henad to some one thing and so deprive all the rest of the means to unity: since every existent must be one thing, the unity is obviously common to all. This means one principle applying to many, the principle whose existence within itself we affirmed to be presupposed by its manifestation outside.
But if a henad exists in some given object and further is observed in something else, then that first henad being real, there cannot be only one henad in existence; there must be a multiplicity of henads.
Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads . If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity.
Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well?
Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously- or rather has produced once for all- not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent- not in the sense of moving from point to point but in its inner changes- it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason.
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...
(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.
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...
(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.
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...
(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.
All the attributes that exist are perfect and immortal. In respect to imperishableness, they are indeed equal. (But) in respect to power, they are dif...
(23) "First Man has his unique mind, within, and thought - just as he is it (thought) - (and) considering, reflecting, rationality, power. All the attributes that exist are perfect and immortal. In respect to imperishableness, they are indeed equal. (But) in respect to power, they are different, like the difference between father and son and thought, and the thought and the remainder. As I said earlier, among the things that were created, the monad is first.
In these lessons we have followed the example of some of the world's greatest thinkers, both ancient and modern--the Hermetic. Masters--and have...
(4) In these lessons we have followed the example of some of the world's greatest thinkers, both ancient and modern--the Hermetic. Masters--and have called this Underlying Power--this Substantial Reality--by the Hermetic name of "THE ALL," which term we consider the most comprehensive of the many terms applied by Man to THAT which transcends names and terms.
Again it is this pattern that exists among the immortals: the monad and the thought are those things that belong to Immortal Man. The thinkings are...
(16) Again it is this pattern that exists among the immortals: the monad and the thought are those things that belong to Immortal Man. The thinkings are for decads, and the hundreds are the teachings, and the thousands are the counsels, and the ten thousands are the powers. Now those who come from the [...] exist with their [...] in every aeon [...].
The teaching is that The Masculine Principle manifested by THE ALL stands, in a way, apart from the actual mental creation of the Universe. It project...
(11) But, the Hermetic teaching does not imply a real duality--THE ALL is ONE--the Two Aspects are merely aspects of manifestation. The teaching is that The Masculine Principle manifested by THE ALL stands, in a way, apart from the actual mental creation of the Universe. It projects its Will toward the Feminine Principle (which may be called "Nature") whereupon the latter begins the actual work of the evolution of the Universe, from simple "centers of activity" on to man, and then on and on still higher, all according to well-established and firmly enforced Laws of Nature. If you prefer the old figures of thought, you may think of the Masculine Principle as GOD, the Father, and of the Feminine Principle as NATURE, the Universal Mother, from whose womb all things have been born. This is more than a mere poetic figure of speech--it is an idea of the actual process of the creation of the Universe. But always remember, that THE ALL is but One, and that in its Infinite Mind the Universe is generated, created and exists.
Chapter 12: Of the Nativity and Proceeding forth or Descent of the Holy Angels, as also of their Government, Order, and Heavenly joyous Life. (106)
Now, as the Ternary of the Deity is one only being or substance in all parts in the whole Father, and is united together, as the members in man's...
(106) Now, as the Ternary of the Deity is one only being or substance in all parts in the whole Father, and is united together, as the members in man's body, and all places are as one place, though one place may have a different function from the others, as also the members of men have; yet it is the one body of God:
All of them exist in the single one, as he clothes himself completely and by his single name he is never called. And in this unique way they are...
(10) All of them exist in the single one, as he clothes himself completely and by his single name he is never called. And in this unique way they are equally the single one and the Totalities. He is neither divided as a body, nor is he separated into the names which he has received, (so that) he is one thing in this way and another in another way. Also, neither does he change in [...], nor does he turn into the names which he thinks of, and become now this, now something else, this thing now being one thing and, at another time, something else, but rather he is wholly himself to the uttermost. He is each and every one of the Totalities forever at the same time. He is what all of them are. He brought the Father to the Totalities. He also is the Totalities, for he is the one who is knowledge for himself and he is each one of the properties. He has the powers and he is beyond all that which he knows, while seeing himself in himself completely and having a Son and form. Therefore, his powers and properties are innumerable and inaudible, because of the begetting by which he begets them. Innumerable and indivisible are the begettings of his words, and his commands and his Totalities. He knows them, which things he himself is, since they are in the single name, and are all speaking in it. And he brings (them) forth, in order that it might be discovered that they exist according to their individual properties in a unified way. And he did not reveal the multitude to the Totalities at once nor did he reveal his equality to those who had come forth from him.
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...
(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.
The Principle of Correspondence "As above, so below; as below, so above." --The Kybalion. This Principle embodies the truth that there is always a Cor...
(2) 2. The Principle of Correspondence "As above, so below; as below, so above." --The Kybalion. This Principle embodies the truth that there is always a Correspondence between the laws and phenomena of the various planes of Being and Life. The old Hermetic axiom ran in these words: "As above, so below; as below, so above." And the grasping of this Principle gives one the means of solving many a dark paradox, and hidden secret of Nature. There are planes beyond our knowing, but when we apply the Principle of Correspondence to them we are able to understand much that would otherwise be unknowable to us. This Principle is of universal application and manifestation, on the various planes of the material, mental, and spiritual universe--it is an Universal Law. The ancient Hermetists considered this Principle as one of the most important mental instruments by which man was able to pry aside the obstacles which hid from view the Unknown. Its use even tore aside the Veil of Isis to the extent that a glimpse of the face of the goddess might be caught. Just as a knowledge of the Principles of Geometry enables man to measure distant suns and their movements, while seated in his observatory, so a knowledge of the Principle of Correspondence enables Man to reason intelligently from the Known to the Unknown. Studying the monad, he understands the archangel.
To everyone they seem to come under Quantity and you have certainly brought Quantity in, where you say that discrete Quantity equally with the continu...
(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.