(2) All things accord in number:

which he very frequently uttered to all his disciples. Or again, Friendship is equality; equality is friendship . Or in the word cosmos , i. e. the world ; or by Jupiter, in the word philosophy , or in the so much celebrated word tetractys . All these and many other inventions of the like kind, were devised by Pythagoras for the benefit and amendment of his associates; and they were considered by those that understood them to be so venerable, and so much the progeny of divine inspiration, that the following was adopted as an oath by those that dwelt together in the common auditory:

(47) Timaeus: the perturbable to the imperturbable; and that, through learning and sharing in calculations which are correct by their nature, by imitation of the absolutely unvarying revolutions of the God we might stabilize the variable revolutions within ourselves. Concerning sound also and hearing, once more we make the same declaration, that they were bestowed by the Gods with the same object and for the same reasons; for it was for these same purposes that speech was ordained, and it makes the greatest contribution thereto; music too, in so far as it uses audible sound,

(13) Tat: Why, father mine! - do not the other lives make use of speech (logos)? Hermes: Nay, son; but use of voice; speech is far different from voice. For speech is general among all men, while voice doth differ in each class of living thing. Tat: But with men also, father mine, according to each race, speech differs. Hermes: Yea, son, but man is one; so also speech is one and is interpreted, and it is found the same in Egypt, and in Persia, and in Greece. Thou seemest, son, to be in ignorance of Reason's (Logos) worth and greatness. For that the Blessed God, Good Daimon, hath declared: "Soul is in Body, Mind in Soul; but Reason (Logos) is in Mind, and Mind in God; and God is Father of [all] these."

(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.

(26) Do not say a few things in many words, but much in a few words. Pythagoras. Stob. p. 216.

Genius is to men either a good or an evil dæmon. Epicharmus. Stob. p. 220.

(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?

(12) Tat: Most clearly hast thou, father mine, set forth the teaching (logos). Hermes: Consider this as well, my son; that these two things God hath bestowed on man beyond all mortal lives - both mind and speech (logos) equal to immortality. He hath the mind for knowing God and uttered speech (logos) for eulogy of Him. And if one useth these for what he ought, he'll differ not a whit from the immortals. Nay, rather, on departing from the body, he will be guided by the twain unto the Choir of Gods and Blessed Ones.

(5) But I return once more to the Discourse (Logos) on Sense. That sense doth share with thought in man, doth constitute him man. But 'tis not [every] man, as I have said, who benefits by thought; for this man is material, that other one substantial. For the material man, as I have said, [consorting] with the bad, doth have his seed of thought from daimons; while the substantial men [consorting] with the Good, are saved by God. Now God is Maker of all things, and in His making, He maketh all [at last] like to Himself; but they, while they're becoming good by exercise of their activity, are unproductive things. It is the working of the Cosmic Course that maketh their becomings what they are, befouling some of them with bad and others of them making clean with good. For Cosmos, too, Asclepius, possesseth sense-and-thought peculiar to itself, not like that of man; 'tis not so manifold, but as it were a better and a simpler one.

(525) And they appear to lead the mind towards truth? Yes, in a very remarkable manner. Then this is knowledge of the kind for which we are seeking, having a double use, military and philosophical; for the man of war must learn the art of number or he will not know how to array his troops, and the philosopher also, because he has to rise out of the sea of change and lay hold of true being, and therefore he must be an arithmetician. That is true. And our guardian is both warrior and philosopher? Certainly. Then this is a kind of knowledge which legislation may fitly prescribe; and we must endeavour to persuade those who are to be the principal men of our State to go and learn arithmetic, not as amateurs, but they must carry on the study until they see the nature of numbers with the mind only; nor again, like merchants or retail-traders, with a view to buying or selling, but for the sake of their military use, and of the soul herself; and because this will be the easiest way for her to pass from becoming to truth and being. That is excellent, he said. Yes, I said, and now having spoken of it, I must add how charming the science is! and in how many ways it conduces to our desired end, if pursued in the spirit of a philosopher, and not of a shopkeeper! How do you mean? I mean, as I was saying, that arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument. You know

(525) how steadily the masters of the art repel and ridicule any one who attempts to divide absolute unity when he is calculating, and if you divide, they multiply 4 , taking care that one shall continue one and not become lost in fractions. That is very true. Now, suppose a person were to say to them: O my friends, what are these wonderful numbers about which you are reasoning, in which, as you say, there is a unity such as you demand, and each unit is equal, invariable, indivisible,—what would they answer? They would answer, as I should conceive, that they were speaking of those numbers which can only be realized in thought. Then you see that this knowledge may be truly called necessary, necessitating as it clearly does the use of the pure intelligence in the attainment of pure truth? Yes; that is a marked characteristic of it. And have you further observed, that those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been. Very true, he said.

(1) I gave the Perfect Sermon (Logos) yesterday, Asclepius; today I think it right, as sequel thereunto, to go through point by point the Sermon about Sense. Now sense and thought do seem to differ, in that the former has to do with matter, the latter has to do with substance. But unto me both seem to be at-one and not to differ - in men I mean. In other lives sense is at-oned with Nature, but in men thought. Now mind doth differ just as much from thought as God doth from divinity. For that divinity by God doth come to be, and by mind thought, the sister of the word (logos) and instruments of one another. For neither doth the word (logos) find utterance without thought, nor is thought manifested without word.

(522) nothing which tended to that good which you are now seeking. You are most accurate, I said, in your recollection; in music there certainly was nothing of the kind. But what branch of knowledge is there, my dear Glaucon, which is of the desired nature; since all the useful arts were reckoned mean by us? Undoubtedly; and yet if music and gymnastic are excluded, and the arts are also excluded, what remains? Well, I said, there may be nothing left of our special subjects; and then we shall have to take something which is not special, but of universal application. What may that be? A something which all arts and sciences and intelligences use in common, and which every one first has to learn among the elements of education. What is that? The little matter of distinguishing one, two, and three—in a word, number and calculation:—do not all arts and sciences necessarily partake of them? Yes. Then the art of war partakes of them? To be sure. Then Palamedes, whenever he appears in tragedy, proves Agamemnon ridiculously unfit to be a general. Did you never remark how he declares that he had invented number, and had numbered the ships and set in array the ranks of the army at Troy; which implies that they had never been numbered before, and Agamemnon must be supposed literally to have been incapable of counting his own feet—how could he if he was ignorant of number? And if that is true, what sort of general must he have been? I should say a very strange one, if this was as you say.

(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.

(606) Therefore, Glaucon, I said, whenever you meet with any of the eulogists of Homer declaring that he has been the educator of Hellas, and that he is profitable for education and for the ordering of human things, and that you should take him up again and again and get to know him and regulate your whole life according to him, we may love and honour those who say these things—they are excellent people, as far as their lights extend; and we are ready to acknowledge that Homer is the greatest of poets and first of tragedy writers; but we must remain firm in our conviction that hymns to the gods and praises of famous men are the only poetry which ought to be admitted into our State. For if you go beyond this and allow the honeyed muse to enter, either in epic or lyric verse, not law and the reason of mankind, which by common consent have ever been deemed best, but pleasure and pain will be the rulers in our State. That is most true, he said. And now since we have reverted to the subject of poetry, let this our defence serve to show the reasonableness of our former judgment in sending away out of our State an art having the tendencies which we have described; for reason constrained us. But that she may not impute to us any harshness or want of politeness, let us tell her that there is an ancient quarrel between philosophy and poetry; of which there are many proofs, such as the saying of ‘the yelping hound howling at her lord,’ or of one ‘mighty in

(11) And let no one fancy that we honour the Name of Love beyond the Oracles, for it is, in my opinion, irrational and stupid not to cling to the force of the meaning, but to the mere words; and this is not the characteristic of those who have wished to comprehend things Divine, but of those who receive empty sounds and keep the same just at the ears from passing through from outside, and are not willing to know what such a word signifies, and in what way one ought to distinctly represent it, through other words of the same force and more explanatory, but who specially affect sounds and signs without meaning, and syllables, and words unknown, which do not pass through to the mental part of their soul, but buzz without, around their lips and ears, as though it were not permitted to signify the number four, by twice two, or straight lines by direct lines, or motherland by fatherland, or any other, which signify the self-same thing, by many parts of speech. We ought to know, according to the correct account, that we use sounds, and syllables, and phrases, and descriptions, and words, on account of the sensible perceptions; since when our soul is moved by the intellectual energies to the things contemplated, the sensible perceptions by aid of sensible objects are superfluous; just as also the intellectual powers, when the soul, having become godlike, throws itself, through a union beyond knowledge, against the rays of the unapproachable light, by sightless efforts. But, when the mind strives to be moved upwards, through objects of sense, to contemplative conceptions, the clearer interpretations are altogether preferable to the sensible perceptions, and the more definite descriptions are things more distinct than things seen; since when objects near are not made clear to the sensible perceptions, neither will these perceptions be well able to present the things perceived to the mind. But that we may not seem, in speaking thus, to be pushing aside the Divine Oracles, let those who libel the Name of Love (Ἔρωτος) hear them. "Be in love with It," they say, "and It will keep thee--Rejoice over It, and It will exalt thee--Honour It, in order that It may encompass thee,"--and whatever else is sung respecting Love, in the Word of God.

(1) It is also said, that Pythagoras was the first who called himself a philosopher; this not being a new name, but previously instructing us in a useful manner in a thing appropriate to the name. For he said that the entrance of men into the present life, resembled the progression of a crowd to some public spectacle. For there men of every description assemble with different views; one hastening to sell his wares for the sake of money and gain; but another that he may acquire renown by exhibiting the strength of his body; and there is also a third class of men, and those the most liberal, who assemble for the sake of surveying the places, the beautiful works of art, the specimens of valor, and the literary productions which are usually exhibited on such occasions.

Thus also in the present life, men of all-various pursuits are collected together in one and the same place. For some are influenced by the desire of riches and luxury; others by the love of power and dominion; and others are possessed with an insane ambition for glory. But the most pure and unadulterated character, is that of the man who gives himself to the contemplation of the most beautiful things, and whom it is proper to call a philosopher. He adds, that the survey of all heaven, and of the stars that revolve in it, is indeed beautiful, when the order of them is considered. For they derive this beauty and order by the participation of the first and the intelligible essence.

But that first essence is the nature of number and reasons [i. e. productive principles,] which pervades through all things, and according to which all these [celestial bodies] are elegantly arranged, and fitly adorned. And wisdom indeed, truly so called, is a certain science which is conversant with the first beautiful objects, and these divine, undecaying, and possessing an invariable sameness of subsistence; by the participation of which other things also may be called beautiful. But philosophy is the appetition of a thing of this kind. The attention therefore to erudition is likewise beautiful, which Pythagoras extended, in order to effect the correction of mankind.

(1) After this we must narrate how, when he had admitted certain persons to be his disciples, he distributed them into different classes according to their respective merits. For it was not fit that all of them should equally participate of the same things, as they were naturally dissimilar; nor was it indeed right that some should participate of all the most honorable auditions, but others of none, or should not at all partake of them. For this would be uncommunicative and unjust. While therefore he imparted a convenient portion of his discourses to each, he benefited as much as possible all of them, and preserved the proportion of justice, by making each a partaker of the auditions according to his desert.

Hence, in conformity to this method, he called some of them Pythagoreans, but others Pythagorists; just as we denominate some men Attics, but others Atticists. Having therefore thus aptly divided their names, some of them he considered to be genuine, but he ordained that others should show themselves to be the emulators of these. He ordered therefore that with the Pythagoreans possessions should be shared in common, and that they should always live together; but that each of the others should possess his own property apart from the rest, and that assembling together in the same place, they should mutually be at leisure for the same pursuits. And thus each of these modes was derived from Pythagoras, and transmitted to his successors.

Again, there were also with the Pythagoreans two forms of philosophy; for there were likewise two genera of those that pursued it, the Acusmatici, and the Mathematici. Of these however the Mathematici are acknowledged to be Pythagoreans by the rest; but the Mathematici do not admit that the Acusmatici are so, or that they derived their instruction from Pythagoras, but from Hippasus. And with respect to Hippasus, some say that he was a Crotonian, but others a Metapontine. But the philosophy of the Acusmatici consists in auditions unaccompanied with demonstrations and a reasoning process; because it merely orders a thing to be done in a certain way, and that they should endeavour to preserve such other things as were said by him, as so many divine dogmas.

They however profess that they will not speak of them, and that they are not to be spoken of; but they conceive those of their sect to be the best furnished with wisdom, who retained what they had heard more than others. But all these auditions are divided into three species. For some of them indeed signify what a thing is; others what it especially is; but others, what ought, or what ought not, to be done. The auditions therefore which signify what a thing is, are such as, What are the islands of the blessed? The sun and moon. What is the oracle at Delphi? The tetractys. What is harmony? That in which the Syrens subsist . But the auditions which signify what a thing especially is, are such as, What is the most just thing?

To sacrifice. What is the wisest thing? Number. But the next to this in wisdom, is that which gives names to things. What is the wisest of the things that are with us, [i. e. which pertain to human concerns]? Medicine. What is the most beautiful? Harmony. What is the most powerful? Mental decision. What is the most excellent? Felicity. What is that which is most truly asserted? That men are depraved. Hence they say that Pythagoras praised the Salaminian poet Hippodomas, because he sings:

(4) But there is yet another way to this knowledge:

Admiring the world of sense as we look out upon its vastness and beauty and the order of its eternal march, thinking of the gods within it, seen and hidden, and the celestial spirits and all the life of animal and plant, let us mount to its archetype, to the yet more authentic sphere: there we are to contemplate all things as members of the Intellectual- eternal in their own right, vested with a self-springing consciousness and life- and, presiding over all these, the unsoiled Intelligence and the unapproachable wisdom.

That archetypal world is the true Golden Age, age of Kronos, who is the Intellectual-Principle as being the offspring or exuberance of God. For here is contained all that is immortal: nothing here but is Divine Mind; all is God; this is the place of every soul. Here is rest unbroken: for how can that seek change, in which all is well; what need that reach to, which holds all within itself; what increase can that desire, which stands utterly achieved? All its content, thus, is perfect, that itself may be perfect throughout, as holding nothing that is less than the divine, nothing that is less than intellective. Its knowing is not by search but by possession, its blessedness inherent, not acquired; for all belongs to it eternally and it holds the authentic Eternity imitated by Time which, circling round the Soul, makes towards the new thing and passes by the old. Soul deals with thing after thing- now Socrates; now a horse: always some one entity from among beings- but the Intellectual-Principle is all and therefore its entire content is simultaneously present in that identity: this is pure being in eternal actuality; nowhere is there any future, for every then is a now; nor is there any past, for nothing there has ever ceased to be; everything has taken its stand for ever, an identity well pleased, we might say, to be as it is; and everything, in that entire content, is Intellectual-Principle and Authentic Existence; and the total of all is Intellectual-Principle entire and Being entire. Intellectual-Principle by its intellective act establishes Being, which in turn, as the object of intellection, becomes the cause of intellection and of existence to the Intellectual-Principle- though, of course, there is another cause of intellection which is also a cause to Being, both rising in a source distinct from either.

Now while these two are coalescents, having their existence in common, and are never apart, still the unity they form is two-sided; there is Intellectual-Principle as against Being, the intellectual agent as against the object of intellection; we consider the intellective act and we have the Intellectual-Principle; we think of the object of that act and we have Being.

Such difference there must be if there is to be any intellection; but similarly there must also be identity

Thus the Primals are seen to be: Intellectual-Principle; Existence; Difference; Identity: we must include also Motion and Rest: Motion provides for the intellectual act, Rest preserves identity as Difference gives at once a Knower and a Known, for, failing this, all is one, and silent.

So too the objects of intellection - identical in virtue of the self-concentration of the principle which is their common ground- must still be distinct each from another; this distinction constitutes Difference.

The Intellectual Kosmos thus a manifold, Number and Quantity arise: Quality is the specific character of each of these ideas which stand as the principles from which all else derives.

(8) Wherefore I've ever heard, my son, Good Daimon also say - (and had He set it down in written words, He would have greatly helped the race of men; for He alone, my son, doth truly, as the Firstborn God, gazing on all things, give voice to words (logoi) divine) - yea, once I heard Him say: "All things are one, and most of all the bodies which the mind alone perceives. Our life is owing to [God's] Energy and Power and Aeon. His Mind is good, so is His Soul as well. And this being so, intelligible things know naught of separation. So, then, Mind, being Ruler of all things, and being Soul of God, can do whate'er it wills."

(88) Timaeus: and weak intellect, inasmuch as two desires naturally exist amongst men, —the desire of food for the body's sake, and the desire of wisdom for the sake of the most divine part we have,—the motions of the stronger part prevail and augment their own power, but they make that of the soul obtuse and dull of wit and forgetful, and thereby they produce within it that greatest of diseases, ignorance. From both these evils the one means of salvation is this—neither to exercise the soul without the body nor the body without the soul, so that they may be evenly matched and sound of health. Thus the student of mathematics,