Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Western Esoteric
Secret Teachings of All Ages
Pythagorean Mathematics (113)
Pythagoras maintained that the soul of man consists of a tetrad, the four powers of the soul being mind, science, opinion, and sense. The tetrad connects all beings, elements, numbers, and seasons; nor can anything be named which does not depend upon the tetractys. It is the Cause and Maker of all things, the intelligible God, Author of celestial and sensible good, Plutarch interprets this tetractys, which he said was also called the world, to be 36, consisting of the first four odd numbers added to the first four even numbers, thus:
And to these parts [are added other] four;—of sense, and soul, of memory, and foresight, by means of which he may become acquainted with the rest of t...
(3) For that, in order that a man should be complete in either part, observe that he hath been composed of elements of either part in sets of four;—with hands, and feet, both of them pairs, and with the other members of his body, by means of which he may do service to the lower (that is to say the terrene) world. And to these parts [are added other] four;—of sense, and soul, of memory, and foresight, by means of which he may become acquainted with the rest of things divine, and judge of them. Hence it is brought about that man investigates the differences and qualities, effects and quantities of things, with critical research; yet, as he is held back with the too heavy weight of body’s imperfection, he cannot properly descry the causes of the nature of [all] things which [really] are the true ones.
Chapter XIV: Greek Plagiarism From the Hebrews. (9)
Again the Barbarian philosophy knows the world of thought and the world of sense - the former archetypal, and the latter the image of that which is...
(9) Again the Barbarian philosophy knows the world of thought and the world of sense - the former archetypal, and the latter the image of that which is called the model; and assigns the former to the Monad, as being perceived by the mind, and the world of sense to the number six. For six is called by the Pythagoreans marriage, as being the genital number; and he places in the Monad the invisible heaven and the holy earth, and intellectual light. For "in the beginning," it is said, "God made the heaven and the earth; and the earth was invisible." And it is added, "And God said, Let there be light; and there was light." And in the material cosmogony He creates a solid heaven (and what is solid is capable of being perceived by sense), and a visible earth, and a light that is seen. Does not Plato hence appear to have left the ideas of living creatures in the intellectual world, and to make intellectual objects into sensible species according to their genera? Rightly then Moses says, that the body which Plato calls "the earthly tabernacle" was formed of the ground, but that the rational soul was breathed by God into man's face. For there, they say, the ruling faculty is situated; interpreting the access by the senses into the first man as the addition of the soul.
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...
(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.
On the Integral Omnipresence of the Authentic Existent (2) (9)
The elements in their totality, as they stand produced, may be thought of as one spheric figure; this cannot be the piecemeal product of many makers...
(9) The elements in their totality, as they stand produced, may be thought of as one spheric figure; this cannot be the piecemeal product of many makers each working from some one point on some one portion. There must be one cause; and this must operate as an entire, not by part executing part; otherwise we are brought back to a plurality of makers. The making must be referred to a partless unity, or, more precisely, the making principle must be a partless unity not permeating the sphere but holding it as one dependent thing. In this way the sphere is enveloped by one identical life in which it is inset; its entire content looks to the one life: thus all the souls are one, a one, however, which yet is infinite.
It is in this understanding that the soul has been taken to be a numerical principle, while others think of it as in its nature a self-increasing number; this latter notion is probably designed to meet the consideration that the soul at no point fails but, retaining its distinctive character, is ample for all, so much so that were the kosmos vaster yet the virtue of soul would still compass it- or rather the kosmos still be sunk in soul entire.
Of course, we must understand this adding of extension not as a literal increase but in the sense that the soul, essentially a unity, becomes adequate to omnipresence; its unity sets it outside of quantitative measurement, the characteristic of that other order which has but a counterfeit unity, an appearance by participation.
The essential unity is no aggregate to be annulled upon the loss of some one of the constituents; nor is it held within any allotted limits, for so it would be the less for a set of things, more extensive than itself, outside its scope; or it must wrench itself asunder in the effort to reach to all; besides, its presence to things would be no longer as whole to all but by part to part; in vulgar phrase, it does not know where it stands; dismembered, it no longer performs any one single function.
Now if this principle is to be a true unity- where the unity is of the essence- it must in some way be able to manifest itself as including the contrary nature, that of potential multiplicity, while by the fact that this multiplicity belongs to it not as from without but as from and by itself, it remains authentically one, possessing boundlessness and multiplicity within that unity; its nature must be such that it can appear as a whole at every point; this, as encircled by a single self-embracing Reason-Principle, which holds fast about that unity, never breaking with itself but over all the universe remaining what it must be.
The unity is in this way saved from the local division of the things in which it appears; and, of course, existing before all that is in place, it could never be founded upon anything belonging to that order of which, on the contrary, it is the foundation; yet, for all that they are based upon it, it does not cease to be wholly self-gathered; if its fixed seat were shaken, all the rest would fall with the fall of their foundation and stay; nor could it be so unintelligent as to tear itself apart by such a movement and, secure within its own being, trust itself to the insecurity of place which, precisely, looks to it for safety.
Chapter XVI: Gnostic Exposition of the Decalogue. (10)
Besides, in addition to these ten human parts, the law appear to give its injunctions to sight, and hearing, and Smell, and touch, and taste, and to...
(10) Besides, in addition to these ten human parts, the law appear to give its injunctions to sight, and hearing, and Smell, and touch, and taste, and to the organs subservient to these, which are double - the hands and the feet. For such is the formation of man. And the soul is introduced, and previous to it the ruling faculty, by which we re.on, not produced in procreation; so that without it there is made up the number ten, of the faculties by which all the activity of man is carried out. For in order, straightway on man's entering existence, his life begins with sensations. We accordingly assert that rational and ruling power is the cause of the constitution of the living creature; also that this, the irrational part, is animated, and is a part of it. Now the vital force, in which is comprehended the power of nutrition and growth, and generally of motion, is assigned to the carnal spirit, which has great susceptibility of motion, and passes in all directions through the senses and the rest of the body, and through the body is the primary subject of sensations. But the power of choice, in which investigation, and study, and knowledge, reside, belongs to the ruling faculty. But all the faculties are placed in relation to one - the ruling faculty: it is through that man lives, and lives in a certain way.
Hermes: This dwelling-place through which we have just passed circle of the twelve types-of-life, this being composed of elements, twelve in number,...
(12) Hermes: This dwelling-place through which we have just passed circle of the twelve types-of-life, this being composed of elements, twelve in number, but of one nature, an omniform idea. For man's delusion there are disunions in them, son, while in their action they are one. Not only can we never part Rashness from Wrath; they cannot even be distinguished. According to right reason (logos), then, they naturally withdraw once and for all, in as much as they are chased out by no less than ten powers, that is, the Ten. For, son, the Ten is that which giveth birth to souls. And Life and Light are unified there, where the One hath being from the Spirit. According then to reason (logos) the One contains the Ten, the Ten the One.
In view of all this we must now work back from the items to the unit, and consider the entire scheme as one enduring thing. We ascend from air,...
(10) In view of all this we must now work back from the items to the unit, and consider the entire scheme as one enduring thing.
We ascend from air, light, sun- or, moon and light and sun- in detail, to these things as constituting a total- though a total of degrees, primary, secondary, tertiary. Thence we come to the Soul, always the one undiscriminated entity. At this point in our survey we have before us the over-world and all that follows upon it. That suite we take to be the very last effect that has penetrated to its furthest reach.
Our knowledge of the first is gained from the ultimate of all, from the very shadow cast by the fire, because this ultimate itself receives its share of the general light, something of the nature of the Forming-Idea hovering over the outcast that at first lay in blank obscurity. It is brought under the scheme of reason by the efficacy of soul whose entire extension latently holds this rationalizing power. As we know, the Reason-Principles carried in animal seed fashion and shape living beings into so many universes in the small. For whatsoever touches soul is moulded to the nature of soul's own Real-Being.
We are not to think that the Soul acts upon the object by conformity to any external judgement; there is no pause for willing or planning: any such procedure would not be an act of sheer nature, but one of applied art: but art is of later origin than soul; it is an imitator, producing dim and feeble copies- toys, things of no great worth- and it is dependent upon all sorts of mechanism by which alone its images can be produced. The soul, on the contrary, is sovereign over material things by might of Real-Being; their quality is determined by its lead, and those elementary things cannot stand against its will. On the later level, things are hindered one by the other, and thus often fall short of the characteristic shape at which their unextended Reason-Principle must be aiming; in that other world the entire shape comes from soul, and all that is produced takes and keeps its appointed place in a unity, so that the engendered thing, without labour as without clash, becomes all that it should be. In that world the soul has elaborated its creation, the images of the gods, dwellings for men, each existing to some peculiar purpose.
Soul could produce none but the things which truly represent its powers: fire produces warmth; another source produces cold; soul has a double efficacy, its act within itself, and its act from within outwards towards the new production.
In soulless entities, the outgo remains dormant, and any efficiency they have is to bring to their own likeness whatever is amenable to their act. All existence has this tendency to bring other things to likeness; but the soul has the distinction of possessing at once an action of conscious attention within itself, and an action towards the outer. It has thus the function of giving life to all that does not live by prior right, and the life it gives is commensurate with its own; that is to say, living in reason, it communicates reason to the body- an image of the reason within itself, just as the life given to the body is an image of Real-Being- and it bestows, also, upon that material the appropriate shapes of which it contains the Reason-Forms.
The content of the creative soul includes the Ideal shapes of gods and of all else: and hence it is that the kosmos contains all.
The Reason, then, is the Mind's image, and Mind God's [image]; while Body is [the image] of the Form; and Form [the image] of the Soul. The subtlest...
(14) The Reason, then, is the Mind's image, and Mind God's [image]; while Body is [the image] of the Form; and Form [the image] of the Soul. The subtlest part of Matter is, then, Air ; of Air, Soul; of Soul, Mind; and of Mind, God. And God surroundeth all and permeateth all; while Mind Surroundeth Soul, Soul Air, Air Matter. Necessity and Providence and Nature are instruments of Cosmos and of Matter's ordering; while of intelligible things each is Essence, and Sameness is their Essence. But of the bodies of the Cosmos each is many; for through possessiong Sameness, [these] composed bodies, though they do change from one into another of themselves, do natheless keep the incorruption of their Sameness.
Chapter XI: The Knowledge Which Comes Through Faith the Surest of All. (6)
There are body and soul, the five senses, speech, the power of reproduction - the intellectual or the spiritual faculty, or whatever you choose to cal...
(6) For out of the heart proceed thoughts." This, as I think, is the true and just measure according to God, by which things capable of measurement are measured, the decad which is comprehensive of man; which summarily the three above-mentioned measures pointed out. There are body and soul, the five senses, speech, the power of reproduction - the intellectual or the spiritual faculty, or whatever you choose to call it. And we must, in a word, ascending above all the others, stop at the mind; as also certainly in the universe overleaping the nine divisions, the first consisting of the four elements put in one place for equal interchange: and then the seven wandering stars and the one that wanders not, the ninth, to the perfect number, which is above the nine, and the tenth division, we must reach to the knowledge of God, to speak briefly, desiring the Maker after the creation. Wherefore the tithes both of the ephah and of the sacrifices were presented to God; and the paschal feast began with the tenth day, being the transition from all trouble, and from all objects of sense.
For man is the sole animal that is twofold. One part of him is simple: the [man] “essential,” as say the Greeks, but which we call the “form of the Di...
(2) But as to Sense and all things similar, I will set forth the whole discourse when [I explain] concerning Spirit. For man is the sole animal that is twofold. One part of him is simple: the [man] “essential,” as say the Greeks, but which we call the “form of the Divine Similitude.” He also is fourfold: that which the Greeks call “hylic,” [but] which we call “cosmic”; of which is made the corporal part, in which is vestured what we just have said is the divine in man, —in which the godhead of the Mind alone, together with its kin, that is the Pure Mind’s senses, findeth home and rest, its self with its own self, as though shut in the body’s walls.
That, then, from which the whole Cosmos is formed, consisteth of Four Elements—Fire, Water, Earth, and Air; Cosmos [itself is] one, [its] Soul [is]...
(1) That, then, from which the whole Cosmos is formed, consisteth of Four Elements—Fire, Water, Earth, and Air; Cosmos [itself is] one, [its] Soul [is] one, and God is one. Now lend to me the whole of thee, —all that thou can’st in mind, all that thou skill’st in penetration. For that the Reason of Divinity may not be known except by an intention of the senses like to it. ’Tis likest to the torrent’s flood, down-dashing headlong from above with all-devouring tide; so that it comes about, that by the swiftness of its speed it is too quick for our attention, not only for the hearers, but also for the very teachers.
Timaeus: the position was this. All these had their origin in the generation of the marrow. For it was in this that the bonds of life by which the...
(73) Timaeus: the position was this. All these had their origin in the generation of the marrow. For it was in this that the bonds of life by which the Soul is bound to the body were fastened, and implanted the roots of the mortal kind; but the marrow itself was generated out of other elements. Taking all these primary triangles which, being unwarped and smooth, were best able to produce with exactness fire and water and air and earth, God separated them, each apart from his own kind,
How the Multiplicity of the Ideal-forms Came Into Being: and Upon the Good (5)
Man, thus, must be some Reason-Principle other than soul. But why should he not be some conjoint- a soul in a certain Reason-Principle- the...
(5) Man, thus, must be some Reason-Principle other than soul. But why should he not be some conjoint- a soul in a certain Reason-Principle- the Reason-Principle being, as it were, a definite activity which however could not exist without that which acts?
This is the case with the Reason-Principles in seed which are neither soulless nor entirely soul. For these productive principles cannot be devoid of soul and there is nothing surprising in such essences being Reason-Principles.
But these principles producing other forms than man, of what phase of soul are they activities? Of the vegetal soul? Rather of that which produces animal life, a brighter soul and therefore one more intensely living.
The soul of that order, the soul that has entered into Matter of that order, is man by having, apart from body, a certain disposition; within body it shapes all to its own fashion, producing another form of Man, man reduced to what body admits, just as an artist may make a reduced image of that again.
It is soul, then, that holds the pattern and Reason-Principles of Man, the natural tendencies, the dispositions and powers- all feeble since this is not the Primal Man- and it contains also the Ideal-Forms of other senses, Forms which themselves are senses, bright to all seeming but images, and dim in comparison with those of the earlier order.
The higher Man, above this sphere, rises from the more godlike soul, a soul possessed of a nobler humanity and brighter perceptions. This must be the Man of Plato's definition , where the addition "Soul as using body" marks the distinction between the soul which uses body directly and the soul, poised above, which touches body only through that intermediary.
The Man of the realm of birth has sense-perception: the higher soul enters to bestow a brighter life, or rather does not so much enter as simply impart itself; for soul does not leave the Intellectual but, maintaining that contact, holds the lower life as pendant from it, blending with it by the natural link of Reason-Principle to Reason-Principle: and man, the dimmer, brightens under that illumination.