Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Secret Teachings of All Ages
Pythagorean Mathematics (101)
Monad--1--is so called because it remains always in the same condition--that is, separate from multitude. Its attributes are as follows: It is called mind, because the mind is stable and has preeminence; hermaphrodism, because it is both male and female; odd and even, for being added to the even it makes odd, and to the odd, even; God, because it is the beginning and end of all, but itself has neither beginning nor end; good, for such is the nature of God; the receptacle of matter, because it produces the duad, which is essentially material.
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.
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.
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.
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.
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.
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 [...].
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.
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 [...].
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.
These things we have learned from the Divine Oracles, and you will find all the sacred Hymnology, so to speak, of the Theologians arranging the...
(4) These things we have learned from the Divine Oracles, and you will find all the sacred Hymnology, so to speak, of the Theologians arranging the Names, of God with a view to make known and praise the beneficent progressions of the Godhead. Hence, we see in almost every theological treatise the Godhead religiously celebrated, both as Monad and unity, on account of the simplicity and oneness of Its supernatural indivisibility from which, as an unifying power, we are unified, and when our divided diversities have been folded together, in a manner supermundane, we are collected into a godlike unit and divinely-imitated union; but, also as Triad, on account of the tri-personal manifestation of the superessential productiveness, from which all paternity in heaven and on earth is, and is named; also, as cause of things existing, since all things were brought into being on account of Its creative goodness, both wise and good, because all things, whilst preserving the properties of their own nature unimpaired, are filled with every inspired harmony and holy comeliness, but pre-eminently, as loving towards man, because It truly and wholly shared, in one of Its Persons (subsistencies), in things belonging to us, recalling to Itself and replacing the human extremity, out of which, in a manner unutterable, the simplex Jesus was composed, and the Everlasting took a temporal duration, and He, Who is superessentially exalted above every rank throughout all nature, became within our nature, whilst retaining the unchangeable and unconfused steadfastness of His own properties. And whatever other divinely-wrought illuminations, conformable to the Oracles, the secret tradition of our inspired leaders bequeathed to us for our enlightenment, in these also we have been initiated; now indeed, according to our capacity, through the sacred veils of the loving-kindness towards man, made known in the Oracles and hierarchical traditions, which envelop things intellectual in things sensible, and things superessential in things that are; and place forms and shapes around the formless and shapeless, and multiply and fashion the supernatural and formless simplicity in the variedness of the divided symbols; but, then, when we have become incorruptible and immortal, and have reached the Christlike and most blessed repose, according to the Divine saying, we shall be "ever with the Lord," fulfilled, through all-pure contemplations, with the visible manifestation of God covering us with glory, in most brilliant splendours, as the disciples in the most Divine Transfiguration, and participating in His gift of spiritual light, with unimpassioned and immaterial mind; and, even in the union beyond conception, through the agnostic and most blessed efforts after rays of surpassing brilliancy, in a more Divine imitation of the supercelestial minds. For we shall be equal to the angels, as the truth of the Oracles affirms, and sons of God, being sons of the resurrection. But now, to the best of our ability, we use symbols appropriate to things Divine, and from these again we elevate ourselves, according to our degree, to the simple and unified truth of the spiritual visions; and after our every conception of things godlike, laying aside our mental energies, we cast ourselves, to the best of our ability, towards the superessential ray, in which all the terms of every kind of knowledge pre-existed in a manner beyond expression, which it is neither possible to conceive nor express, nor entirely in any way to contemplate, on account of Its being pre-eminently above all things, and super-unknown, and Its having previously contained within Itself, superessentially, the whole perfections of all kinds of essential knowledge and power, and Its being firmly fixed by Its absolute power, above all, even the supercelestial minds. For, if all kinds of knowledge are of things existing, and are limited to things existing, that, beyond all essence, is also elevated above all knowledge.
Thus, then, the "Nameless "befits the cause of all, which is also above all, as do all the names of things existing, in order that there may be...
(7) Thus, then, the "Nameless "befits the cause of all, which is also above all, as do all the names of things existing, in order that there may be strictly a kingly rule over the whole; and that all things may be around It and dependent upon It, as cause, as beginning, as end. And Itself, according to the Divine saying, may be the "all in all," and truly sung as of all, producing, directing and perfecting and sustaining guard, and shrine, and turning towards Itself, and that uniformly, irresistibly and pre-eminently. For It is not only cause of sustenance, or life, or perfection,--so that from this or that forethought alone the Goodness above Name should be named, but It previously embraced in Itself all things existing, absolutely and without limit, by the complete benefactions of His one and all-creating forethought, and by all created things in joint accord It is celebrated and named.
The (Names) then, common to the whole Deity, as we have demonstrated from the Oracles, by many instances in the Theological Outlines, are the...
(3) The (Names) then, common to the whole Deity, as we have demonstrated from the Oracles, by many instances in the Theological Outlines, are the Super-Good, the Super-God, the Super-essential, the Super-Living, the Super-Wise, and whatever else belongs to the superlative abstraction; with which also, all those denoting Cause, the Good, the Beautiful, the Being, the Life-producing, the Wise, and whatever Names are given to the Cause of all Good, from His goodly gifts. But the distinctive Names are the superessential name and property of Father, and Son and Spirit, since no interchange or community in these is in any way introduced. But there is a further distinction, viz., the complete and unaltered existence of Jesus amongst us, and all the mysteries of love towards man actually existing within it.
But, as we said when we put forth the Theological Outlines, it is not possible either to express or to conceive what the One, the Unknown, the Superes...
(5) And yet, if It is superior to every expression and every knowledge, and is altogether placed above mind and essence,--being such as embraces and unites and comprehends and anticipates all things, but Itself is altogether incomprehensible to all, and of It, there is neither perception nor imagination, nor surmise, nor name, nor expression, nor contact, nor science;--in what way can our treatise thoroughly investigate the meaning of the Divine Names, when the superessential Deity is shewn to be without Name, and above Name? But, as we said when we put forth the Theological Outlines, it is not possible either to express or to conceive what the One, the Unknown, the Superessential self-existing Good is,--I mean the threefold Unity, the alike God, and the alike Good. But even the unions, such as befit angels, of the holy Powers, whether we must call them efforts after, or receptions from, the super-Unknown and surpassing Goodness, are both unutterable and unknown, and exist in those angels alone who, above angelic knowledge, are deemed worthy of them. The godlike minds (men) made one by these unions, through imitation of angels as far as attainable (since it is during cessation of every mental energy that such an union as this of the deified minds towards the super-divine light takes place) celebrate It most appropriately through the abstraction of all created things--enlightened in this matter, truly and super-naturally from the most blessed union towards It--that It is Cause Indeed of all things existing, but Itself none of them, as being superessentially elevated above all. To none, indeed, who are lovers of the Truth above all Truth, is it permitted to celebrate the supremely-Divine Essentiality--that which is the super-subsistence of the super-goodness,--neither as word or power, neither as mind or life or essence, but as pre-eminently separated from every condition, movement, life, imagination, surmise, name, word, thought, conception, essence, position, stability, union, boundary, infinitude, all things whatever. But since, as sustaining source of goodness, by the very fact of Its being, It is cause of all things that be, from all created things must we celebrate the benevolent Providence of the Godhead; for all things are both around It and for It, and It is before all things, and all things in It consist, and by Its being is the production and sustenance of the whole, and all things aspire to It--the intellectual and rational, by means of knowledge--things inferior to these, through the senses, and other things by living movement, or substantial and habitual aptitude.
Chapter 19: Concerning the Created Heaven, and the Form of the Earth, and of the Water, as also concerning Light and Darkness. Concerning Heaven. (89)
The whole Deity with all its powers and operations, together with its innate or instant being, as also its rising up, penetration, changing and...
(89) The whole Deity with all its powers and operations, together with its innate or instant being, as also its rising up, penetration, changing and alteration, that is to say the whole machine, fabric and work, or the whole generating or production, is all understood in the spirit of the word.
Chapter XII: God Cannot Be Embraced in Words or By the Mind. (10)
We speak not as supplying His name; but for want, we use good names, in order that the mind may have these as points of support, so as not to err in o...
(10) And if we name it, we do not do so properly, terming it either the One, or the Good, or Mind, or Absolute Being, or Father, or God, or Creator or Lord. We speak not as supplying His name; but for want, we use good names, in order that the mind may have these as points of support, so as not to err in other respects. For each one by itself does not express God; but all together are indicative of the power of the Omnipotent. For predicates are expressed either from what belongs to things themselves, or from their mutual relation. But none of these are admissible in reference to God. Nor any more is He apprehended by the science of demonstration. For it depends on primary and better known principles. But there is nothing antecedent to the Unbegotten.
The Triple Powered One provides Being by means of Existence (2)
For he is a Unity, subsisting as a [true cause] and source of [Being], even [an] immaterial [matter and an] innumerable [number and a] formless [form]...
(2) For he is a Unity, subsisting as a [true cause] and source of [Being], even [an] immaterial [matter and an] innumerable [number and a] formless [form] and a [shapeless] [shape] and [a powerlessness with] [power and an insubstantial substance] [and a motionless] [motion and an inactive] [activity, except that he is] [a] provider of [provision] [and] a divinity [of] divinity.
Chapter 19: Concerning the Created Heaven, and the Form of the Earth, and of the Water, as also concerning Light and Darkness. Concerning Heaven. (93)
"When the spirit of man seeth anything, then it giveth a name to that thing, according to the qualification or condition of the thing; but if it is...
(93) "When the spirit of man seeth anything, then it giveth a name to that thing, according to the qualification or condition of the thing; but if it is to do this, then it must form or frame or put itself also into such a form, and generate itself also, with its tone, sound or articulation, just so as the thing to which it will give a name does generate or compose itself. Herein lies the kernel of the whole understanding of the Deity.