IT remains then, that we should speak concerning the triadic division of it, following Parmenides. These three things therefore, have appeared to us from the beginning, according to the separation of the one from being, viz. the one, difference, and being; difference not being the same either with the one or being. For though the one and being were in intelligibles, yet difference first subsists here. Since however power above [i. e. in intelligibles] was collective, but here is the separator of the extremes, there are not only three monads, but also three duads, viz. the one in conjunction with difference, difference in conjunction with being, and the one in conjunction with being.
For difference also is the cause of a separation of this kind, not preserving the union of the one being with genuine purity. There are therefore three monads, and three duads. But these likewise may become three triads, when we begin, at one time from the one, at another time from being, and at another from difference. Hence this triad subsists monadically, and triadically. But this is the same thing as to assert that difference and the first feminine nature generates in itself, monads, duads, triads. For the divided assumption, generates for us different monads; but the conjoined assumption, duads, and triads, some indeed being vanquished by the one,
others by difference, and others by being. And thus far the first deity presents itself to the view, being prolific of the first numbers; according to the one indeed, of unical numbers, but according to difference of generative, and according to being, of essential numbers.
Since however, from this deity which is intelligible, that which is posterior to it proceeds, it is evidently necessary that the monad, duad, and triad, should severally have prolific power. These powers therefore, Parmenides calls once, twice, thrice. For each of these is a power which is the cause of the abovementioned essences that produce either separately, or connectedly. For there with respect to the generations of them, some of them are entirely peculiar, but others are common to secondary natures.
The progeny therefore of these are, the oddlyodd, the evenlyeven and the evenlyodd.
And of these, the oddlyodd, indeed, as we have before observed, is collective into union of the divine progressions. But the evenlyeven is generative of wholes, and proceeds as far as to the last of things. The evenlyodd however, is mixed, having its subsistence from both the even and the odd. Hence we must establish the first as analogous to bound, but the second as analogous to power, and the third as analogous to being. And you may see, how indeed in the first order all things had a primary subsistence, viz. monad, duad, triad; but how in this order, all things are secondarily and subordinately.
And the mixture which is the triad, subsisted there indeed in one way, but here the evenlyodd subsists in another way. For there the extremes were odd, because they were intelligible; but here the even is more abundant, and the intelligible summit only is odd. For the middle of the triad is analogous to power. And there indeed, is the monad, which has all the forms of odd numbers according to cause, and the duad is there, which is occultly all the forms of even numbers, and also the triad, which is number primarily.
But here both the odd and the even number now subsist in a twofold respect, in one place in an unmingled, and in another in a mingled manner.
All things therefore, are here prolifically, but there, paternally and intelligibly.
But that monad does not proceed from intelligibles, but subsists in them in unproceeding union. Hence, after these, and from these, we may survey the whole of number subsisting according to a third progression. "For these things," says Parmenides, "preexisting, no number will be absent."
Every number therefore, is generated through these in the third monad, and both the one and being become many, difference separating each of them. And every part indeed of being participates of the one; but every unity is carried as in a vehicle in a certain portion of being.
Each of these however, is multiplied, intellectually separated, divided into minute parts, and proceeds to infinity. For as in intelligibles, we attribute infinite multitude to the third triad, so here, in this triad we assign infinite number to the third part of the triad. For in short every where, the infinite is the extremity, as proceeding in an allperfect manner, and comprehending indeed all secondary natures, but being itself participated by none of them. In the first monad therefore, there were powers, but intelligibly. In the second, there were progressions and generations, but both intelligibly and intellectually. And in the third, there was allpowerful number, unfolding the whole of itself into light; and which also Parmenides denominates infinite. It is likewise especially manifest that it is not proper to transfer this infinity to quantity. For how can there be an infinite number, since infinity is hostile to the nature of number? And how are the parts of the one equal to the minute parts of being? For in infinites there is not the equal. But this indeed has been thought worthy of attention by those who were prior to us.
CHAPTER XXXII.
THE division therefore into three, having been demonstrated by us, we shall briefly observe, that the one appears to be many according to this order, the one itself proceeding into a multitude of unities, and being in A similar manner becoming generated in conjunction with the one. For those three monads are the intelligible comprehensions of all orders, and they at once preside over all the progressions from intelligibles, produce All of them in an exempt manner, and collect them to the intelligible causes. Since however, Plotinus admits that number is prior to animal itself, and says that the first being produces from itself number, and that this is established as a medium between the one being, and animal itself but is the basis and place of beings, it is worth while to speak likewise concisely about this. For if he says that animal itself has intelligible and occult number, as comprehended in the monad, he speaks rightly, and accords with Plato. But if he says that animal itself comprehends number, now separated, or which has a multiform subsistence, and is the progeny of difference, intelligible multitude is not a thing of this kind.
For there indeed, the one is being, and being is the one. Hence animal itself is according to all things perfect. But in number, the one is separated from being, and being from the one, and each of the parts is no longer an intelligible whole, as an animal itself. For that is a whole of wholes, and every where the one was with being in the parts of it, and animal itself was onlybegotten. But number proceeded after the twofold coordinations, I mean the monad and duad, the odd and the even number.
How therefore, can we place in animal itself the first number?
If however, some one should say that number exists there, it is according to cause and intelligibly. But it is intellectually separated by difference.
And farther still, in addition to these things, if animal itself is surveyed by some one in the demiurgic order, and he denominates it the plenitude of forms, and the ineligible of the demiurgic intellect, it will thus have intellectual number, as being arranged near the intellectual end. But if he should call intelligible animal number, in this case there will be separation and difference in the Gods, whom we have asserted to be established above the whole of things, according to supreme union; For all section and division originate from the intellectual Gods; since here difference proceeds, adorning things in conjunction with the one and being. How therefore, does the division of the unities into minute parts, or the multiform nature of beings pertain to intelligibles?
And how can the multitude of all forms accord with the first animal itself? For the tetrad was there, divided by the monad and triad, a division of this kind: being adapted to the third order of intelligible forms. For as the one being is a monad, but eternity is a monad and duad, (for to be is conjoined with the ever) so animal itself is a monad and triad. Since, however, it comprehends in itself the cause of all number, Timaeus denominates it the tetrad which is comprehensive of the four first effective causes. For the tetrad itself preexists as the fountain of all the production of forms. But in intelligibles the monad, duad and triads subsist unically; but in intellectuals in a divided manner.
Difference therefore necessarily generates all these for us with separation.
For every where, the first of subordinate natures have the peculiar form of the natures that exist prior to them. Hence, the first multitudes proceed indeed from the one, but they are unical, without separation, and without number, imitating the one principle of the whole of things.
Very properly therefore, does Parmenides constitute multitude in intelligibles, according to the end [of the intelligible order]; but number in intellectuals according to the beginning [of the intelligible and at the same time intellectual order.] And these are conjoined with each other.
Parmenides also preestablishes unical and intelligible multitude, as the cause of intellectual numbers. And Timaeus shows that animal itself is onlybegotten, because it was monadically the cause of the whole of things, and not dyadically, nor according to divine difference. That number however, is the first thing in intellectuals, we have abundantly shown.
CHAPTER XXXIII.
BUT Parmenides begins to speak about it as follows: "Proceed therefore, and still farther consider this. What? We have said that the one participates of essence, so far as it is being. We have said so.
And on this account the one being appears to be many." But he completes his discourse about the first monad thus: "Are not three (things odd, and two even? How should they not?" And about the second monad, as follows: "Hence there will be the evenlyeven, and the oddlyodd, and the oddlyeven, and the evenlyodd." But he completes his discourse about the third and all the succeeding triad, as follows : "The one being therefore, is not only many, but it is likewise necessary that the one which is distributed by being should be many.
Entirely so." The first triad, therefore, of the intelligible, and at the same time, intellectual Gods, is through these things unfolded to us by Plato, and which possesses indeed, according to the first monad the first powers of numbers, I mean the odd and the even, and is completed through these principles which were in intelligibles occultly, viz. monad, duad, triad.
But according to the second monad it possesses the second
powers of numbers which subsist from these [i. e. from the first powers].
For the section of the forms of the even number, is allotted a second order. And the oddlyodd is subordinate to the first odd numbers.
But according to the third monad, it possesses the more partial causes of divine numbers. Hence also, a separation into minute parts, infinity, allperfect division, and unical and essential number are here; receiving indeed, the unical and the essential from unity and being, but the separation of number from difference. For every where difference is in the three monads, but it particularly unfolds the multitudes of numbers, according to the third monad, generates more partial Gods, and divides being in conjunction with the Gods. For neither is deity in these imparticipable, because unity is not separate from being, nor is essence destitute of deity, because neither is being deprived of the one.
Since however, all things are in each of the monads, but unically and intelligibly in the first, generatively, and according to the peculiarity of difference in the second, and intellectually, and according to being in the third;—this being the case, Plato when unfolding to us the first monad, very properly begins from the monad, and proceeds as far as to the triad; but when teaching about the second, he begins from evenlyeven numbers, and proceeds as far as to those that are evenlyodd, both which belong to the nature of the even number. And when he adds the third monad, he begins from being, and recurs through difference to the one.
For having shown that being participates of number, he from hence leads us round to unical number, employing the mode of conversion in the conception of this monad.
CHAPTER XXXIV.
If, however, it be requisite to survey the unknown peculiarity of divine numbers, and how the first order of intelligibles and intellectuals, and number which subsists according to this order, is the most ancient of all numbers, in the first place, we should consider the infinity mentioned by Parmenides, and see whether he does not say that intelligible multitude is infinite on account of this number, in consequence of its being unknown and incomprehensible by partial conceptions. For the allperfect, and allpowerful peculiarity of divine numbers is exempt from the comprehension of partible natures, [such as ours]. They are therefore unknown, and on this account are said to be inexplicable, and not to be investigated.
For number also in the last of things, and multitude, together with the known have likewise the unknown. And we are not able to comprehend the progression of every number in consequence of being vanquished by infinity. The incomprehensibility therefore, of this power which is unknown according to a discursive energy, is comprehended according to cause, in intelligible numbers and multitudes. For there would not be a thing of this kind in the last of numbers, unless the unknown preexisted in intelligible numbers, and unless the former were ultimate imitations of the exempt incomprehensibility of the latter.
In the second place, after this, we may also add, that unical numbers are likewise of themselves unknown. For they are more ancient than beings, more single than forms, and being generative of, exist prior to the forms which we call intelligible. But the most venerable of divine operations manifest this, since they employ numbers, as possessing an ineffable efficacy, and through these effect the greatest, and most arcane of works. And prior to these nature ineffably, according to sympathy, imparts different powers to different things, to some solar, but to others lunar powers, and renders the productions of these concordant with numbers. For in these monadic numbers also, the forms of numbers, such as the triad, the pentad, and the heptad, are one thing, but the unions of the forms another thing. For each of these forms is both one, and multitude. Hence form is unknown according to the highest union.
If therefore, monadic number participates of a certain unknown power, much more must the first number possess this peculiarity unically exempt from the whole of things. And besides this, we may also assume the anagogic power of numbers, not only because they define the periods of the physical restitutions, circumscribing our indefinite lation by appropriate measures, perfecting us according to these measures, and conjoining us to our first causes, but because likewise, number in a remarkable manner possesses a certain power of attracting to truth, as Socrates says in the Republic, leading us to intelligibles from a sensible nature. As therefore, the last number is allotted this peculiarity, what ought we to say about the first number? Is it not this, that it unfolds intelligible light, especially persuades to an establishment in intelligibles, and through its own order announces to us the uniform power of principles? If therefore, we rightly assert these things, we shall in a greater degree admire Timaeus, who having placed time over the perfections of souls, and the whole world, through which it would become more similar to animal itself says, that time proceeds according to number, and by number measures the existence of total souls. And as in intellectuals, number is establisbed above the celestial circulation, collecting and causing it to be one, thus also in sensibles Timaeus says, that time being number measures the celestial periods, and comprehends in itself the first causes of the perfection of the periods.
If also, Socrates in the Republic, in the speech of the Muses, speaks about the one and entire period of the universe, which he says a perfect number comprehends, does it not through these things appear chat divine number is perfective of wholes, and restores them to their pristine state, and that it measures all periods? The power likewise of collecting things imperfect to the perfect, accedes to all things from number, which elevates souls from things apparent to those that ane unapparent, illuminates the whole world with the perfection of motion, and defines to all things measures, and the order of periods. But if not only a perfect number contains the period of a divine generated nature*, but another second number after this is the lord of better and worse generations as the same Socrates says, number will not only restore things to their pristine state,but will also be of a generative nature. And it is evident that these things subsist in a divided manner, according to the second and third periods of numbers; but at once, and contractedly in the first of numbers. The first number therefore, is generative, mensurative, and perfective of generated natures.
* Every perpetually circulating body is called by Plato, a divine generated nature.
CHAPTER XXXV.
The first order therefore of intelligibles and intellectuals is thus surveyed by Parmenides. But after this the order which possesses the middle place of intelligibles and intellectuals, and which a little before we called connective, presents itself to the view. It is however denominated in a threefold respect, viz. one, many, whole, parts, finite, infinite. For since the separation of unities and beings from number, extends to it, the one and being, which we have said difference divides, become wholes; But the things proceeding from these, are the parts of these; And wholeness indeed connectedly contains parts, but these are contained by their wholeness, in one way indeed, by the one, but in another by being.
For there indeed, I mean in the summit of the intellectual Gods, unity was the cause of multitude, at the same time being exempt from multitude, and generative of the many. But here unity is coarranged with multitude. Hence also it is a whole which has reference to many unities as to parts. Since however, the connective order is triple, one division of it being intelligible, another intelligible and intellectual, and another intellectual, the first monad indeed subsists according to the one and the many; but the second, according to whole and parts; and the third, according to the finite and the infinite. For where the first triad ends, there the second has its beginning. Hence, in the triad prior to this, Parmenides infers that the one is many. And in this triad, he concludes the same thing together with what remains.
There however, the one was generative of infinites; but here the one is comprehensive of many, the whole of parts, and the finite of infinites.
Hence, there indeed, unity is exempt from the many;
but here it is coarranged with multitude. Hence also, the first coarrangement generates whole together with parts; but the subsistence of whole and parts produces the finite and at the same time infinite.
For these are successive to each other, viz. the one, the whole, the finite, and the things which are as it were in an opposite arrangement to these, the many, parts, infinites. And the one itself is indeed the principle of the rest. But whole has now a habitude with respect to parts, and a representation of the duad, and proceeds into a coarrangement with reference to the parts. The finite however, is now multitude, participating of bound and the one, and is as it were a triad. For it is neither bound alone, as the monad, nor infinite alone, as the duad, but it participates of bound, which is primarily a triad. Every thing finite therefore, is a whole, but not every whole is finite. For the infinite is a whole, whether it is multitude, or magnitude. And every whole indeed, is one, but not every one is a whole. For that which is without habitude to multitude is not a whole. The one therefore, is beyond whole; but whole is beyond the finite.
After the same manner also, infinite parts are said to be the parts of that which is finite. For the infinite of itself has no subsistence; by which also it is evident that the infinite is not in quantity in energy, but in capacity. All parts however are not infinite. For according to bound they are characterized by one of the parts. And again, parts indeed are many, but the many are not entirely parts. The many therefore, are prior to parts: and parts are prior to infinites. Hence, as the many are to the one, so are parts to whole, and so are infinites to the finite.
And these three connectedlycontaining monads, give completion to the middle order of intelligibles and intellectuals. For unity indeed, is the supplier of stable and intelligible connection to all the secondary orders. But wholeness connects the progressions of divine natures, and produces one habitude of the orderly, distribution of wholes. And the finite monad imparts by illumination to the conversions of second natures, connection with the natures prior to them. And one of these indeed is analogous to the one being, on which account also it is intelligible. But another is analogous to the third order, in which there was the one, and the duad which generates infinite multitude. Such is the connective triad, which Parmenides exhibits to us through these things. The one therefore, is one and many, whole and parts, finite and infinite multitude. Let no one however, be disturbed that Plato calls the one or being infinite multitude.
For he calls the one and being when they have proceeded and are divided, infinite in multitude. For all multitude indeed, is referred to the intelligible infinity. But divided multitude, and which has proceeded perfectly, is most signally infinite.
Since therefore, all the primary causes of intellectuals are in this triad, and all things are disseminated in its bosoms, the first Synocheus indeed, comprehends these causes as multitude, being himself an intelligible unity, and the flower as it were of the triad. But the second comprehends indeed secondarily these causes, but coarranged and comultiplied with then. And the third, together with allperfect division, connects the multitude comprehended in himself. Each of them also is connective, but one as bounding, another as giving completion to a whole, and another as uniting. Plato therefore made, and makes as he proceeds his demonstrations of the one. For the whole theory is concerning the one.
But it is evident that being is codivided with the one. For universally, it has been before observed, that every deity proceeding thence is participable, and that every portion of being participates of deity. It is necessary however, not to stop in the one alone, but to consider the same peculiarity as imparted to being in a secondary degree, since Plato also produces the one itself by itself according to the differences of the divine orders; which occasions me to wonder at those who think that all the conclusions of the second hypothesis are concerning intellect, and do not perceive that Plato omitting being surveys the one itself by itself, as proceeding and generated, and receiving different peculiarities.
For how in discoursing concerning intellect could he omit being, according to which intellect has its subsistence, power, and energy. For the one is beyond the nature of intellect; but being gives hyparxis to intellect, and intellect is nothing else than being. This opinion however of these men may be confuted by many other arguments. But if the three connective Gods are divided after the abovementioned manner, and the intelligible connective deity is one many, but the intelligible and at the same time intellectual deity is whole and parts, and the intellectual is finite and infinite, each of them is very properly called much. For each of the Synoches according to his own peculiarity is a multitude. For the first about the many, receives many Synoches of a more partial nature. The second receives these according to parts. And the third, according to infinites.
If therefore, there are certain partial Gods who are allotted this peculiarity, they are comprehended in this first triad.
CHAPTER XXXVI.
MOREOVER, it is easy for every one to see how these things accord with what is written in the Phaedrus. for the connective one accords with the back of the heaven that comprehends these. For the one and the back are the same, comprehending according to one simplicity the whole circulation. But whole is the same with the profundity of the heaven, and with as it were the bulk of it. For the celestial profundity is a whole extended from the back as far as to the arch. And end is the same with the arch. This therefore, is evident beyond every thing, and each of the other conclusions, is to be referred to the same conceptions.
Hence from what has been said, it may be collected, that these three things pertain in a remarkable degree to the Synoches, viz. the one, whole, and the end [or the finite]. For what is so able to connect multitude as the one which is coarranged with it? What is so connectedlycomprehensive of parts as whole? And how is it possible that the end
[or bound,] should not be the cause of binding together things which are borne along to infinity. It terminates therefore, their progression, and brings back their dispersed section to the one essence of connection. And thus much concerning the connective triad.
CHAPTER XXXVII.
BUT the third, as they say, to the saviour, and let us also following Plato in what remains celebrate the perfective order of the Gods.
Because, therefore, the end of the connective order was the finite, [or the bounded] the perfective order has extremes. For the end [or bound] is the extremity. There however indeed the one was said to be the finite, but here it is said to have an extremity, as receiving according to participation that which has the power of terminating many things. And there indeed, the one was end or bound, which also connectedly contains the infinite; but here having an extremity, it will also have a middle and beginning, and will be perfect.
For that which receives its completion from all these, is perfect.
Here, therefore, the perfection which consists of parts is apparent.
For the consummation of the parts, produces the perfect.
Moreover, because such a one as this has a
middle and extremes, it will have the figure of a circumference, or it will be rectilinear, or it will be mixed [from the right and circular line].
For all these require a middle and extremes; some indeed with simplicity, but others with connexion. Three peculiarities, therefore, again present themselves to our view; the first, indeed, being that which we said was to have extremes; the second, being according to the perfect; and the third, according to figure. And there are also three perfective leaders of wholes; one indeed being intelligible; another, intelligible and intellectual; and the third, intellectual.
The intelligible leader, therefore, is said to have extremes, as being directly arranged under the end of the connective Gods, and in the boundaries of himself intelligibly comprehending all the intellectual orders. But the intelligible and intellectual leader, is defined according to the perfect, comprehending in himself the beginnings, middles, and ends of beings, and giving completion to the middle bond of the whole perfective triad.
And the intellectual leader proceeds according to triadic figure, being the cause of bound and divine perfection; and imparting termination to things indefinite, but intellectual perfection to things imperfect.
And this triad indeed is produced according to the
connective triad. For the end in them is the cause of the possession of the extremity. But it is also produced from itself. For that which has extremes, having become a whole, constitutes the perfect through end
[or bound]. But the perfect comprehending beginnings, middles and ends, unfolds figure. And thus the perfective triad proceeds supernally, as far as to the last of things, pervading to all things, and perfecting both whole and partial causes.
CHAPTER XXXVIII.
AND do you not see how each of the triads conjoins the summit of itself with the ends placed above it? For the one many was the end of the collective and unknown triad; and the same is the beginning of the connective triad. The end of the connective triad was the finite; and this again is the beginning of the perfective triad. For to have extremes manifests that which consists of ends or bounds. And thus the whole middle order is connected with and united to itself, and is truly the bond of total orders, itself establishing an admirable communion with itself, but conjoining intellectuals to intelligibles