(17) The division, then, of a whole into the parts, is, for the most part, conceived with reference to magnitude; that into the accidents can never be entirely explicated, if, necessarily, essence is inherent in each of the existences.

(9) For the One is indivisible; wherefore also it is infinite, not considered with reference to inscrutability, but with reference to its being without dimensions, and not having a limit. And therefore it is without form and name.

(8) The light of our world can be allocated because it springs from a corporeal mass of known position, but conceive an immaterial entity, independent of body as being of earlier nature than all body, a nature firmly self-based or, better, without need of base: such a principle, incorporeal, autonomous, having no source for its rising, coming from no place, attached to no material mass, this cannot be allotted part here and part there: that would be to give it both a previous position and a present attachment. Finally, anything participating in such a principle can participate only as entirety with entirety; there can be no allotment and no partition.

A principle attached to body might be exposed, at least by way of accident, to such partition and so be definable as passive and partible in view of its close relationship with the body of which it is so to speak a state or a Form; but that which is not inbound with body, which on the contrary body must seek, will of necessity go utterly free of every bodily modification and especially of the very possibility of partition which is entirely a phenomenon of body, belonging to its very essence. As partibility goes with body, so impartibility with the bodiless: what partition is possible where there is no magnitude? If a thing of magnitude participates to any degree in what has no magnitude, it must be by a participation without division; divisibility implies magnitude.

When we affirm unity in multiplicity, we do not mean that the unity has become the multiples; we link the variety in the multiples with the unity which we discern, undivided, in them; and the unity must be understood as for ever distinct from them, from separate item and from total; that unity remains true to itself, remains itself, and so long as it remains itself cannot fail within its own scope , yet it is not to be thought of as coextensive with the material universe or with any member of the All; utterly outside of the quantitative, it cannot be coextensive with anything.

Extension is of body; what is not of body, but of the opposed order, must be kept free of extension; but where there is no extension there is no spatial distinction, nothing of the here and there which would end its freedom of presence. Since, then, partition goes with place- each part occupying a place of its own- how can the placeless be parted? The unity must remain self-concentrated, immune from part, however much the multiple aspire or attain to contact with it. This means that any movement towards it is movement towards its entirety, and any participation attained is participation in its entirety. Its participants, then, link with it as with something unparticipated, something never appropriated: thus only can it remain intact within itself and within the multiples in which it is manifested. And if it did not remain thus intact, it would cease to be itself; any participation, then, would not be in the object of quest but in something never quested.

(19) Are we to think of the indivisible phase of the soul and the divided as making one thing in a coalescence; or is the indivisible in a place of its own and under conditions of its own, the divisible being a sequent upon it, a separate part of it, as distinct as the reasoning phase is from the unreasoning?

The answer to this question will emerge when we make plain the nature and function to be attributed to each.

The indivisible phase is mentioned without further qualification; but not so the divisible; "that soul" we read "which becomes divisible in bodies"- and even this last is presented as becoming partible, not as being so once for all.

"In bodies": we must then, satisfy ourselves as to what form of soul is required to produce life in the corporeal, and what there must be of soul present throughout such a body, such a completed organism.

Now, every sensitive power- by the fact of being sensitive throughout- tends to become a thing of parts: present at every distinct point of sensitiveness, it may be thought of as divided. In the sense, however, that it is present as a whole at every such point, it cannot be said to be wholly divided; it "becomes divisible in body." We may be told that no such partition is implied in any sensations but those of touch; but this is not so; where the participant is body that divisibility in the sensitive agent will be a condition of all other sensations, though in less degree than in the case of touch. Similarly the vegetative function in the soul, with that of growth, indicates divisibility; and, admitting such locations as that of desire at the liver and emotional activity at the heart, we have the same result. It is to be noted, however, as regards these sensations, that the body may possibly not experience them as a fact of the conjoint thing but in another mode, as rising within some one of the elements of which it has been participant : reasoning and the act of the intellect, for instance, are not vested in the body; their task is not accomplished by means of the body which in fact is detrimental to any thinking on which it is allowed to intrude.

Thus the indivisible phase of the soul stands distinct from the divisible; they do not form a unity, but, on the contrary, a whole consisting of parts, each part a self-standing thing having its own peculiar virtue. None the less, if that phase which becomes divisible in body holds indivisibility by communication from the superior power, then this one same thing may be at once indivisible and divisible; it will be, as it were, a blend, a thing made up of its own divisible self with, in addition, the quality that it derives from above itself.

(5) How then can a multitude of essential beings be really one?

Obviously either the one essence will be entire in all, or the many will rise from a one which remains unaltered and yet includes the one- many in virtue of giving itself, without self-abandonment, to its own multiplication.

It is competent thus to give and remain, because while it penetrates all things it can never itself be sundered: this is an identity in variety.

There is no reason for dismissing this explanation: we may think of a science with its constituents standing as one total, the source of all those various elements: again, there is the seed, a whole, producing those new parts in which it comes to its division; each of the new growths is a whole while the whole remains undiminished: only the material element is under the mode of part, and all the multiplicity remains an entire identity still.

It may be objected that in the case of science the constituents are not each the whole.

But even in the science, while the constituent selected for handling to meet a particular need is present actually and takes the lead, still all the other constituents accompany it in a potential presence, so that the whole is in every part: only in this sense is the whole science distinguished from the part: all, we may say, is here simultaneously effected: each part is at your disposal as you choose to take it; the part invites the immediate interest, but its value consists in its approach to the whole.

The detail cannot be considered as something separate from the entire body of speculation: so treated it would have no technical or scientific value; it would be childish divagation. The one detail, when it is a matter of science, potentially includes all. Grasping one such constituent of his science, the expert deduces the rest by force of sequence.

the geometrician, in his analysis, shows that the single proposition includes all the items that go to constitute it and all the propositions which can be developed from it.

It is our feebleness that leads to doubt in these matters; the body obscures the truth, but There all stands out clear and separate.

(66) This birth or geniture is now in three distinct parts, every part being several and total and yet not one of them is divided asunder from the others. The Gate of the Holy Trinity.

(8) You have conferred multiplicity, you have found and remained One, while still conferring multiplicity through division.

(16) Now one Division divides that which is divided into species, as a genus; and another into parts, as a whole; and another into accidents.

(9) If in such a partition of the unity, that which entered into each participant were an entire- always identical with the first- then, in the progressive severance, the firsts would become numerous, each particular becoming a first: and then what prevents these many firsts from reconstituting the collective unity? Certainly not the bodies they have entered, for those firsts cannot be present in the material masses as their Forms if they are to remain identical with the First from which they come. On the other hand, taking the part conceived as present in the multiple to be simply a power , at once such a part ceases to be the unity; we have then to ask how these powers come to be cut off, to have abandoned their origin; they certainly have not moved away with no purpose in their movement.

Again, are those powers, entering the universe of sense, still within the First or not?

If they are not, we have the absurdity that the First has been lessened, disempowered, stripped of power originally possessed. Besides, how could powers thus cut off subsist apart from the foundations of their being? Suppose these powers to be at once within the First and elsewhere; then the universe of sense contains either the entire powers or parts of them; if parts of powers, the other parts are There; if entires, then either the powers There are present here also undivided- and this brings us back to an identity omnipresent in integral identity- or they are each an entire which has taken division into a multiplicity of similars so that attached to every essence there is one power only- that particularly appropriated to it- the other powers remaining powers unattached: yet power apart from Being is as impossible as Being apart from power; for There power is Being or something greater than Being.

Or, again, suppose the powers coming Thence are other than their source- lesser, fainter, as a bright light dwindles to a dim- but each attached to its essence as a power must always be: such secondary powers would be perfectly uniform and at once we are forced to admit the omnipresence of the one same power or at the least the presence- as in one and the same body- of some undivided identity integral at every point.

And if this is the case with a particular body, why not with the entire universe?

If we think of the single power as being endlessly divided, it is no longer a power entire; partition means lessening of power; and, with part of power for part of body, the conditions of consciousness cease.

Further, a vestigial cut off from its source disappears- for example, a reflected light- and in general an emanant loses its quality once it is severed from the original which it reproduces: just so the powers derived from that source must vanish if they do not remain attached to it.

This being so, where these powers appear, their source must be present with them; thus, once more, that source must itself be omnipresent as an undivided whole.

(81) The incomposite-composite numbers are those which have no common divisor, although each of itself is capable of division, such as 9 and 25. For example, 9 is divisible by 3 and 25 by 5, but neither is divisible by the divisor of the other; thus they have no common divisor. Because they have individual divisors, they are called composite; and because they have no common divisor, they are called in, composite. Accordingly, the term incomposite-composite was created to describe their properties.

(11) It is infinite also by right of being a pure unity with nothing towards which to direct any partial content. Absolutely One, it has never known measure and stands outside of number, and so is under no limit either in regard to any extern or within itself; for any such determination would bring something of the dual into it. And having no constituent parts it accepts no pattern, forms no shape.

Reason recognising it as such a nature, you may not hope to see it with mortal eyes, nor in any way that would be imagined by those who make sense the test of reality and so annul the supremely real. For what passes for the most truly existent is most truly non-existent- the thing of extension least real of all- while this unseen First is the source and principle of Being and sovereign over Reality.

You must turn appearances about or you will be left void of God. You will be like those at the festivals who in their gluttony cram themselves with things which none going to the gods may touch; they hold these goods to be more real than the vision of the God who is to be honoured and they go away having had no share in the sanctities of the shrine.

In these celebrations of which we speak, the unseen god leaves those in doubt of his existence who think nothing patent but what may be known to the flesh: it happens as if a man slept a life through and took the dream world in perfect trust; wake him, and he would refuse belief to the report of his open eyes and settle down to sleep again.

(1) In our attempt to elucidate the Essence of the soul, we show it to be neither a material fabric nor, among immaterial things, a harmony. The theory that it is some final development, some entelechy, we pass by, holding this to be neither true as presented nor practically definitive.

No doubt we make a very positive statement about it when we declare it to belong to the Intellectual Kind, to be of the divine order; but a deeper penetration of its nature is demanded.

In that allocation we were distinguishing things as they fall under the Intellectual or the sensible, and we placed the soul in the former class; now, taking its membership of the Intellectual for granted, we must investigate by another path the more specific characteristics of its nature.

There are, we hold, things primarily apt to partition, tending by sheer nature towards separate existence: they are things in which no part is identical either with another part or with the whole, while, also their part is necessarily less than the total and whole: these are magnitudes of the realm of sense, masses, each of which has a station of its own so that none can be identically present in entirety at more than one point at one time.

But to that order is opposed Essence ; this is in no degree susceptible of partition; it is unparted and impartible; interval is foreign to it, cannot enter into our idea of it: it has no need of place and is not, in diffusion or as an entirety, situated within any other being: it is poised over all beings at once, and this is not in the sense of using them as a base but in their being neither capable nor desirous of existing independently of it; it is an essence eternally unvaried: it is common to all that follows upon it: it is like the circle's centre to which all the radii are attached while leaving it unbrokenly in possession of itself, the starting point of their course and of their essential being, the ground in which they all participate: thus the indivisible is the principle of these divided existences and in their very outgoing they remain enduringly in contact with that stationary essence.

So far we have the primarily indivisible- supreme among the Intellectual and Authentically Existent- and we have its contrary, the Kind definitely divisible in things of sense; but there is also another Kind, of earlier rank than the sensible yet near to it and resident within it- an order, not, like body, primarily a thing of part, but becoming so upon incorporation. The bodies are separate, and the ideal form which enters them is correspondingly sundered while, still, it is present as one whole in each of its severed parts, since amid that multiplicity in which complete individuality has entailed complete partition, there is a permanent identity; we may think of colour, qualities of all kinds, some particular shape, which can be present in many unrelated objects at the one moment, each entire and yet with no community of experience among the various manifestations. In the case of such ideal-forms we may affirm complete partibility.

But, on the other hand, that first utterly indivisible Kind must be accompanied by a subsequent Essence, engendered by it and holding indivisibility from it but, in virtue of the necessary outgo from source, tending firmly towards the contrary, the wholly partible; this secondary Essence will take an intermediate Place between the first substance, the undivided, and that which is divisible in material things and resides in them. Its presence, however, will differ in one respect from that of colour and quantity; these, no doubt, are present identically and entire throughout diverse material masses, but each several manifestation of them is as distinct from every other as the mass is from the mass.

The magnitude present in any mass is definitely one thing, yet its identity from part to part does not imply any such community as would entail common experience; within that identity there is diversity, for it is a condition only, not the actual Essence.

The Essence, very near to the impartible, which we assert to belong to the Kind we are now dealing with, is at once an Essence and an entrant into body; upon embodiment, it experiences a partition unknown before it thus bestowed itself.

In whatsoever bodies it occupies- even the vastest of all, that in which the entire universe is included- it gives itself to the whole without abdicating its unity.

This unity of an Essence is not like that of body, which is a unit by the mode of continuous extension, the mode of distinct parts each occupying its own space. Nor is it such a unity as we have dealt with in the case of quality.

The nature, at once divisible and indivisible, which we affirm to be soul has not the unity of an extended thing: it does not consist of separate sections; its divisibility lies in its presence at every point of the recipient, but it is indivisible as dwelling entire in the total and entire in any part.

To have penetrated this idea is to know the greatness of the soul and its power, the divinity and wonder of its being, as a nature transcending the sphere of Things.

Itself devoid of mass, it is present to all mass: it exists here and yet is There, and this not in distinct phases but with unsundered identity: thus it is "parted and not parted," or, better, it has never known partition, never become a parted thing, but remains a self-gathered integral, and is "parted among bodies" merely in the sense that bodies, in virtue of their own sundered existence, cannot receive it unless in some partitive mode; the partition, in other words, is an occurrence in body not in soul.

(2) It can be demonstrated that soul must, necessarily, be of just this nature and that there can be no other soul than such a being, one neither wholly partible but both at once.

If it had the nature of body it would consist of isolated members each unaware of the conditions of every other; there would be a particular soul- say a soul of the finger- answering as a distinct and independent entity to every local experience; in general terms, there would be a multiplicity of souls administering each individual; and, moreover, the universe would be governed not by one soul but by an incalculable number, each standing apart to itself. But, without a dominant unity, continuity is meaningless.

The theory that "Impressions reach the leading-principle by progressive stages" must be dismissed as mere illusion.

In the first place, it affirms without investigation a "leading" phase of the soul.

What can justify this assigning of parts to the soul, the distinguishing one part from another? What quantity, or what difference of quality, can apply to a thing defined as a self-consistent whole of unbroken unity?

Again, would perception be vested in that leading principle alone, or in the other phases as well?

If a given experience bears only on that "leading principle," it would not be felt as lodged in any particular members of the organism; if, on the other hand, it fastens on some other phase of the soul- one not constituted for sensation- that phase cannot transmit any experience to the leading principle, and there can be no sensation.

Again, suppose sensation vested in the "leading-principle" itself: then, a first alternative, it will be felt in some one part of that , the other part excluding a perception which could serve no purpose; or, in the second alternative, there will be many distinct sensitive phases, an infinite number, with difference from one to another. In that second case, one sensitive phase will declare "I had this sensation primarily"; others will have to say "I felt the sensation that rose elsewhere"; but either the site of the experience will be a matter of doubt to every phase except the first, or each of the parts of the soul will be deceived into allocating the occurrence within its own particular sphere.

If, on the contrary, the sensation is vested not merely in the "leading principle," but in any and every part of the soul, what special function raises the one rather than the other into that leading rank, or why is the sensation to be referred to it rather than elsewhere? And how, at this, account for the unity of the knowledge brought in by diverse senses, by eyes, by ears?

On the other hand, if the soul is a perfect unity- utterly strange to part, a self-gathered whole- if it continuously eludes all touch of multiplicity and divisibility- then, no whole taken up into it can ever be ensouled; soul will stand as circle-centre to every object , and the entire mass of a living being is soulless still.

There is, therefore, no escape: soul is, in the degree indicated, one and many, parted and impartible. We cannot question the possibility of a thing being at once a unity and multi-present, since to deny this would be to abolish the principle which sustains and administers the universe; there must be a Kind which encircles and supports all and conducts all with wisdom, a principle which is multiple since existence is multiple, and yet is one soul always since a container must be a unity: by the multiple unity of its nature, it will furnish life to the multiplicity of the series of an all; by its impartible unity, it will conduct a total to wise ends.

In the case of things not endowed with intelligence, the "leading-principle" is their mere unity- a lower reproduction of the soul's efficiency.

This is the deeper meaning of the profound passage , where we read "By blending the impartible, eternally unchanging essence with that in division among bodies, he produced a third form of essence partaking of both qualities."

Soul, therefore, is, in this definite sense, one and many; the Ideal-Form resident in body is many and one; bodies themselves are exclusively many; the Supreme is exclusively one.

(12) Just as the present aeon, though a unity, is divided by units of time and units of time are divided into years and years are divided into seasons and seasons into months, and months into days, and days into hours, and hours into moments, so too the aeon of the Truth, since it is a unity and multiplicity, receives honor in the small and the great names according to the power of each to grasp it - by way of analogy - like a spring which is what it is, yet flows into streams and lakes and canals and branches, or like a root spread out beneath trees and branches with its fruit, or like a human body, which is partitioned in an indivisible way into members of members, primary members and secondary, great and small.

(10) Another method of division is possible: substances may be classed as hot-dry, dry-cold, cold-moist, or however we choose to make the coupling. We may then proceed to the combination and blending of these couples, either halting at that point and going no further than the compound, or else subdividing by habitation- on the earth, in the earth- or by form and by the differences exhibited by living beings, not qua living, but in their bodies viewed as instruments of life.

Differentiation by form or shape is no more out of place than a division based on qualities- heat, cold and the like. If it be objected that qualities go to make bodies what they are, then, we reply, so do blendings, colours, shapes. Since our discussion is concerned with Sensible Substance, it is not strange that it should turn upon distinctions related to sense-perception: this Substance is not Being pure and simple, but the Sensible Being which we call the Universe.

We have remarked that its apparent subsistence is in fact an assemblage of Sensibles, their existence guaranteed to us by sense-perception. But since their combination is unlimited, our division must be guided by the Form-Ideas of living beings, as for example the Form-Idea of Man implanted in Body; the particular Form acts as a qualification of Body, but there is nothing unreasonable in using qualities as a basis of division.

We may be told that we have distinguished between simple and composite bodies, even ranking them as opposites. But our distinction, we reply, was between material and organic bodies and raised no question of the composite. In fact, there exists no means of opposing the composite to the simple; it is necessary to determine the simples in the first stage of division, and then, combining them on the basis of a distinct underlying principle, to differentiate the composites in virtue of their places and shapes, distinguishing for example the heavenly from the earthly.

These observations will suffice for the Being , or rather the Becoming, which obtains in the Sensible realm.

(13) It has been remarked that the continuous is effectually distinguished from the discrete by their possessing the one a common, the other a separate, limit.

The same principle gives rise to the numerical distinction between odd and even; and it holds good that if there are differentiae found in both contraries, they are either to be abandoned to the objects numbered, or else to be considered as differentiae of the abstract numbers, and not of the numbers manifested in the sensible objects. If the numbers are logically separable from the objects, that is no reason why we should not think of them as sharing the same differentiae.

But how are we to differentiate the continuous, comprising as it does line, surface and solid? The line may be rated as of one dimension, the surface as of two dimensions, the solid as of three, if we are only making a calculation and do not suppose that we are dividing the continuous into its species; for it is an invariable rule that numbers, thus grouped as prior and posterior, cannot be brought into a common genus; there is no common basis in first, second and third dimensions. Yet there is a sense in which they would appear to be equal- namely, as pure measures of Quantity: of higher and lower dimensions, they are not however more or less quantitative.

Numbers have similarly a common property in their being numbers all; and the truth may well be, not that One creates two, and two creates three, but that all have a common source.

Suppose, however, that they are not derived from any source whatever, but merely exist; we at any rate conceive them as being derived, and so may be assumed to regard the smaller as taking priority over the greater: yet, even so, by the mere fact of their being numbers they are reducible to a single type.

What applies to numbers is equally true of magnitudes; though here we have to distinguish between line, surface and solid- the last also referred to as "body"- in the ground that, while all are magnitudes, they differ specifically.

It remains to enquire whether these species are themselves to be divided: the line into straight, circular, spiral; the surface into rectilinear and circular figures; the solid into the various solid figures- sphere and polyhedANSWER: whether these last should be subdivided, as by the geometers, into those contained by triangular and quadrilateral planes: and whether a further division of the latter should be performed.

(26) You alone see purely the first, undying, unborn ones and the first divisions, as you were divided.

(6) The Intellectual Beings, thus, are multiple and one; in virtue of their infinite nature their unity is a multiplicity, many in one and one over many, a unit-plurality. They act as entire upon entire; even upon the partial thing they act as entire; but there is the difference that at first the partial accepts this working only partially though the entire enters later. Thus, when Man enters into human form there exists a particular man who, however, is still Man. From the one thing Man- man in the Idea- material man has come to constitute many individual men: the one identical thing is present in multiplicity, in multi-impression, so to speak, from the one seal.

This does not mean that Man Absolute, or any Absolute, or the Universe in the sense of a Whole, is absorbed by multiplicity; on the contrary, the multiplicity is absorbed by the Absolute, or rather is bound up with it. There is a difference between the mode in which a colour may be absorbed by a substance entire and that in which the soul of the individual is identically present in every part of the body: it is in this latter mode that Being is omnipresent.

(3) And there is the question How can the infinite have existence and remain unlimited: whatever is in actual existence is by that very fact determined numerically.

But, first, if multiplicity holds a true place among Beings, how can it be an evil?

As existent it possesses unity; it is a unit-multiple, saved from stark multiplicity; but it is of a lessened unity and, by that inwoven multiplicity, it is evil in comparison with unity pure. No longer steadfast in that nature, but fallen, it is the less, while in virtue of the unity thence retained it keeps some value; multiplicity has value in so far as it tends to return to, unity.

But how explain the unlimited? It would seem that either it is among beings and so is limited or, if unlimited, is not among beings but, at best, among things of process such as Time. To be brought to limit it must be unlimited; not the limited but the unlimited is the subject of limitation, since between the limited and the unlimited there is no intermediate to accept the principle of limitation. The unlimited recoils by very nature from the Idea of limit, though it may be caught and held by it from without:- the recoil, of course, is not from one place to another; the limitless can have nothing to do with place which arises only with the limiting of the unlimited. Hence what is known as the flux of the unlimited is not to be understood as local change; nor does any other sort of recognisable motion belong to it in itself; therefore the limitless cannot move: neither can it be at rest: in what, since all place is later? Its movement means little more than that it is not fixed in rest.

Is it, then, suspended at some one point, or rocking to and fro?

No; any such poising, with or without side motion, could be known only by place .

How, then, are we to form any conception of its being?

We must fasten on the bare notion and take what that gives us- opposites that still are not opposed: we think of large and small and the unlimited becomes either, of stationary and moving, and it will be either of these. But primarily it can be neither in any defined degree, or at once it is under limit. Limitless in this unlimited and undefined way, it is able to appear as either of a pair of opposites: draw near, taking care to throw no net of limit over it, and you have something that slips away; you come upon no unity for so it would be defined; approach the thing as a unit, and you find it manifold; call it a manifold, and again you falsify, for when the single thing is not a unity neither is the total a manifold. In one manifestation it takes the appearance of movement, in another of rest, as the mind envisages it.

And there is movement in its lack of consciousness; it has passed out of Intellectual-Principle, slid away. That it cannot break free but is under compulsion from without to keep to its circling with no possibility of advance, in this would be its rest. Thus it is not true to speak of Matter as being solely in flux.

(2) But One, because He is uniquely all, as beseems an excess of unique Oneness, and is Cause of all without departing from the One. For there is no single existing being, which does not participate in the one, but as every number participates in an unit, and one dual and one decade is spoken of, and one half, and one third and tenth, so everything, and part of everything participates in the one, and by the fact that the One is, all existing things are. And the Cause of all is not One, as one of many, but before every one and multitude, and determinative of every one and multitude. For there is no multitude which does not partake in some way or other of the one. Yea, that which is many by parts, is one in the whole; and the many by the accidents, is one by the subject; and the many by the number or the powers, is one by the species, and the many by the species, is one by the genus; and the many by the progressions, is one by the source. And there is no single thing which does not participate in some way in the one, which uniformly pre-held in the uniqueness throughout all, all and whole, all, even the things opposed. And indeed, without the one there will not be a multitude, but without the multitude there will be the one, even as the unit previous to every multiplied number; and, if any one should suppose, that all things are united to all, the All will be one in the whole.