(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.

(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.

(71) Magnitude is divided into two parts--magnitude which is stationary and magnitude which is movable, the stationary pare having priority. Multitude is also divided into two parts, for it is related both to itself and to other things, the first relationship having priority. Pythagoras assigned the science of arithmetic to multitude related to itself, and the art of music to multitude related to other things. Geometry likewise was assigned to stationary magnitude, and spherics (used partly in the sense of astronomy) to movable magnitude. Both multitude and magnitude were circumscribed by the circumference of mind. The atomic theory has proved size to be the result of number, for a mass is made up of minute units though mistaken by the uninformed for a single simple substance.

(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.

(8) The division into elements must, in short, be abandoned, especially in regard to Sensible Substance, known necessarily by sense rather than by reason. We must no longer look for help in constituent parts, since such parts will not be substances, or at any rate not sensible substances.

Our plan must be to apprehend what is constant in stone, earth, water and the entities which they compose- the vegetal and animal forms, considered purely as sensibles- and to confine this constant within a single genus. Neither Matter nor Form will thus be overlooked, for Sensible Substance comports them; fire and earth and the two intermediaries consist of Matter and Form, while composite things are actually many substances in one. They all, moreover, have that common property which distinguishes them from other things: serving as subjects to these others, they are never themselves present in a subject nor predicated of any other thing. Similarly, all the characteristics which we have ascribed to Substance find a place in this classification.

But Sensible Substance is never found apart from magnitude and quality: how then do we proceed to separate these accidents? If we subtract them- magnitude, figure, colour, dryness, moistness- what is there left to be regarded as Substance itself? All the substances under consideration are, of course, qualified.

There is, however, something in relation to which whatever turns Substance into qualified Substance is accidental: thus, the whole of fire is not Substance, but only a part of it- if the term "part" be allowed.

What then can this "part" be? Matter may be suggested. But are we actually to maintain that the particular sensible substance consists of a conglomeration of qualities and Matter, while Sensible Substance as a whole is merely the sum of these coagulations in the uniform Matter, each one separately forming a quale or a quantum or else a thing of many qualities? Is it true to say that everything whose absence leaves subsistence incomplete is a part of the particular substance, while all that is accidental to the substance already existent takes independent rank and is not submerged in the mixture which constitutes this so-called substance?

I decline to allow that whatever combines in this way with anything else is Substance if it helps to produce a single mass having quantity and quality, whereas taken by itself and divorced from this complementary function it is a quality: not everything which composes the amalgam is Substance, but only the amalgam as a whole.

And let no one take exception on the ground that we produce Sensible Substance from non-substances. The whole amalgam itself is not True Substance; it is merely an imitation of that True Substance which has Being apart from its concomitants, these indeed being derived from it as the possessor of True Being. In the lower realm the case is different: the underlying ground is sterile, and from its inability to produce fails to attain to the status of Being; it remains a shadow, and on this shadow is traced a sketch- the world of Appearance.

(2) Now the reasoning faculty which undertakes this problem is not a unity but a thing of parts; it brings the bodily nature into the enquiry, borrowing its principles from the corporeal: thus it thinks of the Essential Existence as corporeal and as a thing of parts; it baulks at the unity because it does not start from the appropriate principles. We, however, must be careful to bring the appropriately convincing principles to the discussion of the Unity, of perfect Being: we must hold to the Intellectual principles which alone apply to the Intellectual Order and to Real Being.

On the one hand there is the unstable, exposed to all sorts of change, distributed in place, not so much Being as Becoming: on the other, there is that which exists eternally, not divided, subject to no change of state, neither coming into being nor falling from it, set in no region or place or support, emerging from nowhere, entering into nothing, fast within itself.

In dealing with that lower order we would reason from its own nature and the characteristics it exhibits; thus, on a plausible foundation, we achieve plausible results by a plausible system of deduction: similarly, in dealing with the Intellectual, the only way is to grasp the nature of the essence concerned and so lay the sure foundations of the argument, not forgetfully straying over into that other order but basing our treatment on what is essential to the Nature with which we deal.

In every entity the essential nature is the governing principle and, as we are told, a sound definition brings to light many even of the concomitants: where the essential nature is the entire being, we must be all the more careful to keep to that, to look to that, to refer all to that.

(3) That also which is added by you, “ or of accidents ,” is foreign from these genera. For in composites, and things which exist together with, or in others, or are comprehended by others, some things are conceived to be precedaneous, but others consequent; and some as essences, but others, as afterwards acceding to essences. For there is a certain coarrangement of them, and incongruity and interval intervenes. But, in the more excellent genera, all things must be conceived in τῳ ειναι , i. e. in merely existing ; and wholes have a precedaneous subsistence, are separate by themselves, and have not their hypostasis from, or in others; so that there is not any thing in them which is accidental. Hence the peculiarity of them is not characterized from accidents.

(2) Our first observations must be directed to what passes in the Sensible realm for Substance. It is, we shall agree, only by analogy that the nature manifested in bodies is designated as Substance, and by no means because such terms as Substance or Being tally with the notion of bodies in flux; the proper term would be Becoming.

But Becoming is not a uniform nature; bodies comprise under the single head simples and composites, together with accidentals or consequents, these last themselves capable of separate classification.

Alternatively, Becoming may be divided into Matter and the Form imposed upon Matter. These may be regarded each as a separate genus, or else both may be brought under a single category and receive alike the name of Substance.

But what, we may ask, have Matter and Form in common? In what sense can Matter be conceived as a genus, and what will be its species? What is the differentia of Matter? In which genus, Matter or Form, are we to rank the composite of both? It may be this very composite which constitutes the Substance manifested in bodies, neither of the components by itself answering to the conception of Body: how, then, can we rank them in one and the same genus as the composite? How can the elements of a thing be brought within the same genus as the thing itself? Yet if we begin with bodies, our first-principles will be compounds.

Why not resort to analogy? Admitted that the classification of the Sensible cannot proceed along the identical lines marked out for the Intellectual: is there any reason why we should not for Intellectual-Being substitute Matter, and for Intellectual Motion substitute Sensible Form, which is in a sense the life and consummation of Matter? The inertia of Matter would correspond with Stability, while the Identity and Difference of the Intellectual would find their counterparts in the similarity and diversity which obtain in the Sensible realm.

But, in the first place, Matter does not possess or acquire Form as its life or its Act; Form enters it from without, and remains foreign to its nature. Secondly, Form in the Intellectual is an Act and a motion; in the Sensible Motion is different from Form and accidental to it: Form in relation to Matter approximates rather to Stability than to Motion; for by determining Matter's indetermination it confers upon it a sort of repose.

In the higher realm Identity and Difference presuppose a unity at once identical and different: a thing in the lower is different only by participation in Difference and in relation to some other thing; Identity and Difference are here predicated of the particular, which is not, as in that realm, a posterior.

As for Stability, how can it belong to Matter, which is distorted into every variety of mass, receiving its forms from without, and even with the aid of these forms incapable of offspring.

This mode of division must accordingly be abandoned.

(9) But how can we conceive a thing having existence without having magnitude?

We have only to think of things whose identity does not depend on their quantity- for certainly magnitude can be distinguished from existence as can many other forms and attributes.

In a word, every unembodied Kind must be classed as without quantity, and Matter is unembodied.

Besides quantitativeness itself does not possess quantity, which belongs only to things participating in it, a consideration which shows that Quantitativeness is an Idea-Principle. A white object becomes white by the presence of whiteness; what makes an organism white or of any other variety of colour is not itself a specific colour but, so to speak, a specific Reason-Principle: in the same way what gives an organism a certain bulk is not itself a thing of magnitude but is Magnitude itself, the abstract Absolute, or the Reason-Principle.

This Magnitude-Absolute, then, enters and beats the Matter out into Magnitude?

Not at all: the Matter was not previously shrunken small: there was no littleness or bigness: the Idea gives Magnitude exactly as it gives every quality not previously present.

(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.

(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.

(4) If we had to ascertain the nature of body and the place it holds in the universe, surely we should take some sample of body, say stone, and examine into what constituents it may be divided. There would be what we think of as the substrate of stone, its quantity- in this case, a magnitude; its quality- for example, the colour of stone. As with stone, so with every other body: we should see that in this thing, body, there are three distinguishable characteristics- the pseudo-substance, the quantity, the quality- though they all make one and are only logically trisected, the three being found to constitute the unit thing, body. If motion were equally inherent in its constitution, we should include this as well, and the four would form a unity, the single body depending upon them all for its unity and characteristic nature.

The same method must be applied in examining the Intellectual Substance and the genera and first-principles of the Intellectual sphere.

But we must begin by subtracting what is peculiar to body, its coming-to-be, its sensible nature, its magnitude- that is to say, the characteristics which produce isolation and mutual separation. It is an Intellectual Being we have to consider, an Authentic Existent, possessed of a unity surpassing that of any sensible thing.

Now the wonder comes how a unity of this type can be many as well as one. In the case of body it was easy to concede unity-with-plurality; the one body is divisible to infinity; its colour is a different thing from its shape, since in fact they are separated. But if we take Soul, single, continuous, without extension, of the highest simplicity- as the first effort of the mind makes manifest- how can we expect to find multiplicity here too? We believed that the division of the living being into body and soul was final: body indeed was manifold, composite, diversified; but in soul we imagined we had found a simplex, and boldly made a halt, supposing that we had come to the limit of our course.

Let us examine this soul, presented to us from the Intellectual realm as body from the Sensible. How is its unity a plurality? How is its plurality a unity? Clearly its unity is not that of a composite formed from diverse elements, but that of a single nature comprising a plurality.

This problem attacked and solved, the truth about the genera comprised in Being will thereby, as we asserted, be elucidated also.

(16) An Ideal-Principle approaches and leads Matter towards some desired dimension, investing this non-existent underlie with a magnitude from itself which never becomes incorporate- for Matter, if it really incorporated magnitude, would be a mass.

Eliminate this Ideal-Form and the substratum ceases to be a thing of magnitude, or to appear so: the mass produced by the Idea was, let us suppose, a man or a horse; the horse-magnitude came upon the Matter when a horse was produced upon it; when the horse ceases to exist upon the Matter, the magnitude of the horse departs also. If we are told that the horse implies a certain determined bulk and that this bulk is a permanent thing, we answer that what is permanent in this case is not the magnitude of the horse but the magnitude of mass in general. That same Magnitude might be fire or earth; on their disappearance their particular magnitudes would disappear with them. Matter, then, can never take to itself either pattern or magnitude; if it did, it would no longer be able to turn from being fire, let us say, into being something else; it would become and be fire once for all.

In a word, though Matter is far extended- so vastly as to appear co-extensive with all this sense-known Universe- yet if the Heavens and their content came to an end, all magnitude would simultaneously pass from Matter with, beyond a doubt, all its other properties; it would be abandoned to its own Kind, retaining nothing of all that which, in its own peculiar mode, it had hitherto exhibited.

Where an entrant force can effect modification it will inevitably leave some trace upon its withdrawal; but where there can be no modification, nothing can be retained; light comes and goes, and the air is as it always was.

That a thing essentially devoid of magnitude should come to a certain size is no more astonishing than that a thing essentially devoid of heat should become warm: Matter's essential existence is quite separate from its existing in bulk, since, of course, magnitude is an immaterial principle as pattern is. Besides, if we are not to reduce Matter to nothing, it must be all things by way of participation, and Magnitude is one of those all things.

In bodies, necessarily compounds, Magnitude though not a determined Magnitude must be present as one of the constituents; it is implied in the very notion of body; but Matter- not a Body- excludes even undetermined Magnitude.

(12) Enough upon that side of the question. But how does the perfection of numbers, lifeless things, depend upon their particular unity? Just as all other inanimates find their perfection in their unity.

If it should be objected that numbers are simply non-existent, we should point out that our discussion is concerned with beings considered from the aspect of their unity.

We may again be asked how the point- supposing its independent existence granted- participates in perfection. If the point is chosen as an inanimate object, the question applies to all such objects: but perfection does exist in such things, for example in a circle: the perfection of the circle will be perfection for the point; it will aspire to this perfection and strive to attain it, as far as it can, through the circle.

But how are the five genera to be regarded? Do they form particulars by being broken up into parts? No; the genus exists as a whole in each of the things whose genus it is.

But how, at that, can it remain a unity? The unity of a genus must be considered as a whole-in-many.

Does it exist then only in the things participating in it? No; it has an independent existence of its own as well. But this will, no doubt, become clearer as we proceed.

(14) How are we to classify the straight line? Shall we deny that it is a magnitude?

The suggestion may be made that it is a qualified magnitude. May we not, then, consider straightness as a differentia of "line"? We at any rate draw on Quality for differentiae of Substance.

The straight line is, thus, a quantity plus a differentia; but it is not on that account a composite made up of straightness and line: if it be a composite, the composite possesses a differentiae of its own.

But why is not the product of three lines included in Quantity? The answer is that a triangle consists not merely of three lines but of three lines in a particular disposition, a quadrilateral of four lines in a particular disposition: even the straight line involves disposition as well as quantity.

Holding that the straight line is not mere quantity, we should naturally proceed to assert that the line as limited is not mere quantity, but for the fact that the limit of a line is a point, which is in the same category, Quantity. Similarly, the limited surface will be a quantity, since lines, which have a far better right than itself to this category, constitute its limits. With the introduction of the limited surface- rectangle, hexagon, polygon- into the category of Quantity, this category will be brought to include every figure whatsoever.

If however by classing the triangle and the rectangle as qualia we propose to bring figures under Quality, we are not thereby precluded from assigning the same object to more categories than one: in so far as it is a magnitude- a magnitude of such and such a size- it will belong to Quantity; in so far as it presents a particular shape, to Quality.

It may be urged that the triangle is essentially a particular shape. Then what prevents our ranking the sphere also as a quality?

To proceed on these lines would lead us to the conclusion that geometry is concerned not with magnitudes but with Quality. But this conclusion is untenable; geometry is the study of magnitudes. The differences of magnitudes do not eliminate the existence of magnitudes as such, any more than the differences of substances annihilate the substances themselves.

Moreover, every surface is limited; it is impossible for any surface to be infinite in extent.

Again, when I find Quality bound up with Substance, I regard it as substantial quality: I am not less, but far more, disposed to see in figures or shapes varieties of Quantity. Besides, if we are not to regard them as varieties of magnitude, to what genus are we to assign them?

Suppose, then, that we allow differences of magnitude; we commit ourselves to a specific classification of the magnitudes so differentiated.

(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.

(3) But perhaps we should rather speak of some single category, embracing Intellectual Substance, Matter, Form, and the Composite of Matter and Form. One might refer to the family of the Heraclids as a unity in the sense, not of a common element in all its members, but of a common origin: similarly, Intellectual Substance would be Substance in the first degree, the others being substances by derivation and in a lower degree.

But what is the objection to including everything in a single category, all else of which existence is predicated being derived from that one thing, Existence or Substance? Because, granted that things be no more than modifications of Substance, there is a distinct grading of substances themselves. Moreover, the single category does not put us in a position to build on Substance, or to grasp it in its very truth as the plausible source of the other substances.

Supposing we grant that all things known as substances are homogeneous as possessing something denied to the other genera, what precisely is this something, this individuality, this subject which is never a predicate, this thing not present in any thing as in a subject, this thing which does not owe its essential character to any other thing, as a quality takes character from a body and a quantity from a substance, as time is related to motion and motion to the moved?

The Second Substance is, it is true, a predicate. But predication in this case signifies a different relation from that just considered; it reveals the genus inherent in the subject and the subject's essential character, whereas whiteness is predicated of a thing in the sense of being present in the thing.

The properties adduced may indeed be allowed to distinguish Substance from the other Existents. They afford a means of grouping substances together and calling them by a common name. They do not however establish the unity of a genus, and they do not bring to light the concept and the nature of Substance.

These considerations are sufficient for our purpose: let us now proceed to investigate the nature of Quantity.

(11) We are bound however to enquire under what mode unity is contained in Being. How is what is termed the "dividing" effected- especially the dividing of the genera Being and unity? Is it the same division, or is it different in the two cases?

First then: In what sense, precisely, is any given particular called and known to be a unity? Secondly: Does unity as used of Being carry the same connotation as in reference to the Absolute?

Unity is not identical in all things; it has a different significance according as it is applied to the Sensible and the Intellectual realms- Being too, of course, comports such a difference- and there is a difference in the unity affirmed among sensible things as compared with each other; the unity is not the same in the cases of chorus, camp, ship, house; there is a difference again as between such discrete things and the continuous. Nevertheless, all are representations of the one exemplar, some quite remote, others more effective: the truer likeness is in the Intellectual; Soul is a unity, and still more is Intellect a unity and Being a unity.

When we predicate Being of a particular, do we thereby predicate of it unity, and does the degree of its unity tally with that of its being? Such correspondence is accidental: unity is not proportionate to Being; less unity need not mean less Being. An army or a choir has no less Being than a house, though less unity.

It would appear, then, that the unity of a particular is related not so much to Being as to a standard of perfection: in so far as the particular attains perfection, so far it is a unity; and the degree of unity depends on this attainment. The particular aspires not simply to Being, but to Being-in-perfection: it is in this strain towards their perfection that such beings as do not possess unity strive their utmost to achieve it.

Things of nature tend by their very nature to coalesce with each other and also to unify each within itself; their movement is not away from but towards each other and inwards upon themselves. Souls, moreover, seem to desire always to pass into a unity over and above the unity of their own substance. Unity in fact confronts them on two sides: their origin and their goal alike are unity; from unity they have arisen, and towards unity they strive. Unity is thus identical with Goodness ; for no being ever came into existence without possessing, from that very moment, an irresistible tendency towards unity.

From natural things we turn to the artificial. Every art in all its operation aims at whatsoever unity its capacity and its models permit, though Being most achieves unity since it is closer at the start.

That is why in speaking of other entities we assert the name only, for example man; when we say "one man," we have in mind more than one; and if we affirm unity of him in any other connection, we regard it as supplementary : but when we speak of Being as a whole we say it is one Being without presuming that it is anything but a unity; we thereby show its close association with Goodness.

Thus for Being, as for the others, unity turns out to be, in some sense, Principle and Term, not however in the same sense as for things of the physical order- a discrepancy leading us to infer that even in unity there are degrees of priority.

How, then, do we characterize the unity in Being? Are we to think of it as a common property seen alike in all its parts? In the first place, the point is common to lines and yet is not their genus, and this unity we are considering may also be common to numbers and not be their genus- though, we need hardly say, the unity of Unity-Absolute is not that of the numbers, one, two and the rest. Secondly, in Being there is nothing to prevent the existence of prior and posterior, simple and composite: but unity, even if it be identical in all the manifestations of Being, having no differentiae can produce no species; but producing no species it cannot be a genus.

(17) This procedure, if approved, will entail a distinction between psychic and bodily qualities, the latter belonging specifically to body.

If we decide to refer all souls to the higher, we are still at liberty to perform for Sensible qualities a division founded upon the senses themselves- the eyes, the ears, touch, taste, smell; and if we are to look for further differences, colours may be subdivided according to varieties of vision, sounds according to varieties of hearing, and so with the other senses: sounds may also be classified qualitatively as sweet, harsh, soft.

Here a difficulty may be raised: we divide the varieties of Substance and their functions and activities, fair or foul or indeed of any kind whatsoever, on the basis of Quality, Quantity rarely, if ever, entering into the differences which produce species; Quantity, again, we divide in accordance with qualities of its own: how then are we to divide Quality itself into species? what differences are we to employ, and from what genus shall we take them? To take them from Quality itself would be no less absurd than setting up substances as differences of substances.

How, then, are we to distinguish black from white? how differentiate colours in general from tastes and tangible qualities? By the variety of sense-organs? Then there will be no difference in the objects themselves.

But, waiving this objection, how deal with qualities perceived by the same sense-organ? We may be told that some colours integrate, others disintegrate the vision, that some tastes integrate, others disintegrate the tongue: we reply that, first, it is the actual experiences that we are discussing and it is to these that the notions of integration and disintegration must be applied; secondly, a means of differentiating these experiences has not been offered.

It may be suggested that we divide them by their powers, and this suggestion is so far reasonable that we may well agree to divide the non-sensuous qualities, the sciences for example, on this basis; but we see no reason for resorting to their effects for the division of qualities sensuous. Even if we divide the sciences by their powers, founding our division of their processes upon the faculties of the mind, we can only grasp their differences in a rational manner if we look not only to their subject-matter but also to their Reason-Principles.

But, granted that we may divide the arts by their Reason-Principles and theorems, this method will hardly apply to embodied qualities. Even in the arts themselves an explanation would be required for the differences between the Reason-Principles themselves. Besides, we have no difficulty in seeing that white differs from black; to account for this difference is the purpose of our enquiry.