(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.

(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.

(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.

(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.

(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.

(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.

(13) It cannot reasonably be thought that the notion of unity is derived from the object since this is physical- man, animal, even stone, a presentation of that order is something very different from unity ; if that presentation were unity, the mind could never affirm unity unless of that given thing, man, for example.

Then again, just as in the case of "On the right" or other such affirmation of relation, the mind does not affirm in some caprice but from observation of contrasted position, so here it affirms unity in virtue of perceiving something real; assuredly the assertion of unity is not a bare attitude towards something non-existent. It is not enough that a thing be alone and be itself and not something else: and that very "something else" tells of another unity. Besides Otherness and Difference are later; unless the mind has first rested upon unity it cannot affirm Otherness or Difference; when it affirms Aloneness it affirms unity-with-aloneness; thus unity is presupposed in Aloneness.

Besides, that in us which asserts unity of some object is first a unity, itself; and the object is a unity before any outside affirmation or conception.

A thing must be either one thing or more than one, manifold: and if there is to be a manifold there must be a precedent unity. To talk of a manifold is to talk of what has something added to unity; to think of an army is to think of a multitude under arms and brought to unity. In refusing to allow the manifold to remain manifold, the mind makes the truth clear; it draws a separate many into one, either supplying a unity not present or keen to perceive the unity brought about by the ordering of the parts; in an army, even, the unity is not a fiction but as real as that of a building erected from many stones, though of course the unity of the house is more compact.

If, then, unity is more pronounced in the continuous, and more again where there is no separation by part, this is clearly because there exists, in real existence, something which is a Nature or Principle of Unity. There cannot be a greater and less in the non-existent: as we predicate Substance of everything in sense, but predicate it also of the Intellectual order and more strictly there- since we hold that the greater and more sovereign substantiality belongs to the Real Beings and that Being is more marked in Substance, even sensible Substance, than in the other Kinds- so, finding unity to exhibit degree of more and less, differing in sense-things as well as in the Intellectual, we must similarly admit that Unity exists under all forms though still by reference, only, to that primal Unity.

As Substance and Real Being, despite the participation of the sensible, are still of the Intellectual and not the sensible order, so too the unity observed present in things of sense by participation remains still an Intellectual and to be grasped by an Intellectual Act. The mind, from a thing present to it, comes to knowledge of something else, a thing not presented; that is, it has a prior knowledge. By this prior knowledge it recognises Being in a particular being; similarly when a thing is one it can affirm unity as it can affirm also duality and multiplicity.

It is impossible to name or conceive anything not making one or two or some number; equally impossible that the thing should not exist without which nothing can possibly be named or conceived; impossible to deny the reality of that whose existence is a necessary condition of naming or affirming anything; what is a first need, universally, to the formation of every concept and every proposition must exist before reasoning and thinking; only as an existent can it be cited to account for the stirring of thought. If Unity is necessary to the substantial existence of all that really is- and nothing exists which is not one- Unity must precede Reality and be its author. It is therefore, an existent Unity, not an existent that develops Unity; considered as Being-with-Unity it would be a manifold, whereas in the pure Unity there is no Being save in so far as Unity attends to producing it. As regards the word "This," it is nat a bare word; it affirms an indicated existence without using the name, it tells of a certain presence, whether a substance or some other existent; any This must be significant; it is no attitude of the mind applying itself to a non-existent; the This shows a thing present, as much as if we used the strict name of the object.

(9) So much for one of the genera- the "Substance," so called, of the Sensible realm.

But what are we to posit as its species? how divide this genus?

The genus as a whole must be identified with body. Bodies may be divided into the characteristically material and the organic: the material bodies comprise fire, earth, water, air; the organic the bodies of plants and animals, these in turn admitting of formal differentiation.

The next step is to find the species of earth and of the other elements, and in the case of organic bodies to distinguish plants according to their forms, and the bodies of animals either by their habitations- on the earth, in the earth, and similarly for the other elements- or else as light, heavy and intermediate. Some bodies, we shall observe, stand in the middle of the universe, others circumscribe it from above, others occupy the middle sphere: in each case we shall find bodies different in shape, so that the bodies of the living beings of the heavens may be differentiated from those of the other elements.

Once we have classified bodies into the four species, we are ready to combine them on a different principle, at the same time intermingling their differences of place, form and constitution; the resultant combinations will be known as fiery or earthy on the basis of the excess or predominance of some one element.

The distinction between First and Second Substances, between Fire and a given example of fire, entails a difference of a peculiar kind- the difference between universal and particular. This however is not a difference characteristic of Substance; there is also in Quality the distinction between whiteness and the white object, between grammar and some particular grammar.

The question may here be asked: "What deficiency has grammar compared with a particular grammar, and science as a whole in comparison with a science?" Grammar is certainly not posterior to the particular grammar: on the contrary, the grammar as in you depends upon the prior existence of grammar as such: the grammar as in you becomes a particular by the fact of being in you; it is otherwise identical with grammar the universal.

Turn to the case of Socrates: it is not Socrates who bestows manhood upon what previously was not Man, but Man upon Socrates; the individual man exists by participation in the universal.

Besides, Socrates is merely a particular instance of Man; this particularity can have no effect whatever in adding to his essential manhood.

We may be told that Man is Form alone, Socrates Form in Matter. But on this very ground Socrates will be less fully Man than the universal; for the Reason-Principle will be less effectual in Matter. If, on the contrary, Man is not determined by Form alone, but presupposes Matter, what deficiency has Man in comparison with the material manifestation of Man, or the Reason-Principle in isolation as compared with its embodiment in a unit of Matter?

Besides, the more general is by nature prior; hence, the Form-Idea is prior to the individual: but what is prior by nature is prior unconditionally. How then can the Form take a lower rank? The individual, it is true, is prior in the sense of being more readily accessible to our cognisance; this fact, however, entails no objective difference.

Moreover, such a difference, if established, would be incompatible with a single Reason-Principle of Substance; First and Second Substance could not have the same Principle, nor be brought under a single genus.

(14) To the argument touching relation we have an answer surely legitimate:

The Unity is not of a nature to lose its own manner of being only because something else stands in a state which it does not itself share; to stray from its unity it must itself suffer division into duality or the still wider plurality.

If by division the one identical mass can become a duality without loss of quantity, clearly the unity it possessed and by this destructive division lost was something distinct. What may be alternatively present and absent to the same subject must be classed among Real-Beings, regardless of position; an accidental elsewhere, it must have reality in itself whether it be manifested in things of sense or in the Intellectual- an accidental in the Laters but self-existent in the higher, especially in the First in its aspect of Unity developing into Being. We may be told that Unity may lose that character without change in itself, becoming duality by association with something else; but this is not true; unity does not become two things; neither the added nor what takes the addition becomes two; each remains the one thing it was; the duality is predicable of the group only, the unity remaining unchanged in each of those unchanged constituents.

Two and the Dyad are not essentially relative: if the only condition to the construction of duality were meeting and association such a relation might perhaps constitute Twoness and Duality; but in fact we see Duality produced by the very opposite process, by the splitting apart of a unity. This shows that duality- or any other such numerical form- is no relation produced either by scission or association. If one configuration produces a certain thing it is impossible that the opposite should produce the same so that the thing may be identified with the relation.

What then is the actual cause?

Unity is due to the presence of Unity; duality to that of Duality; it is precisely as things are white by Whiteness, just by Justice, beautiful by Beauty. Otherwise we must reject these universals and call in relation here also: justice would arise from a certain attitude in a given situation, Beauty from a certain pattern of the person with nothing present able to produce the beauty, nothing coming from without to effect that agreeable appearance.

You see something which you pronounce to be a unity; that thing possesses also size, form, and a host of other characteristics you might name; size, bulk, sweetness, bitterness and other Ideas are actually present in the thing; it surely cannot be thought that, while every conceivable quality has Real-Being, quantity has not and that while continuous quantity exists, discrete quantity does not and this though continuous quantity is measured by the discrete. No: as size by the presence of Magnitude, and Oneness by the presence of Unity, so with Duality and all the other numerical modes.

As to the How of participation, the enquiry is that of all participation in Ideal Forms; we must note, however, that the presence of the Decad in the looser totals is different from its presence in the continuous; there is difference again in its presence within many powers where multiplicity is concentred in unity; arrived at the Intellectuals, there too we discover Number, the Authentic Number, no longer entering the alien, Decad-Absolute not Decad of some particular Intellectual group.

(9) The above considerations- to which others, doubtless, might be added- suffice to show that these five are primary genera. But that they are the only primary genera, that there are no others, how can we be confident of this? Why do we not add unity to them? Quantity? Quality? Relation, and all else included by our various forerunners?

As for unity: If the term is to mean a unity in which nothing else is present, neither Soul nor Intellect nor anything else, this can be predicated of nothing, and therefore cannot be a genus. If it denotes the unity present in Being, in which case we predicate Being of unity, this unity is not primal.

Besides, unity, containing no differences, cannot produce species, and not producing species, cannot be a genus. You cannot so much as divide unity: to divide it would be to make it many. Unity, aspiring to be a genus, becomes a plurality and annuls itself.

Again, you must add to it to divide it into species; for there can be no differentiae in unity as there are in Substance. The mind accepts differences of Being, but differences within unity there cannot be. Every differentia introduces a duality destroying the unity; for the addition of any one thing always does away with the previous quantity.

It may be contended that the unity which is implicit in Being and in Motion is common to all other things, and that therefore Being and unity are inseparable. But we rejected the idea that Being is a genus comprising all things, on the ground that these things are not beings in the sense of the Absolute Being, but beings in another mode: in the same way, we assert, unity is not a genus, the Primary Unity having a character distinct from all other unities.

Admitted that not everything suffices to produce a genus, it may yet be urged that there is an Absolute or Primary Unity corresponding to the other primaries. But if Being and unity are identified, then since Being has already been included among the genera, it is but a name that is introduced in unity: if, however, they are both unity, some principle is implied: if there is anything in addition , unity is predicated of this added thing; if there is nothing added, the reference is again to that unity predicated of nothing. If however the unity referred to is that which accompanies Being, we have already decided that it is not unity in the primary sense.

But is there any reason why this less complete unity should not still possess Primary Being, seeing that even its posterior we rank as Being, and "Being" in the sense of the Primary Being? The reason is that the prior of this Being cannot itself be Being- or else, if the prior is Being, this is not Primary Being: but the prior is unity; .

Furthermore, unity, abstracted from Being, has no differentiae.

Again, even taking it as bound up with Being: If it is a consequent of Being, then it is a consequent of everything, and therefore the latest of things: but the genus takes priority. If it is simultaneous with Being, it is simultaneous with everything: but a genus is not thus simultaneous. If it is prior to Being, it is of the nature of a Principle, and therefore will belong only to Being; but if it serves as Principle to Being, it is not its genus: if it is not genus to Being, it is equally not a genus of anything else; for that would make Being a genus of all other things.

In sum, the unity exhibited in Being on the one hand approximates to Unity-Absolute and on the other tends to identify itself with Being: Being is a unity in relation to the Absolute, is Being by virtue of its sequence upon that Absolute: it is indeed potentially a plurality, and yet it remains a unity and rejecting division refuses thereby to become a genus.

(524) Most true. This was what I meant when I spoke of impressions which invited the intellect, or the reverse—those which are simultaneous with opposite impressions, invite thought; those which are not simultaneous do not. I understand, he said, and agree with you. And to which class do unity and number belong? I do not know, he replied. Think a little and you will see that what has preceded will supply the answer; for if simple unity could be adequately perceived by the sight or by any other sense, then, as we were saying in the case of the finger, there would be nothing to attract towards being; but when there is some contradiction always present, and one is the reverse of one and involves the conception of plurality, then thought begins to be aroused within us, and the soul perplexed and wanting to arrive at a decision asks ‘What is absolute unity?’ This is the way in which the study of the one has a power of drawing and converting the mind to the contemplation of true being. And surely, he said, this occurs notably in the case of one; for we see the same thing to be both one and infinite in multitude? Yes, I said; and this being true of one must be equally true of all number? Certainly. And all arithmetic and calculation have to do with number? Yes.

(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.

(5) As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the divine, unless by a deliberate apostasy.

Bringing itself close to the divine Intellect, becoming, as it were, one with this, it seeks still further: What Being, now, has engendered this God, what is the Simplex preceding this multiple; what the cause at once of its existence and of its existing as a manifold; what the source of this Number, this Quantity?

Number, Quantity, is not primal: obviously before even duality, there must stand the unity.

The Dyad is a secondary; deriving from unity, it finds in unity the determinant needed by its native indetermination: once there is any determination, there is Number, in the sense, of course, of the real Number. And the soul is such a number or quantity. For the Primals are not masses or magnitudes; all of that gross order is later, real only to the sense-thought; even in seed the effective reality is not the moist substance but the unseen- that is to say Number and the Reason-Principle .

Thus by what we call the Number and the Dyad of that higher realm, we mean Reason Principles and the Intellectual-Principle: but while the Dyad is, as regards that sphere, undetermined- representing, as it were, the underly of The One- the later Number - that which rises from the Dyad and The One- is not Matter to the later existents but is their forming-Idea, for all of them take shape, so to speak, from the ideas rising within this. The determination of the Dyad is brought about partly from its object- The One- and partly from itself, as is the case with all vision in the act of sight: intellection is vision occupied upon The One.

(1) We have now explained our conception of Reality and considered how far it agrees with the teaching of Plato. We have still to investigate the opposed principle .

There is the possibility that the genera posited for the Intellectual sphere will suffice for the lower also; possibly with these genera others will be required; again, the two series may differ entirely; or perhaps some of the sensible genera will be identical with their intellectual prototypes, and others different- "identical," however, being understood to mean only analogous and in possession of a common name, as our results will make dear.

We must begin on these lines:

The subject of our discussion is the Sensible realm: Sensible Existence is entirely embraced by what we know as the Universe: our duty, then, would seem to be clear enough- to take this Universe and analyse its nature, classifying its constituent parts and arranging them by species. Suppose that we were making a division of speech: we should reduce its infinity to finite terms, and from the identity appearing in many instances evolve a unity, then another and another, until we arrived at some definite number; each such unit we should call a species if imposed upon individuals, a genus if imposed upon species. Thus, every species of speech- and similarly all phenomena- might be referred to a unity; speech- or element- might be predicated of them all.

This procedure however is as we have already shown, impossible in dealing with the subject of our present enquiry. New genera must be sought for this Universe-genera distinct from those of the Intellectual, inasmuch as this realm is different from that, analogous indeed but never identical, a mere image of the higher. True, it involves the parallel existence of Body and Soul, for the Universe is a living form: essentially however Soul is of the Intellectual and does not enter into the structure of what is called Sensible Being.

Remembering this fact, we must- however great the difficulty- exclude Soul from the present investigation, just as in a census of citizens, taken in the interests of commerce and taxation, we should ignore the alien population. As for the experiences to which Soul is indirectly subject in its conjunction with Body and by reason of Body's presence, their classification must be attempted at a later stage, when we enquire into the details of Sensible Existence.

(2) But are we really obliged to posit the existence of such genera?

Take Substance, for Substance must certainly be our starting-point: what are the grounds for regarding Substance as one single genus?

It has been remarked that Substance cannot be a single entity common to both the Intellectual and the Sensible worlds. We may add that such community would entail the existence of something prior to Intellectual and Sensible Substances alike, something distinct from both as predicated of both; and this prior would be neither body nor unembodied; for it were one or the other, body would be unembodied, or the unembodied would be the body.

This conclusion must not however prevent our seeking in the actual substance of the Sensible world an element held in common by Matter, by Form and by their Composite, all of which are designated as substances, though it is not maintained that they are Substance in an equal degree; Form is usually held to be Substance in a higher degree than Matter, and rightly so, in spite of those who would have Matter to be the more truly real.

There is further the distinction drawn between what are known as First and Second Substances. But what is their common basis, seeing that the First are the source from which the Second derive their right to be called substances?

But, in sum, it is impossible to define Substance: determine its property, and still you have not attained to its essence. Even the definition, "That which, numerically one and the same, is receptive of contraries," will hardly be applicable to all substances alike.

(10) In what sense is the particular manifestation of Being a unity? Clearly, in so far as it is one thing, it forfeits its unity; with "one" and "thing" we have already plurality. No species can be a unity in more than an equivocal sense: a species is a plurality, so that the "unity" here is that of an army or a chorus. The unity of the higher order does not belong to species; unity is, thus, ambiguous, not taking the same form in Being and in particular beings.

It follows that unity is not a genus. For a genus is such that wherever it is affirmed its opposites cannot also be affirmed; anything of which unity and its opposites are alike affirmed- and this implies the whole of Being- cannot have unity as a genus. Consequently unity can be affirmed as a genus neither of the primary genera- since the unity of Being is as much a plurality as a unity, and none of the other genera is a unity to the entire exclusion of plurality- nor of things posterior to Being, for these most certainly are a plurality. In fact, no genus with all its items can be a unity; so that unity to become a genus must forfeit its unity. The unit is prior to number; yet number it must be, if it is to be a genus.

Again, the unit is a unit from the point of view of number: if it is a unit generically, it will not be a unit in the strict sense.

Again, just as the unit, appearing in numbers, not regarded as a genus predicated of them, but is thought of as inherent in them, so also unity, though present in Being, cannot stand as genus to Being or to the other genera or to anything whatever.

Further, as the simplex must be the principle of the non-simplex, though not its genus- for then the non-simplex too would be simplex,- so it stands with unity; if unity is a Principle; it cannot be a genus to its subsequents, and therefore cannot be a genus of Being or of other things. If it is nevertheless to be a genus, everything of which it is a genus must be taken as a unit- a notion which implies the separation of unity from substance: it will not, therefore, be all-embracing. just as Being is not a genus of everything but only of species each of which is a being, so too unity will be a genus of species each of which is a unity. But that raises the question of what difference there is between one thing and another in so far as they are both units, corresponding to the difference between one being and another.

Unity, it may be suggested, is divided in its conjunction with Being and Substance; Being because it is so divided is considered a genus- the one genus manifested in many particulars; why then should not unity be similarly a genus, inasmuch as its manifestations are as many as those of Substance and it is divided into as many particulars?

In the first place, the mere fact that an entity inheres in many things is not enough to make it a genus of those things or of anything else: in a word, a common property need not be a genus. The point inherent in a line is not a genus of lines, or a genus at all; nor again, as we have observed, is the unity latent in numbers a genus either of the numbers or of anything else: genus demands that the common property of diverse objects involve also differences arising out of its own character, that it form species, and that it belong to the essence of the objects. But what differences can there be in unity? What species does it engender? If it produces the same species as we find in connection with Being, it must be identical with Being: only the name will differ, and the term Being may well suffice.

(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.