(14) For I must needs say that their scheme of formulation is my master; from it I have the first elements of my knowledge, and it is not my purpose to controvert or amend their formulae (for I cannot do it, neither have I learned them), but rather leave them where they are.

(13) Through this, the inherent character, distinctive marks and conditions of being and powers, according to their development, are made clear.

(122) O no: But I must write in part or by pieces, for the Reader's better understanding, that he might thereby apprehend somewhat, and so attain the sense and meaning thereof.

(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.

(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.

(12) If then we do not propose to divide Quality in this manner, what basis of division have we?

We must examine whether qualities may not prove to be divisible on the principle that some belong to the body and others to the soul. Those of the body would be subdivided according to the senses, some being attributed to sight, others to hearing and taste, others to smell and touch. Those of the soul would presumably be allotted to appetite, emotion, reason; though, again, they may be distinguished by the differences of the activities they condition, in so far as activities are engendered by these qualities; or according as they are beneficial or injurious, the benefits and injuries being duly classified. This last is applicable also to the classification of bodily qualities, which also produce differences of benefit and injury: these differences must be regarded as distinctively qualitative; for either the benefit and injury are held to be derived from Quality and the quale, or else some other explanation must be found for them.

A point for consideration is how the quale, as conditioned by Quality, can belong to the same category: obviously there can be no single genus embracing both.

Further, if "boxer" is in the category of Quality, why not "agent" as well? And with agent goes "active." Thus "active" need not go into the category of Relation; nor again need "passive," if "patient" is a quale. Moreover, agent" is perhaps better assigned to the category of Quality for the reason that the term implies power, and power is Quality. But if power as such were determined by Substance , the agent, though ceasing to be a quale, would not necessarily become a relative. Besides, "active" is not like "greater": the greater, to be the greater, demands a less, whereas "active" stands complete by the mere possession of its specific character.

It may however be urged that while the possession of that character makes it a quale, it is a relative in so far as it directs upon an external object the power indicated by its name. Why, then, is not "boxer" a relative, and "boxing" as well? Boxing is entirely related to an external object; its whole theory pre-supposes this external. And in the case of the other arts- or most of them- investigation would probably warrant the assertion that in so far as they affect the soul they are qualities, while in so far as they look outward they are active and as being directed to an external object are relatives. They are relatives in the other sense also that they are thought of as habits.

Can it then be held that there is any distinct reality implied in activity, seeing that the active is something distinct only according as it is a quale? It may perhaps be held that the tendency towards action of living beings, and especially of those having freewill, implies a reality of activity .

But what is the function of the active in connection with those non-living powers which we have classed as qualities? Doubtless to recruit any object it encounters, making the object a participant in its content.

But if one same object both acts and is acted upon, how do we then explain the active? Observe also that the greater- in itself perhaps a fixed three yards' length- will present itself as both greater and less according to its external contacts.

It will be objected that greater and less are due to participation in greatness and smallness; and it might be inferred that a thing is active or passive by participation in activity or passivity.

This is the place for enquiring also whether the qualities of the Sensible and Intellectual realms can be included under one head- a question intended only for those who ascribe qualities to the higher realm as well as the lower. And even if Ideal Forms of qualities are not posited, yet once the term "habit" is used in reference to Intellect, the question arises whether there is anything common to that habit and the habit we know in the lower.

Wisdom too is generally admitted to exist There. Obviously, if it shares only its name with our wisdom, it is not to be reckoned among things of this sphere; if, however, the import is in both cases the same, then Quality is common to both realms- unless, of course, it be maintained that everything There, including even intellection, is Substance.

This question, however, applies to all the categories: are the two spheres irreconcilable, or can they be co-ordinated with a unity?

(2) In the first place, therefore, we shall divide the genera of the proposed problems, in order that we may know the quantity and quality of them. And, in the next place, we shall show from what theologies the doubts are assumed, and according to what sciences they are investigated. For some things that are badly confused, require a certain distinction; others are conversant with the cause through which they subsist, and are apprehended; others, which we propose according to a certain contrariety, draw our decision on both sides; and some things require from us the whole development of mystic doctrines. Such, therefore, being the nature of the subjects of discussion, they are assumed from many places, and from different sciences. For some things introduce animadversions from what the wise men of the Chaldeans have delivered; others produce objections from what the prophets of the Egyptians teach; and there are some that, adhering to the theory of philosophers, make inquiries conformably to them. There are now likewise some, that from other opinions, which do not deserve to be mentioned, elicite a certain dubitation; and others originate from the common conceptions of mankind. These things, therefore, are of themselves variously disposed, and are multiformly connected with each other. Hence, through all these causes, a certain discussion is requisite for the management of them in a becoming manner.

(9) the Pure intelligence so called because it purifies the Numerations, it proves and corrects the designing of their representation, and disposes their unity with which they are combined without diminution or division.

(42) In case the opposite of a thing is not known to us, because it has not as yet been discovered by or made known to us, nevertheless in such case we are fully justified in ascribing to the unknown opposite the qualities and characteristics diametrically opposed to the known opposite. The rule is this: "Whatever is affirmed of one of a pair of opposites must be denied to the other"; and " whatever is denied to the one, must be affirmed of the other." So true and infallible is this rule that it may be applied and employed as the basis of logical reasoning from the known to the unknown, for the purpose of discovering the latter.

(7) Now if we do not mean anything by Relation but are victims of words, none of the relations mentioned can exist: Relation will be a notion void of content.

Suppose however that we do possess ourselves of objective truth when in comparing two points of time we pronounce one prior, or posterior, to the other, that priority does entail something distinct from the objects to which it refers; admit an objective truth behind the relation of left and right: does this apply also to magnitudes, and is the relation exhibiting excess and deficiency also something distinct from the quantities involved?

Now one thing is double of another quite apart from our speech or thought; one thing possesses and another is possessed before we notice the fact; equals do not await our comparison but- and this applies to Quality as well as Quantity- rest upon an identity existing between the objects compared: in all the conditions in which we assert Relation the mutual relation exists over and above the objects; we perceive it as already existent; our knowledge is directed upon a thing, there to be known- a clear testimony to the reality of Relation.

In these circumstances we can no longer put the question of its existence. We have simply to distinguish: sometimes the relation subsists while the objects remain unaltered and even apart; sometimes it depends upon their combination; sometimes, while they remain unchanged, the relation utterly ceases, or, as happens with right and near, becomes different. These are the facts which chiefly account for the notion that Relation has no reality in such circumstances.

Our task, thus, is to give full value to this elusive character of Relation, and, then to enquire what there is that is constant in all these particular cases and whether this constant is generic or accidental; and having found this constant, we must discover what sort of actuality it possesses.

It need hardly be said that we are not to affirm Relation where one thing is simply an attribute of another, as a habit is an attribute of a soul or of a body; it is not Relation when a soul belongs to this individual or dwells in that body. Relation enters only when the actuality of the relationships is derived from no other source than Relation itself; the actuality must be, not that which is characteristic of the substances in question, but that which is specifically called relative. Thus double with its correlative, half gives actuality neither to two yards' length or the number two, nor to one yard's length or the number one; what happens is that, when these quantities are viewed in their relation, they are found to be not merely two and one respectively, but to produce the assertion and to exhibit the fact of standing one to the other in the condition of double and half. Out of the objects in a certain conjunction this condition of being double and half has issued as something distinct from either; double and half have emerged as correlatives, and their being is precisely this of mutual dependence; the double exists by its superiority over the half, and the half by its inferiority; there is no priority to distinguish double from half; they arise simultaneously.

It is another question whether they endure simultaneously. Take the case of father and son, and such relationships; the father dies, but the other is still his son, and so with brothers. Moreover, we see likeness where one of the like people is dead.

(6) "If we say that something exists or does not exist, in deference to the function it fulfils or does not fulfil, then there is nothing which does not exist, nothing which does exist. To know that east and west are convertible and yet necessary terms,—this is the due adjustment of functions. "If we say that anything is good or evil because it is either good or evil in our eyes, then there is nothing which is not good, nothing which is not evil. To know that Yao and Chieh were both good and both evil from their opposite points of view,—this is the expression of a standard. "Of old Yao abdicated in favour of Shun, and the latter ruled. Kuei abdicated in favour of Chih, and the latter failed. T'ang and Wu got the empire by fighting. By fighting, Poh Kung lost it. From which it may be seen that the rationale of abdicating or fighting, of acting like Yao or like Chieh, must be determined according to the opportunity, and may not be regarded as a constant quantity. "A battering-ram can knock down a wall, but it cannot repair the breach. Different things are differently applied. "Ch'ih-Chi and Hua Liu could travel 1,000 li in one day, but for catching rats they were not equal to a wild cat. Different animals possess different aptitudes.

(28) We have already indicated that Activity and Passivity are to be regarded as motions, and that it is possible to distinguish absolute motions, actions, passions.

As for the remaining so-called genera, we have shown that they are reducible to those which we have posited.

With regard to the relative, we have maintained that Relation belongs to one object as compared with another, that the two objects coexist simultaneously, and that Relation is found wherever a substance is in such a condition as to produce it; not that the substance is a relative, except in so far as it constitutes part of a whole- a hand, for example, or head or cause or principle or element.

We may also adopt the ancient division of relatives into creative principles, measures, excesses and deficiencies, and those which in general separate objects on the basis of similarities and differences.

Our investigation into the kinds of Being is now complete.

(1) Philosophy at a very early stage investigated the number and character of the Existents. Various theories resulted: some declared for one Existent, others for a finite number, others again for an infinite number, while as regards the nature of the Existents- one, numerically finite, or numerically infinite- there was a similar disagreement. These theories, in so far as they have been adequately examined by later workers, may be passed over here; our attention must be directed upon the results of those whose examination has led them to posit on their awn account certain well-defined genera.

These thinkers rejected pure unity on the ground of the plurality observed even in the Intellectual world; they rejected an infinite number as not reconcilable with the facts and as defying knowledge: considering the foundations of being to be "genera" rather than elements strictly so called, they concluded for a finite number. Of these "genera" some found ten, others less, others no doubt more.

But here again there is a divergence of views. To some the genera are first-principles; to others they indicate only a generic classification of the Existents themselves.

Let us begin with the well-known tenfold division of the Existents, and consider whether we are to understand ten genera ranged under the common name of Being, or ten categories. That the term Being has not the same sense in all ten is rightly maintained.

But a graver problem confronts us at the outset: Are the ten found alike in the Intellectual and in the Sensible realms? Or are all found in the Sensible and some only in the Intellectual? All in the Intellectual and some in the Sensible is manifestly impossible.

At this point it would be natural to investigate which of the ten belong to both spheres, and whether the Existents of the Intellectual are to be ranged under one and the same genus with the Existents in the Sensible, or whether the term "Existence" is equivocal as applied to both realms. If the equivocation exists, the number of genera will be increased: if there is no equivocation, it is strange to find the one same "Existence" applying to the primary and to the derivative Existents when there is no common genus embracing both primal and secondary.

These thinkers are however not considering the Intellectual realm in their division, which was not intended to cover all the Existents; the Supreme they overlooked.

(21) The claim of Motion to be established as a genus will depend upon three conditions: first, that it cannot rightly be referred to any other genus; second, that nothing higher than itself can be predicated of it in respect of its essence; third, that by assuming differences it will produce species. These conditions satisfied, we may consider the nature of the genus to which we shall refer it.

Clearly it cannot be identified with either the Substance or the Quality of the things which possess it. It cannot, further, be consigned to Action, for Passivity also comprises a variety of motions; nor again to Passivity itself, because many motions are actions: on the contrary, actions and passions are to be referred to Motion.

Furthermore, it cannot lay claim to the category of Relation on the mere ground that it has an attributive and not a self-centred existence: on this ground, Quality too would find itself in that same category; for Quality is an attribute and contained in an external: and the same is true of Quantity.

If we are agreed that Quality and Quantity, though attributive, are real entities, and on the basis of this reality distinguishable as Quality and Quantity respectively: then, on the same principle, since Motion, though an attribute has a reality prior to its attribution, it is incumbent upon us to discover the intrinsic nature of this reality. We must never be content to regard as a relative something which exists prior to its attribution, but only that which is engendered by Relation and has no existence apart from the relation to which it owes its name: the double, strictly so called, takes birth and actuality in juxtaposition with a yard's length, and by this very process of being juxtaposed with a correlative acquires the name and exhibits the fact of being double.

What, then, is that entity, called Motion, which, though attributive, has an independent reality, which makes its attribution possible- the entity corresponding to Quality, Quantity and Substance?

But first, perhaps, we should make sure that there is nothing prior to Motion and predicated of it as its genus.

Change may be suggested as a prior. But, in the first place, either it is identical with Motion, or else, if change be claimed as a genus, it will stand distinct from the genera so far considered: secondly, Motion will evidently take rank as a species and have some other species opposed to it- becoming, say- which will be regarded as a change but not as a motion.

What, then, is the ground for denying that becoming is a motion? The fact, perhaps, that what comes to be does not yet exist, whereas Motion has no dealings with the non-existent. But, on that ground, becoming will not be a change either. If however it be alleged that becoming is merely a type of alteration or growth since it takes place when things alter and grow, the antecedents of becoming are being confused with becoming itself. Yet becoming, entailing as it does these antecedents, must necessarily be a distinct species; for the event and process of becoming cannot be identified with merely passive alteration, like turning hot or white: it is possible for the antecedents to take place without becoming as such being accomplished, except in so far as the actual alteration has "come to be"; where, however, an animal or a vegetal life is concerned, becoming takes place only upon its acquisition of a Form.

The contrary might be maintained: that change is more plausibly ranked as a species than is Motion, because change signifies merely the substitution of one thing for another, whereas Motion involves also the removal of a thing from the place to which it belongs, as is shown by locomotion. Even rejecting this distinction, we must accept as types of Motion knowledge and musical performance- in short, changes of condition: thus, alteration will come to be regarded as a species of Motion- namely, motion displacing.

(511) they start from hypotheses and do not ascend to a principle, those who contemplate them appear to you not to exercise the higher reason upon them, although when a first principle is added to them they are cognizable by the higher reason. And the habit which is concerned with geometry and the cognate sciences I suppose that you would term understanding and not reason, as being intermediate between opinion and reason. You have quite conceived my meaning, I said; and now, corresponding to these four divisions, let there be four faculties in the soul—reason answering to the highest, understanding to the second, faith (or conviction) to the third, and perception of shadows to the last—and let there be a scale of them, and let us suppose that the several faculties have clearness in the same degree that their objects have truth. I understand, he replied, and give my assent, and accept your arrangement.

(18) These problems at any rate all serve to show that, while in general it is necessary to look for differences by which to separate things from each other, to hunt for differences of the differences themselves is both futile and irrational. We cannot have substances of substances, quantities of quantities, qualities of qualities, differences of differences; differences must, where possible, be found outside the genus, in creative powers and the like: but where no such criteria are present, as in distinguishing dark-green from pale-green, both being regarded as derived from white and black, what expedient may be suggested?

Sense-perception and intelligence may be trusted to indicate diversity but not to explain it: explanation is outside the province of sense-perception, whose function is merely to produce a variety of information; while, as for intelligence, it works exclusively with intuitions and never resorts to explanations to justify them; there is in the movements of intelligence a diversity which separates one object from another, making further differentiation unnecessary.

Do all qualities constitute differentiae, or not? Granted that whiteness and colours in general and the qualities dependent upon touch and taste can, even while they remain species , become differentiae of other things, how can grammar and music serve as differentiae? Perhaps in the sense that minds may be distinguished as grammatical and musical, especially if the qualities are innate, in which case they do become specific differentiae.

It remains to decide whether there can be any differentia derived from the genus to which the differentiated thing belongs, or whether it must of necessity belong to another genus? The former alternative would produce differentiae of things derived from the same genus as the differentiae themselves- for example, qualities of qualities. Virtue and vice are two states differing in quality: the states are qualities, and their differentiae qualities- unless indeed it be maintained that the state undifferentiated is not a quality, that the differentia creates the quality.

But consider the sweet as beneficial, the bitter as injurious: then bitter and sweet are distinguished, not by Quality, but by Relation. We might also be disposed to identify the sweet with the thick, and the Pungent with the thin: "thick" however hardly reveals the essence but merely the cause of sweetness- an argument which applies equally to pungency.

We must therefore reflect whether it may be taken as an invariable rule that Quality is never a differentia of Quality, any more than Substance is a differentia of Substance, or Quantity of Quantity.

Surely, it may be interposed, five differs from three by two. No: it exceeds it by two; we do not say that it differs: how could it differ by a "two" in the "three"? We may add that neither can Motion differ from Motion by Motion. There is, in short, no parallel in any of the other genera.

In the case of virtue and vice, whole must be compared with whole, and the differentiation conducted on this basis. As for the differentia being derived from the same genus as themselves, namely, Quality, and from no other genus, if we proceed on the principle that virtue is bound up with pleasure, vice with lust, virtue again with the acquisition of food, vice with idle extravagance, and accept these definitions as satisfactory, then clearly we have, here too, differentiae which are not qualities.

(13) These properties, whether manifest or latent, are of the nature of the Three Potencies.

(25) There are those who lay down four categories and make a fourfold division into Substrates, Qualities, States, and Relative States, and find in these a common Something, and so include everything in one genus.

Against this theory there is much to be urged, but particularly against this posing of a common Something and a single all-embracing genus. This Something, it may be submitted, is unintelligible to themselves, is indefinable, and does not account either for bodies or for the bodiless. Moreover, no room is left for a differentia by which this Something may be distinguished. Besides, this common Something is either existent or non-existent: if existent, it must be one or other of its species;- if non-existent, the existent is classed under the non-existent. But the objections are countless; we must leave them for the present and consider the several heads of the division.

To the first genus are assigned Substrates, including Matter, to which is given a priority over the others; so that what is ranked as the first principle comes under the same head with things which must be posterior to it since it is their principle.

First, then: the prior is made homogeneous with the subsequent. Now this is impossible: in this relation the subsequent owes its existence to the prior, whereas among things belonging to one same genus each must have, essentially, the equality implied by the genus; for the very meaning of genus is to be predicated of the species in respect of their essential character. And that Matter is the basic source of all the rest of things, this school, we may suppose, would hardly deny.

Secondly: since they treat the Substrate as one thing, they do not enumerate the Existents; they look instead for principles of the Existents. There is however a difference between speaking of the actual Existents and of their principles.

If Matter is taken to be the only Existent, and all other things as modifications of Matter, it is not legitimate to set up a single genus to embrace both the Existent and the other things; consistency requires that Being be distinguished from its modifications and that these modifications be duly classified.

Even the distinction which this theory makes between Substrates and the rest of things is questionable. The Substrate is one thing and admits of no differentia- except perhaps in so far as it is split up like one mass into its various parts; and yet not even so, since the notion of Being implies continuity: it would be better, therefore, to speak of the Substrate, in the singular.

(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.

(32) Thereafter comes the completion of the series of transformations of the three nature potencies, since their purpose is attained.