(9) It follows that in the cases specified above- agent, knowledge and the rest- the relation must be considered as in actual operation, and the Act and the Reason-Principle in the Act must be assumed to be real: in all other cases there will be simply participation in an Ideal-Form, in a Reason-Principle.

If Reality implied embodiment, we should indeed be forced to deny Reality to these conditions called relative; if however we accord the pre-eminent place to the unembodied and to the Reason-Principles, and at the same time maintain that relations are Reason-Principles and participate in Ideal-Forms, we are bound to seek their causes in that higher sphere. Doubleness, it is clear, is the cause of a thing being double, and from it is derived halfness.

Some correlatives owe their designations to the same Form, others to opposite Forms; it is thus that two objects are simultaneously double and half of each other, and one great and the other small. It may happen that both correlatives exist in one object-likeness and unlikeness, and, in general, identity and difference, so that the same thing will be at once like and unlike, identical and different.

The question arises here whether sharing in the same Form could make one man depraved and another more depraved. In the case of total depravity, clearly the two are made equal by the absence of a Form. Where there is a difference of degree, the one has participated in a Form which has failed to predominate, the other in a Form which has failed still more: or, if we choose the negative aspect, we may think of them both as failing to participate in a Form which naturally belonged to them.

Sensation may be regarded as a Form of double origin ; and similarly with knowledge.

Habit is an Act directed upon something had and binding it as it were with the subject having , as the Act of production binds producer and product.

Measurement is an Act of the measurer upon the measured object: it too is therefore a kind of Reason-Principle.

Now if the condition of being related is regarded as a Form having a generic unity, Relation must be allowed to be a single genus owing its reality to a Reason-Principle involved in all instances. If however the Reason-Principles stand opposed and have the differences to which we have referred, there may perhaps not be a single genus, but this will not prevent all relatives being expressed in terms of a certain likeness and falling under a single category.

But even if the cases of which we have spoken can be subsumed under a single head, it is nevertheless impossible to include in a single genus all that goes with them in the one common category: for the category includes negations and derivatives- not only, for example, double but also its negative, the resultant doubleness and the act of doubling. But we cannot include in one genus both the thing and its negative- double and not-double, relative and not-relative- any more than in dealing with the genus animal we can insert in it the nonanimal. Moreover, doubleness and doubling have only the relation to double that whiteness has to white; they cannot be classed as identical with it.

(20) We have to ascertain whether there is not to every quality a contrary. In the case of virtue and vice, even the mean appears to be contrary to the extremes.

But when we turn to colours, we do not find the intermediates so related. If we regard the intermediates as blendings of the extremes, we must not posit any contrariety other than that between black and white, but must show that all other colours are combinations of these two. Contrariety however demands that there be some one distinct quality in the intermediates, though this quality may be seen to arise from a combination.

It may further be suggested that contraries not only differ from each other, but also entail the greatest possible difference. But "the greatest possible difference" would seem to presuppose that intermediates have already been established: eliminate the series, and how will you define "the greatest possible"? Sight, we may be told, will reveal to us that grey is nearer than black to white; and taste may be our judge when we have hot, cold and no intermediate.

That we are accustomed to act upon these assumptions is obvious enough; but the following considerations may perhaps commend themselves:

White and yellow are entirely different from each other- a statement which applies to any colour whatsoever as compared with any other; they are accordingly contrary qualities. Their contrariety is independent of the presence of intermediates: between health and disease no intermediate intrudes, and yet they are contraries.

It may be urged that the products of a contrariety exhibit the greatest diversity. But "the greatest diversity" is clearly meaningless, unless we can point to lower degrees of diversity in the means. Thus, we cannot speak of "the greatest diversity" in reference to health and disease. This definition of contrariety is therefore inadmissible.

Suppose that we say "great diversity" instead of "the greatest": if "great" is equivalent to greater and implies a less, immediate contraries will again escape us; if, on the other hand, we mean strictly "great" and assume that every quality shows a great divergence from every other, we must not suppose that the divergence can be measured by a comparative.

Nonetheless, we must endeavour to find a meaning for the term "contrary." Can we accept the principle that when things have a certain similarity which is not generic nor in any sense due to admixture, but a similarity residing in their forms- if the term be permitted- they differ in degree but are not contraries; contraries being rather those things which have no specific identity? It would be necessary to stipulate that they belong to the same genus, Quality, in order to cover those immediate contraries which have nothing conducing to similarity, inasmuch as there are no intermediates looking both ways, as it were, and having a mutual similarity to each other; some contraries are precluded by their isolation from similarity.

If these observations be sound, colours which have a common ground will not be contraries. But there will be nothing to prevent, not indeed every colour from being contrary to every other, but any one colour from being contrary to any other; and similarly with tastes. This will serve as a statement of the problem.

As for Degree , it was given as our opinion that it exists in the objects participating in Quality, though whether it enters into qualities as such- into health and justice- was left open to question. If indeed these qualities possess an extension quite apart from their participants, we must actually ascribe to them degrees: but in truth they belong to a sphere where each entity is the whole and does not admit of degree.

(8) But we are digressing: we must resume our enquiry into the cause of dissimilarity among relations. Yet we must first be informed what reality, common to all cases, is possessed by this Existence derived from mutual conditions.

Now the common principle in question cannot be a body. The only alternative is that, if it does exist, it be something bodiless, either in the objects thus brought together or outside of them.

Further, if Relation always takes the same form, the term is univocal ; if not, that is if it differs from case to case, the term is equivocal, and the same reality will not necessarily be implied by the mere use of the term Relation.

How then shall we distinguish relations? We may observe that some things have an inactive or dormant relation, with which their actuality is entirely simultaneous; others, combining power and function with their relation, have the relation in some mode always even though the mode be merely that of potentiality, but attain to actual being only in contact with their correlatives. Or perhaps all distinctions may be reduced to that between producer and product, where the product merely gives a name to the producer of its actuality: an example of this is the relation of father to son, though here both producer and product have a sort of actuality, which we call life.

Are we thus, then, to divide Relation, and thereby reject the notion of an identical common element in the different kinds of Relation, making it a universal rule that the relation takes a different character in either correlative? We must in this case recognise that in our distinction between productive and non-productive relations we are overlooking the equivocation involved in making the terms cover both action and passion, as though these two were one, and ignoring the fact that production takes a different form in the two correlatives. Take the case of equality, producing equals: nothing is equal without equality, nothing identical without identity. Greatness and smallness both entail a presence- the presence of greatness and smallness respectively. When we come to greater and smaller, the participants in these relations are greater and smaller only when greatness and smallness are actually observed in them.

(6) In considering Relation we must enquire whether it possesses the community of a genus, or whether it may on other grounds be treated as a unity.

Above all, has Relation- for example, that of right and left, double and half- any actuality? Has it, perhaps, actuality in some cases only, as for instance in what is termed "posterior" but not in what is termed "prior"? Or is its actuality in no case conceivable?

What meaning, then, are we to attach to double and half and all other cases of less and more; to habit and disposition, reclining, sitting, standing; to father, son, master, slave; to like, unlike, equal, unequal; to active and passive, measure and measured; or again to knowledge and sensation, as related respectively to the knowable and the sensible?

Knowledge, indeed, may be supposed to entail in relation to the known object some actual entity corresponding to that object's Ideal Form, and similarly with sensation as related to the sense-object. The active will perform some constant function in relation to the passive, as will the measure in relation to the measured.

But what will emerge from the relation of like to like? Nothing will emerge. Likeness is the inherence of qualitative identity; its entire content is the quality present in the two objects.

From equality, similarly, nothing emerges. The relation merely presupposes the existence of a quantitative identity;- is nothing but our judgement comparing objects essentially independent and concluding, "This and that have the same magnitude, the same quality; this has produced that; this is superior to that."

Again, what meaning can sitting and standing have apart from sitter and stander? The term "habit" either implies a having, in which case it signifies possession, or else it arises from something had, and so denotes quality; and similarly with disposition.

What then in these instances can be the meaning of correlatives apart from our conception of their juxtaposition? "Greater" may refer to very different magnitudes; "different" to all sorts of objects: the comparison is ours; it does not lie in the things themselves.

Right and left, before and behind, would seem to belong less to the category of Relation than to that of Situation. Right means "situated at one point," left means "situated at another." But the right and left are in our conception, nothing of them in the things themselves.

Before and after are merely two times; the relation is again of our making.

(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.

(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?

(12) It follows that we must allow contrariety to Quantity: whenever we speak of great and small, our notions acknowledge this contrariety by evolving opposite images, as also when we refer to many and few; indeed, "few" and "many" call for similar treatment to "small" and "great."

"Many," predicated of the inhabitants of a house, does duty for "more": "few" people are said to be in the theatre instead of "less."

"Many," again, necessarily involves a large numerical plurality. This plurality can scarcely be a relative; it is simply an expansion of number, its contrary being a contraction.

The same applies to the continuous , the notion of which entails prolongation to a distant point.

Quantity, then, appears whenever there is a progression from the unit or the point: if either progression comes to a rapid halt, we have respectively "few" and "small"; if it goes forward and does not quickly cease, "many" and "great."

What, we may be asked, is the limit of this progression? What, we retort, is the limit of beauty, or of heat? Whatever limit you impose, there is always a "hotter"; yet "hotter" is accounted a relative, "hot" a pure quality.

In sum, just as there is a Reason-Principle of Beauty, so there must be a Reason-Principle of greatness, participation in which makes a thing great, as the Principle of beauty makes it beautiful.

To judge from these instances, there is contrariety in Quantity. Place we may neglect as not strictly coming under the category of Quantity; if it were admitted, "above" could only be a contrary if there were something in the universe which was "below": as referring to the partial, the terms "above" and "below" are used in a purely relative sense, and must go with "right" and "left" into the category of Relation.

Syllable and discourse are only indirectly quantities or substrates of Quantity; it is voice that is quantitative: but voice is a kind of Motion; it must accordingly in any case be referred to Motion, as must activity also.

(11) Passing to Quantity and the quantum, we have to consider the view which identifies them with number and magnitude on the ground that everything quantitative is numbered among Sensible things or rated by the extension of its substrate: we are here, of course, discussing not Quantity in isolation, but that which causes a piece of wood to be three yards long and gives the five in "five horses,"

Now we have often maintained that number and magnitude are to be regarded as the only true quantities, and that Space and Time have no right to be conceived as quantitative: Time as the measure of Motion should be assigned to Relation, while Space, being that which circumscribes Body, is also a relative and falls under the same category; though continuous, it is, like Motion, not included in Quantity.

On the other hand, why do we not find in the category of Quantity "great" and "small"? It is some kind of Quantity which gives greatness to the great; greatness is not a relative, though greater and smaller are relatives, since these, like doubleness, imply an external correlative.

What is it, then, which makes a mountain small and a grain of millet large? Surely, in the first place, "small" is equivalent to "smaller." It is admitted that the term is applied only to things of the same kind, and from this admission we may infer that the mountain is "smaller" rather than "small," and that the grain of millet is not large in any absolute sense but large for a grain of millet. In other words, since the comparison is between things of the same kind, the natural predicate would be a comparative.

Again, why is not beauty classed as a relative? Beauty, unlike greatness, we regard as absolute and as a quality; "more beautiful" is the relative. Yet even the term "beautiful" may be attached to something which in a given relation may appear ugly: the beauty of man, for example, is ugliness when compared with that of the gods; "the most beautiful of monkeys," we may quote, "is ugly in comparison with any other type." Nonetheless, a thing is beautiful in itself; as related to something else it is either more or less beautiful.

Similarly, an object is great in itself, and its greatness is due, not to any external, but to its own participation in the Absolute Great.

Are we actually to eliminate the beautiful on the pretext that there is a more beautiful? No more then must we eliminate the great because of the greater: the greater can obviously have no existence whatever apart from the great, just as the more beautiful can have no existence without the beautiful.

(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.

(15) How far is it true that equality and inequality are characteristic of Quantity?

Triangles, it is significant, are said to be similar rather than equal. But we also refer to magnitudes as similar, and the accepted connotation of similarity does not exclude similarity or dissimilarity in Quantity. It may, of course, be the case that the term "similarity" has a different sense here from that understood in reference to Quality.

Furthermore, if we are told that equality and inequality are characteristic of Quantity, that is not to deny that similarity also may be predicated of certain quantities. If, on the contrary, similarity and dissimilarity are to be confined to Quality, the terms as applied to Quantity must, as we have said, bear a different meaning.

But suppose similarity to be identical in both genera; Quantity and Quality must then be expected to reveal other properties held in common.

May the truth be this: that similarity is predicable of Quantity only in so far as Quantity possesses differences? But as a general rule differences are grouped with that of which they are differences, especially when the difference is a difference of that thing alone. If in one case the difference completes the substance and not in another, we inevitably class it with that which it completes, and only consider it as independent when it is not complementary: when we say "completes the substance," we refer not to Subtance as such but to the differentiated substance; the particular object is to be thought of as receiving an accession which is non-substantial.

We must not however fad to observe that we predicate equality of triangles, rectangles, and figures generally, whether plane or solid: this may be given as a ground for regarding equality and inequality as characteristic of Quantity.

It remains to enquire whether similarity and dissimilarity are characteristic of Quality.

We have spoken of Quality as combining with other entities, Matter and Quantity, to form the complete Sensible Substance; this Substance, so called, may be supposed to constitute the manifold world of Sense, which is not so much an essence as a quale. Thus, for the essence of fire we must look to the Reason-Principle; what produces the visible aspect is, properly speaking, a quale.

Man's essence will lie in his Reason-Principle; that which is perfected in the corporeal nature is a mere image of the Reason-Principle a quale rather than an essence.

Consider: the visible Socrates is a man, yet we give the name of Socrates to that likeness of him in a portrait, which consists of mere colours, mere pigments: similarly, it is a Reason-Principle which constitutes Socrates, but we apply the name Socrates to the Socrates we see: in truth, however, the colours and shapes which make up the visible Socrates are but reproductions of those in the Reason-Principle, while this Reason-Principle itself bears a corresponding relation to the truest Reason-Principle of Man. But we need not elaborate this point.

(9) Ruling, then, over himself and what belongs to him, and possessing a sure grasp, of divine science, he makes a genuine approach to the truth. For the knowledge and apprehension of intellectual objects must necessarily be called certain scientific knowledge, whose function in reference to divine things is to consider what is the First Cause, and what that "by whom all things were made, and without whom nothing was made; " and what things, on the other hand, are as pervasive, and what is comprehensive; what conjoined, what disjoined; and what is the position which each one of them holds, and what power and what service each contributes. And again. among human things, what man himself is, and what he has naturally or preternaturally; and how, again, it becomes him to do or to suffer; and what are his virtues and what his vices; and about things good, bad, and indifferent; also about fortitude, and prudence, and self-restraint, and the virtue which is in all respects complete, namely, righteousness.

(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.

(1) If, however, it be necessary, dismissing these particulars, to speak what appears to me to be the truth, you do not rightly infer “ that a knowledge of this mathematical science cannot be obtained, because there is much dissonance concerning it, or because Chæremon, or some other, has written against it .” For if this reason were admitted, all things will be incomprehensible. For all sciences have ten thousand controvertists, and the doubts with which they are attended are innumerable. As, therefore, we are accustomed to say in opposition to the contentious, that contraries in things that are true are naturally discordant, and that it is not falsities alone that are hostile to each other; thus, also, we say respecting this mathematical science, that it is indeed true; but that those who wander from the scope of it, being ignorant of the truth, contradict it. This, however happens not in this science alone, but likewise in all the sciences, which are imparted by the Gods to men.

(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.

(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.