1. We have now explained our conception of Reality [True Being] and considered how far it agrees with the teaching of Plato. We have still to investigate the opposed principle [the principle of Becoming].

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

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

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

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

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

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

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

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

This mode of division must accordingly be abandoned.

3. How then do we go to work?

Let us begin by distinguishing Matter, Form, the Mixture of both, and the Attributes of the Mixture. The Attributes may be subdivided into those which are mere predicates, and those serving also as accidents. The accidents may be either inclusive or included; they may, further, be classified as activities, experiences, consequents.

Matter will be found common to all substances, not however as a genus, since it has no differentiae -- unless indeed differentiae be ascribed to it on the ground of its taking such various forms as fire and air.

It may be held that Matter is sufficiently constituted a genus by the fact that the things in which it appears hold it in common, or in that it presents itself as a whole of parts. In this sense Matter will indeed be a genus, though not in the accepted sense of the term. Matter, we may remark, is also a single element, if the element as such is able to constitute a genus.

Further, if to a Form be added the qualification "bound up with, involved in Matter," Matter separates that Form from other Forms: it does not however embrace the whole of Substantial Form [as, to be the genus of Form, it must].

We may, again, regard Form as the creator of Substance and make the Reason-Principle of Substance dependent upon Form: yet we do not come thereby to an understanding of the nature of Substance.

We may, also, restrict Substance to the Composite. Matter and Form then cease to be substances. If they are Substance equally with the Composite, it remains to enquire what there is common to all three.

The "mere predicates" fall under the category of Relation: such are cause and element. The accidents included in the composite substances ire found to be either Quality or Quantity; those which are inclusive are of the nature of Space and Time. Activities and experiences comprise Motions; consequents Space and Time, which are consequents respectively of the Composites and of Motion.

The first three entities [Matter, Form, Composite] go, as we have discovered, to make a single common genus, the Sensible counterpart of Substance. Then follow in order Relation, Quantity, Quality, Time-during-which, Place-in-which, Motion; though, with Time and Space already included [under Relation], Time-during-which and Place-in-which become superfluous.

Thus we have five genera, counting the first three entities as one. If the first three are not massed into a unity, the series will be Matter, Form, Composite, Relation, Quantity, Quality, Motion. The last three may, again, be included in Relation, which is capable of bearing this wider extension.

4. What, then, we have to ask, is the constant element in the first three entities? What is it that identifies them with their inherent Substance?

Is it the capacity to serve as a base? But Matter, we maintain, serves as the base and seat of Form: Form, thus, will be excluded from the category of Substance. Again, the Composite is the base and seat of attributes: hence, Form combined with Matter will be the basic ground of Composites, or at any rate of all posteriors of the Composite -- Quantity, Quality, Motion, and the rest.

But perhaps we may think Substance validly defined as that which is not predicated of anything else. White and black are predicated of an object having one or other of these qualities; double presupposes something distinct from itself -- we refer not to the half, but to the length of wood of which doubleness is affirmed. father qua father is a predicate; knowledge is predicated of the subject in whom the knowledge exists; space is the limit of something, time the measure of something. Fire, on the other hand, is predicated of nothing; wood as such is predicated of nothing; and so with man, Socrates, and the composite substance in general.

Equally the Substantial Form is never a predicate, since it never acts as a modification of anything. Form is not an attribute of Matter hence, is not predicable of Matter it is simply a constituent of the Couplement. On the other hand, the Form of a man is not different from the man himself [and so does not "modify" the Couplement].

Matter, similarly, is part of a whole, and belongs to something else only as to a whole and not as to a separate thing of which it is predicated. White, on the contrary, essentially belongs to something distinct from itself.

We conclude that nothing belonging to something else and predicated of it can be Substance. Substance is that which belongs essentially to itself, or, in so far as it is a part of the differentiated object, serves only to complete the Composite. Each or either part of the Composite belongs to itself, and is only affirmed of the Composite in a special sense: only qua part of the whole is it predicated of something else; qua individual it is never in its essential nature predicated of an external.

It may be claimed as a common element in Matter, Form and the Couplement that they are all substrates. But the mode in which Matter is the substrate of Form is different from that in which Form and the Couplement are substrates of their modifications.

And is it strictly true to say that Matter is the substrate of Form? Form is rather the completion which Matter's nature as pure potentiality demands.

Moreover, Form cannot be said to reside in Matter [as in a substrate]. When one thing combines with another to form a unity, the one does not reside in the other; both alike are substrates of a third: thus, Man [the Form] and a man [the Composite] are substrates of their experiences, and are prior to their activities and consequents.

Substance, then, is that from which all other things proceed and to which they owe their existence; it is the centre of passivity and the source of action.

5. These are incontrovertible facts in regard to the pseudo-substance of the Sensible realm: if they apply also in some degree to the True Substance of the Intellectual, the coincidence is, doubtless, to be attributed to analogy and ambiguity of terms.

We are aware that "the first" is so called only in relation to the things which come after it: "first" has no absolute significance; the first of one series is subsequent to the last of another. "Substrate," similarly, varies in meaning [as applied to the higher and to the lower], while as for passivity its very existence in the Intellectual is questionable; if it does exist there, it is not the passivity of the Sensible.

It follows that the fact of "not being present in a subject [or substrate] is not universally true of Substance, unless presence in a subject be stipulated as not including the case of the part present in the whole or of one thing combining with another to form a distinct unity; a thing will not be present as in a subject in that with which it co-operates in the information of a composite substance. Form, therefore, is not present in Matter as in a subject, nor is Man so present in Socrates, since Man is part of Socrates.

Substance, then, is that which is not present in a subject. But if we adopt the definition "neither present in a subject nor predicated of a subject," we must add to the second "subject" the qualification "distinct," in order that we may not exclude the case of Man predicated of a particular man. When I predicate Man of Socrates, it is as though I affirmed, not that a piece of wood is white, but that whiteness is white; for in asserting that Socrates is a man, I predicate Man [the universal] of a particular man, I affirm Man of the manhood in Socrates; I am really saying only that Socrates is Socrates, or that this particular rational animal is an animal.

It may be objected that non-presence in a subject is not peculiar to Substance, inasmuch as the differentia of a substance is no more present in a subject than the substance itself; but this objection results from taking a part of the whole substance, such as "two-footed" in our example, and asserting that this part is not present in a subject: if we take, not "two-footed" which is merely an aspect of Substance, but "two-footedness" by which we signify not Substance but Quality, we shall find that this "two-footedness" is indeed present in a subject.

We may be told that neither Time nor Place is present in a subject. But if the definition of Time as the measure of Motion be regarded as denoting something measured, the "measure" will be present in Motion as in a subject, while Motion will be present in the moved: if, on the contrary, it be supposed to signify a principle of measurement, the "measure" will be present in the measurer.

Place is the limit of the surrounding space, and thus is present in that space.

The truth is, however, that the "Substance" of our enquiry may be apprehended in directly opposite ways: it may be determined by one of the properties we have been discussing, by more than one, by all at once, according as they answer to the notions of Matter, Form and the Couplement.

6. Granted, it may be urged, that these observations upon the nature of Substance are sound, we have not yet arrived at a statement of its essence. Our critic doubtless expects to see this "Sensible": but its essence, its characteristic being, cannot be seen.

Do we infer that fire and water are not Substance? They certainly are not Substance because they are visible. Why, then? Because they possess Matter? No. Or Form? No. Nor because they involve a Couplement of Matter and Form. Then why are they Substance? By existing. But does not Quantity exist, and Quality? This anomaly is to be explained by an equivocation in the term "existence."

What, then, is the meaning of "existence" as applied to fire, earth and the other elements? What is the difference between this existence and existence in the other categories? It is the difference between being simply -- that which merely is -- and being white. But surely the being qualified by "white" is the same as that having no qualification? It is not the same: the latter is Being in the primary sense, the former is Being only by participation and in a secondary degree. Whiteness added to Being produces a being white; Being added to whiteness produces a white being: thus, whiteness becomes an accident of Being, and Being an accident of whiteness.

The case is not equivalent to predicating white of Socrates and Socrates of white: for Socrates remains the same, though white would appear to have a different meaning in the two propositions, since in predicating Socrates of white we include Socrates in the [whole] sphere of whiteness, whereas in the proposition "Socrates is white" whiteness is plainly an attribute of Socrates.

"Being is white" implies, similarly, that Being possesses whiteness as an attribute, while in the proposition "whiteness is Being [or, is a being]" Being is regarded as comprising whiteness in its own extension.

In sum, whiteness has existence because it is bound up with Being and present in it: Being is, thus, the source of its existence. Being is Being on its own account, but the white is due to whiteness -- not because it is "present in" whiteness, but because whiteness is present in it.

The Being of the Sensible resembles the white in not originating in itself. It must therefore be regarded as dependent for its being upon the Authentic Being, as white is dependent upon the Authentic Whiteness, and the Authentic Whiteness dependent for its whiteness upon participation in that Supreme Being whose existence is underived.

7. But Matter, it may be contended, is the source of existence to the Sensible things implanted in it. From what source, then, we retort, does Matter itself derive existence and being?

That Matter is not a Primary we have established elsewhere. If it be urged that other things can have no subsistence without being implanted in Matter, we admit the claim for Sensible things. But though Matter be prior to these, it is not thereby precluded from being posterior to many things-posterior, in fact, to all the beings of the Intellectual sphere. Its existence is but a pale reflection, and less complete than that of the things implanted in it. These are Reason-Principles and more directly derived from Being: Matter has of itself no Reason-Principle whatever; it is but a shadow of a Principle, a vain attempt to achieve a Principle.

But, our critic may pursue, Matter gives existence to the things implanted in it, just as Socrates gives existence to the whiteness implanted in himself? We reply that the higher being gives existence to the lower, the lower to the higher never.

But once concede that Form is higher in the scale of Being than Matter, and Matter can no longer be regarded as a common ground of both, nor Substance as a genus embracing Matter, Form and the Couplement. True, these will have many common properties, to which we have already referred, but their being [or existence] will nonetheless be different. When a higher being comes into contact with a lower, the lower, though first in the natural order, is yet posterior in the scale of Reality: consequently, if Being does not belong in equal degrees to Matter, to Form and to the Couplement, Substance can no longer be common to all three in the sense of being their genus: to their posteriors it will bear a still different relation, serving them as a common base by being bound up with all alike. Substance, thus, resembles life, dim here, clearer there, or portraits of which one is an outline, another more minutely worked. By measuring Being by its dim manifestation and neglecting a fuller revelation elsewhere, we may come to regard this dim existence as a common ground.

But this procedure is scarcely permissible. Every being is a distinct whole. The dim manifestation is in no sense a common ground, just as there is no common ground in the vegetal, the sensory and the intellectual forms of life.

We conclude that the term "Being" must have different connotations as applied to Matter, to Form and to both conjointly, in spite of the single source pouring into the different streams.

Take a second derived from a first and a third from the second: it is not merely that the one will rank higher and its successor be poorer and of lower worth; there is also the consideration that, even deriving from the same source, one thing, subjected in a certain degree to fire, will give us an earthen jar, while another, taking less of the heat, does not produce the jar.

Perhaps we cannot even maintain that Matter and Form are derived from a single source; they are clearly in some sense different.

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.

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 [the universal] 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.

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 [Substance], or rather the Becoming, which obtains in the Sensible realm.

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.

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 [magnitude], 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 [quantity or no quantity] be referred to Motion, as must activity also.

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 polyhedra: 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.

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

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

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

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

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

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

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

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

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

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

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

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 [qualitative] 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.

16. When each of the entities bound up with the pseudo-substance is taken apart from the rest, the name of Quality is given to that one among them, by which without pointing to essence or quantity or motion we signify the distinctive mark, the type or aspect of a thing -- for example, the beauty or ugliness of a body. This beauty -- need we say? -- is identical in name only with Intellectual Beauty: it follows that the term "Quality" as applied to the Sensible and the Intellectual is necessarily equivocal; even blackness and whiteness are different in the two spheres.

But the beauty in the germ, in the particular Reason-Principle -- is this the same as the manifested beauty, or do they coincide only in name? Are we to assign this beauty -- and the same question applies to deformity in the soul -- to the Intellectual order, or to the Sensible? That beauty is different in the two spheres is by now clear. If it be embraced in Sensible Quality, then virtue must also be classed among the qualities of the lower. But merely some virtues will take rank as Sensible, others as Intellectual qualities.

It may even be doubted whether the arts, as Reason-Principles, can fairly be among Sensible qualities; Reason-Principles, it is true, may reside in Matter, but "matter" for them means Soul. On the other hand, their being found in company with Matter commits them in some degree to the lower sphere. Take the case of lyrical music: it is performed upon strings; melody, which may be termed a part of the art, is sensuous sound -- though, perhaps, we should speak here not of parts but of manifestations [Acts]: yet, called manifestations, they are nonetheless sensuous. The beauty inherent in body is similarly bodiless; but we have assigned it to the order of things bound up with body and subordinate to it.

Geometry and arithmetic are, we shall maintain, of a twofold character; in their earthly types they rank with Sensible Quality, but in so far as they are functions of pure Soul, they necessarily belong to that other world in close proximity to the Intellectual. This, too, is in Plato's view the case with music and astronomy.

The arts concerned with material objects and making use of perceptible instruments and sense-perception must be classed with Sensible Quality, even though they are dispositions of the Soul, attendant upon its apostasy.

There is also every reason for consigning to this category the practical virtues whose function is directed to a social end: these do not isolate Soul by inclining it towards the higher; their manifestation makes for beauty in this world, a beauty regarded not as necessary but as desirable.

On this principle, the beauty in the germ, and still more the blackness and whiteness in it, will be included among Sensible Qualities.

Are we, then, to rank the individual soul, as containing these Reason-Principles, with Sensible Substance? But we do not even identify the Principles with body; we merely include them in Sensible Quality on the ground that they are connected with body and are activities of body. The constituents of Sensible Substance have already been specified; we have no intention whatever of adding to them Substance bodiless.

As for Qualities, we hold that they are invariably bodiless, being affections arising within Soul; but, like the Reason-Principles of the individual soul, they are associated with Soul in its apostasy, and are accordingly counted among the things of the lower realm: such affections, torn between two worlds by their objects and their abode, we have assigned to Quality, which is indeed not bodily but manifested in body.

But we refrain from assigning Soul to Sensible Substance, on the ground that we have already referred to Quality [which is Sensible] those affections of Soul which are related to body. On the contrary, Soul, conceived apart from affection and Reason-Principle, we have restored to its origin, leaving in the lower realm no substance which is in any sense Intellectual.

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 [of colour and taste, and not the sense-organs] 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.

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 [of Quality], 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.

19. With Quality we have undertaken to group the dependent qualia, in so far as Quality is bound up with them; we shall not however introduce into this category the qualified objects [qua objects], that we may not be dealing with two categories at once; we shall pass over the objects to that which gives them their [specific] name.

But how are we to classify such terms as "not white"? If "not white" signifies some other colour, it is a quality. But if it is merely a negation of an enumeration of things not white, it will be either a meaningless sound, or else a name or definition of something actual: if a sound, it is a kind of motion; if a name or definition, it is a relative, inasmuch as names and definitions are significant. But if not only the things enumerated are in some one genus, but also the propositions and terms in question must be each of them significative of some genus, then we shall assert that negative propositions and terms posit certain things within a restricted field and deny others. Perhaps, however, it would be better, in view of their composite nature, not to include the negations in the same genus as the affirmations.

What view, then, shall we take of privations? If they are privations of qualities, they will themselves be qualities: "toothless" and "blind," for example, are qualities. "Naked" and "dothed," on the other hand, are neither of them qualities but states: they therefore comport a relation to something else.

[With regard to passive qualities:]

Passivity, while it lasts, is not a quality but a motion; when it is a past experience remaining in one's possession, it is a quality; if one ceases to possess the experience then regarded as a finished occurrence, one is considered to have been moved -- in other words, to have been in Motion. But in none of these cases is it necessary to conceive of anything but Motion; the idea of time should be excluded; even present time has no right to be introduced.

"Well" and similar adverbial expressions are to be referred to the single generic notion [of Quality].

It remains to consider whether blushing should be referred to Quality, even though the person blushing is not included in this category. The fact of becoming flushed is rightly not referred to Quality; for it involves passivity -- in short, Motion. But if one has ceased to become flushed and is actually red, this is surely a case of Quality, which is independent of time. How indeed are we to define Quality but by the aspect which a substance presents? By predicating of a man redness, we clearly ascribe to him a quality.

We shall accordingly maintain that states alone, and not dispositions, constitute qualities: thus, "hot" is a quality but not "growing hot," "ill" but not "turning ill."

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 [apparently] 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 [subsisting in Quality], 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.

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 [implied in the antecedents] has "come to be"; where, however, an animal or a vegetal life is concerned, becoming [or birth] 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.

22. But suppose that we identify alteration with Motion on the ground that Motion itself results in difference: how then do we proceed to define Motion?

It may roughly be characterized as the passage from the potentiality to its realization. That is potential which can either pass into a Form -- for example, the potential statue -- or else pass into actuality -- such as the ability to walk: whenever progress is made towards the statue, this progress is Motion; and when the ability to walk is actualized in walking, this walking is itself Motion: dancing is, similarly, the motion produced by the potential dancer taking his steps.

In the one type of Motion a new Form comes into existence created by the motion; the other constitutes, as it were, the pure Form of the potentiality, and leaves nothing behind it when once the motion has ceased. Accordingly, the view would not be unreasonable which, taking some Forms to be active, others inactive, regarded Motion as a dynamic Form in opposition to the other Forms which are static, and further as the cause of whatever new Form ensues upon it. To proceed to identify this bodily motion with life would however be unwarrantable; it must be considered as identical only in name with the motions of Intellect and Soul.

That Motion is a genus we may be all the more confident in virtue of the difficulty -- the impossibility even -- of confining it within a definition.

But how can it be a Form in cases where the motion leads to deterioration, or is purely passive? Motion, we may suggest, is like the heat of the sun causing some things to grow and withering others. In so far as Motion is a common property, it is identical in both conditions; its apparent difference is due to the objects moved.

Is, then, becoming ill identical with becoming well? As motions they are identical. In what respect, then, do they differ? In their substrates? or is there some other criterion?

This question may however be postponed until we come to consider alteration: at present we have to discover what is the constant element in every motion, for only on this basis can we establish the claim of Motion to be a genus.

Perhaps the one term covers many meanings; its claim to generic status would then correspond to that of Being.

As a solution of the problem we may suggest that motions conducing to the natural state or functioning in natural conditions should perhaps, as we have already asserted, be regarded as being in a sense Forms, while those whose direction is contrary to nature must be supposed to be assimilated to the results towards which they lead.

But what is the constant element in alteration, in growth and birth and their opposites, in local change? What is that which makes them all motions? Surely it is the fact that in every case the object is never in the same state before and after the motion, that it cannot remain still and in complete inactivity but, so long as the motion is present, is continually urged to take a new condition, never acquiescing in Identity but always courting Difference; deprived of Difference, Motion perishes.

Thus, Difference may be predicated of Motion, not merely in the sense that it arises and persists in a difference of conditions, but in the sense of being itself perpetual difference. It follows that Time, as being created by Motion, also entails perpetual difference: Time is the measure of unceasing Motion, accompanying its course and, as it were, carried along its stream.

In short, the common basis of all Motion is the existence of a progression and an urge from potentiality and the potential to actuality and the actual: everything which has any kind of motion whatsoever derives this motion from a pre-existent potentiality within itself of activity or passivity.

23. The Motion which acts upon Sensible objects enters from without, and so shakes, drives, rouses and thrusts its participants that they may neither rest nor preserve their identity -- and all to the end that they may be caught into that restlessness, that flustering excitability which is but an image of Life.

We must avoid identifying Motion with the objects moved: by walking we do not mean the feet but the activity springing from a potentiality in the feet. Since the potentiality is invisible, we see of necessity only the active feet -- that is to say, not feet simply, as would be the case if they were at rest, but something besides feet, something invisible but indirectly seen as an accompaniment by the fact that we observe the feet to be in ever-changing positions and no longer at rest. We infer alteration, on the other hand, from the qualitative change in the thing altered.

Where, then, does Motion reside, when there is one thing that moves and another that passes from an inherent potentiality to actuality? In the mover? How then will the moved, the patient, participate in the motion? In the moved? Then why does not Motion remain in it, once having come? It would seem that Motion must neither be separated from the active principle nor allowed to reside in it; it must proceed from agent to patient without so inhering in the latter as to be severed from the former, passing from one to the other like a breath of wind.

Now, when the potentiality of Motion consists in an ability to walk, it may be imagined as thrusting a man forward and causing him to be continually adopting a different position; when it lies in the capacity to heat, it heats; when the potentiality takes hold of Matter and builds up the organism, we have growth; and when another potentiality demolishes the structure, the result is decay, that which has the potentiality of demolition experiencing the decay. Where the birth-giving principle is active, we find birth; where it is impotent and the power to destroy prevails, destruction takes place -- not the destruction of what already exists, but that which intervenes upon the road to existence.

Health comes about in the same way -- when the power which produces health is active and predominant; sickness is the result of the opposite power working in the opposite direction.

Thus, Motion is conditioned, not only by the objects in which it occurs, but also by its origins and its course, and it is a distinctive mark of Motion to be always qualified and to take its quality from the moved.

24. With regard to locomotion: if ascending is to be held contrary to descending, and circular motion different [in kind] from motion in a straight line, we may ask how this difference is to be defined -- the difference, for example, between throwing over the head and under the feet.

The driving power is one -- though indeed it might be maintained that the upward drive is different from the downward, and the downward passage of a different character from the upward, especially if it be a natural motion, in which case the up-motion constitutes lightness, the down-motion heaviness.

But in all these motions alike there is the common tendency to seek an appointed place, and in this tendency we seem to have the differentia which separates locomotion from the other species.

As for motion in a circle and motion in a straight line, if the former is in practice indistinguishable from the latter, how can we regard them as different? The only difference lies in the shape of the course, unless the view be taken that circular motion is "impure," as not being entirely a motion, not involving a complete surrender of identity.

However, it appears in general that locomotion is a definite unity, taking its differences from externals.

25. The nature of integration and disintegrations calls for scrutiny. Are they different from the motions above mentioned, from coming-to-be and passing-away, from growth and decay, from change of place and from alteration? or must they be referred to these? or, again, must some of these be regarded as types of integration and disintegration?

If integration implies that one element proceeds towards another, implies in short an approach, and disintegration, on the other hand, a retreat into the background, such motions may be termed local; we have clearly a case of two things moving in the direction of unity, or else making away from each other.

If however the things achieve a sort of fusion, mixture, blending, and if a unity comes into being, not when the process of combination is already complete, but in the very act of combining, to which of our specified motions shall we refer this type? There will certainly be locomotion at first, but it will be succeeded by something different; just as in growth locomotion is found at the outset, though later it is supplanted by quantitative motion. The present case is similar: locomotion leads the way, but integration or disintegration does not inevitably follow; integration takes place only when the impinging elements become intertwined, disintegration only when they are rent asunder by the contact.

On the other hand, it often happens that locomotion follows disintegration, or else occurs simultaneously, though the experience of the disintegrated is not conceived in terms of locomotion: so too in integration a distinct experience, a distinct unification, accompanies the locomotion and remains separate from it.

Are we then to posit a new species for these two motions, adding to them, perhaps, alteration? A thing is altered by becoming dense -- in other words, by integration; it is altered again by being rarefied -- that is, by disintegration. When wine and water are mixed, something is produced different from either of the pre-existing elements: thus, integration takes place, resulting in alteration.

But perhaps we should recall a previous distinction, and while holding that integrations and disintegrations precede alterations, should maintain that alterations are nonetheless distinct from either; that, further, not every alteration is of this type [presupposing, that is to say, integration or disintegration], and, in particular, rarefication and condensation are not identical with disintegration and integration, nor in any sense derived from them: to suppose that they were would involve the admission of a vacuum.

Again, can we use integration and disintegration to explain blackness and whiteness? But to doubt the independent existence of these qualities means that, beginning with colours, we may end by annihilating almost all qualities, or rather all without exception; for if we identify every alteration, or qualitative change, with integration and disintegration, we allow nothing whatever to come into existence; the same elements persist, nearer or farther apart.

Finally, how is it possible to class learning and being taught as integrations?

26. We may now take the various specific types of Motion, such as locomotion, and once again enquire for each one whether it is not to be divided on the basis of direction, up, down, straight, circular -- a question already raised; whether the organic motion should be distinguished from the inorganic -- they are clearly not alike; whether, again, organic motions should be subdivided into walking, swimming and flight.

Perhaps we should also distinguish, in each species, natural from unnatural motions: this distinction would however imply that motions have differences which are not external. It may indeed be the case that motions create these differences and cannot exist without them; but Nature may be supposed to be the ultimate source of motions and differences alike.

Motions may also be classed as natural, artificial and purposive: "natural" embracing growth and decay; "artificial" architecture and shipbuilding; "purposive" enquiry, learning, government, and, in general, all speech and action.

Again, with regard to growth, alteration and birth, the division may proceed from the natural and unnatural, or, speaking generally, from the characters of the moved objects.

27. What view are we to take of that which is opposed to Motion, whether it be Stability or Rest? Are we to consider it as a distinct genus, or to refer it to one of the genera already established? We should, no doubt, be well advised to assign Stability to the Intellectual, and to look in the lower sphere for Rest alone.

First, then, we have to discover the precise nature of this Rest. If it presents itself as identical with Stability, we have no right to expect to find it in the sphere where nothing is stable and the apparently stable has merely a less strenuous motion.

Suppose the contrary: we decide that Rest is different from Stability inasmuch as Stability belongs to the utterly immobile, Rest to the stationary which, though of a nature to move, does not move. Now, if Rest means coming to rest, it must be regarded as a motion which has not yet ceased but still continues; but if we suppose it to be incompatible with Motion, we have first to ask whether there is in the Sensible world anything without motion.

Yet nothing can experience every type of motion; certain motions must be ruled out in order that we may speak of the moving object as existing: may we not, then, say of that which has no locomotion and is at rest as far as pertains to that specific type of motion, simply that it does not move?

Rest, accordingly, is the negation of Motion: in other words, it has no generic status. It is in fact related only to one type of motion, namely, locomotion; it is therefore the negation of this motion that is meant.

But, it may be asked, why not regard Motion as the negation of Stability? We reply that Motion does not appear alone; it is accompanied by a force which actualizes its object, forcing it on, as it were, giving it a thousand forms and destroying them all: Rest, on the contrary, comports nothing but the object itself, and signifies merely that the object has no motion.

Why, then, did we not in discussing the Intellectual realm assert that Stability was the negation of Motion? Because it is not indeed possible to consider Stability as an annulling of Motion, for when Motion ceases Stability does not exist, but requires for its own existence the simultaneous existence of Motion; and what is of a nature to move is not stationary because Stability of that realm is motionless, but because Stability has taken hold of it; in so far as it has Motion, it will never cease to move: thus, it is stationary under the influence of Stability, and moves under the influence of Motion. In the lower realm, too, a thing moves in virtue of Motion, but its Rest is caused by a deficiency; it has been deprived of its due motion.

What we have to observe is the essential character of this Sensible counterpart of Stability.

Consider sickness and health. The convalescent moves in the sense that he passes from sickness to health. What species of rest are we to oppose to this convalescence? If we oppose the condition from which he departs, that condition is sickness, not Stability; if that into which he passes, it is health, again not the same as Stability.

It may be declared that health or sickness is indeed some form of Stability: we are to suppose, then, that Stability is the genus of which health and sickness are species; which is absurd.

Stability may, again, be regarded as an attribute of health: according to this view, health will not be health before possessing Stability.

These questions may however be left to the judgement of the individual.

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.