(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.

(9) Accordingly we must first take the genus, in which are the points that are nearest those above; and after this the next difference. And the succession of differences, when cut and divided, completes the "What it is." There is no necessity for expressing all the differences of each thing, but those which form the species.

(1) With respect to your inquiry, “ what the peculiarities are in each of the more excellent genera, by which they are separated from each other? ” if you understand by peculiarities the specific differences under the same genus, which are distinguished by opposite qualities, as the rational and irrational under animal; we by no means admit peculiarities of this kind, in things which neither have one common essence, nor an equal contradistinction, nor receive a composition from something common, which is indefinite, and defines the peculiarity. But if you apprehend the peculiarity to be, as in prior and secondary natures, differing in their whole essence and whole genus, a certain simple condition of being, definite in itself; in this case, your conception of peculiarities will be reasonable. For these peculiarities of things, which have an eternal subsistence, are simple, and entirely exempt. The inquiry, however, proceeds imperfectly. For it was necessary, in the first place, to inquire what the peculiarities are of the more excellent genera, according to essence; in the next place, what they are according to power; and thus afterwards, what they are according to energy.

(10) Another method of division is possible: substances may be classed as hot-dry, dry-cold, cold-moist, or however we choose to make the coupling. We may then proceed to the combination and blending of these couples, either halting at that point and going no further than the compound, or else subdividing by habitation- on the earth, in the earth- or by form and by the differences exhibited by living beings, not qua living, but in their bodies viewed as instruments of life.

Differentiation by form or shape is no more out of place than a division based on qualities- heat, cold and the like. If it be objected that qualities go to make bodies what they are, then, we reply, so do blendings, colours, shapes. Since our discussion is concerned with Sensible Substance, it is not strange that it should turn upon distinctions related to sense-perception: this Substance is not Being pure and simple, but the Sensible Being which we call the Universe.

We have remarked that its apparent subsistence is in fact an assemblage of Sensibles, their existence guaranteed to us by sense-perception. But since their combination is unlimited, our division must be guided by the Form-Ideas of living beings, as for example the Form-Idea of Man implanted in Body; the particular Form acts as a qualification of Body, but there is nothing unreasonable in using qualities as a basis of division.

We may be told that we have distinguished between simple and composite bodies, even ranking them as opposites. But our distinction, we reply, was between material and organic bodies and raised no question of the composite. In fact, there exists no means of opposing the composite to the simple; it is necessary to determine the simples in the first stage of division, and then, combining them on the basis of a distinct underlying principle, to differentiate the composites in virtue of their places and shapes, distinguishing for example the heavenly from the earthly.

These observations will suffice for the Being , or rather the Becoming, which obtains in the Sensible realm.

(7) It is, then, not by availing himself of these as virtues that our Gnostic will be deeply learned. But by using them as helps in distinguishing what is common and what is peculiar, he will admit the truth. For the cause of all error and false opinion, is inability to distinguish in what respect things are common, and in what respects they differ. For unless, in things that are distinct, one closely watch speech, he will inadvertently confound what is common and what is peculiar And where this takes place, he must of necessity fall into pathless tracts and error.

(4) At the end, likewise, of your inquiry, you introduce a distinction according to nature. For your question asks, “ How essences are known by energies, by physical motions, and by accidents? ” The very contrary, however, to all this takes place. For if energies and motions were constitutive of essences, they would be the lords of the difference which is between them. But if essences generate energies, the former being separate prior to the latter, will impart to motions, energies, and accidents, that by which they differ from each other. This, therefore, subsists contrarily to what you suppose, for the purpose of discovering the peculiarity which you now investigate.

(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.

(2) But it reasonably follows, according to continuity of alliance, that the medium which begins from the most excellent natures, should proceed to such as are less excellent; but that the medium which primarily produces a contact with the last of things, should also in a certain respect communicate with the natures that transcend it. From these media, also, the completion may be seen of the first and last genera, and this entirely connascent, in a similar manner, in existence, in power, and in energy. As we have, therefore, in these two ways, perfectly completed the division of the four genera, we shall deem it sufficient in the others, to exhibit the extreme peculiarities alone, for the sake of conciseness, and because what remains, i. e. the comprehension of the media, is in a certain respect evident. But the media themselves, as being known from the extremes, we shall omit; making a definition of the extremes in the shortest way, as follows.

(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.

(11) But if these considerations are sound, why has Quality more than one species? What is the ground for distinguishing between habit and disposition, seeing that no differentia of Quality is involved in permanence and non-permanence? A disposition of any kind is sufficient to constitute a quality; permanence is a mere external addition. It might however be urged that dispositions are but incomplete "forms"- if the term may pass- habits being complete ones. But incomplete, they are not qualities; if already qualities, the permanence is an external addition.

How do physical powers form a distinct species? If they are classed as qualities in virtue of being powers, power, we have seen, is not a necessary concomitant of qualities. If, however, we hold that the natural boxer owes his quality to a particular disposition, power is something added and does not contribute to the quality, since power is found in habits also.

Another point: why is natural ability to be distinguished from that acquired by learning? Surely, if both are qualities, they cannot be differentiae of Quality: gained by practice or given in nature, it is the same ability; the differentia will be external to Quality; it cannot be deduced from the Ideal Form of boxing. Whether some qualities as distinguished from others are derived from experience is immaterial; the source of the quality makes no difference- none, I mean, pointing to variations and differences of Quality.

A further question would seem to be involved: If certain qualities are derived from experience but here is a discrepancy in the manner and source of the experience, how are they to be included in the same species? And again, if some create the experience, others are created by it, the term Quality as applied to both classes will be equivocal.

And what part is played by the individual form? If it constitutes the individual's specific character, it is not a quality; if, however, it is what makes an object beautiful or ugly after the specific form has been determined, then it involves a Reason-Principle.

Rough and smooth, tenuous and dense may rightly be classed as qualities. It is true that they are not determined by distances and approximations, or in general by even or uneven dispositions, of parts; though, were they so determined, they might well even then be qualities.

Knowledge of the meaning of "light" and "heavy" will reveal their place in the classification. An ambiguity will however be latent in the term "light," unless it be determined by comparative weight: it would then implicate leanness and fineness, and involve another species distinct from the four .

(18) Whence both these divisions are to be rejected, and only the division of the genus into species is approved, by which both the identity that is in the genus is characterized, and the diversity which subsists in the specific differences.

(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.

(3) So great, therefore, being the difference between the energies of dæmons, heroes, and souls throughout, it is no longer proper to doubt, what it is which separates them from each other; but they are to be distinguished by the peculiar nature of each. And so far as they are able to form one conjunction, so far the communion of them must be surveyed. For thus it will be possible truly to comprehend and define separately the conception which ought to be formed of them.

(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.

(7) What, then, are the several entities observable in this plurality?

We have found Substance and life simultaneously present in Soul. Now, this Substance is a common property of Soul, but life, common to all souls, differs in that it is a property of Intellect also.

Having thus introduced Intellect and its life we make a single genus of what is common to all life, namely, Motion. Substance and the Motion, which constitutes the highest life, we must consider as two genera; for even though they form a unity, they are separable to thought which finds their unity not a unity; otherwise, it could not distinguish them.

Observe also how in other things Motion or life is clearly separated from Being- a separation impossible, doubtless, in True Being, but possible in its shadow and namesake. In the portrait of a man much is left out, and above all the essential thing, life: the "Being" of sensible things just such a shadow of True Being, an abstraction from that Being complete which was life in the Archetype; it is because of this incompleteness that we are able in the Sensible world to separate Being from life and life from Being.

Being, then, containing many species, has but one genus. Motion, however, is to be classed as neither a subordinate nor a supplement of Being but as its concomitant; for we have not found Being serving as substrate to Motion. Motion is being Act; neither is separated from the other except in thought; the two natures are one; for Being is inevitably actual, not potential.

No doubt we observe Motion and Being separately, Motion as contained in Being and Being as involved in Motion, and in the individual they may be mutually exclusive; but the dualism is an affirmation of our thought only, and that thought sees either form as a duality within a unity.

Now Motion, thus manifested in conjunction with Being, does not alter Being's nature- unless to complete its essential character- and it does retain for ever its own peculiar nature: at once, then, we are forced to introduce Stability. To reject Stability would be more unreasonable than to reject Motion; for Stability is associated in our thought and conception with Being even more than with Motion; unalterable condition, unchanging mode, single Reason-Principle- these are characteristics of the higher sphere.

Stability, then, may also be taken as a single genus. Obviously distinct from Motion and perhaps even its contrary, that it is also distinct from Being may be shown by many considerations. We may especially observe that if Stability were identical with Being, so also would Motion be, with equal right. Why identity in the case of Stability and not in that of Motion, when Motion is virtually the very life and Act both of Substance and of Absolute Being? However, on the very same principle on which we separated Motion from Being with the understanding that it is the same and not the same- that they are two and yet one- we also separate Stability from Being, holding it, yet, inseparable; it is only a logical separation entailing the inclusion among the Existents of this other genus. To identify Stability with Being, with no difference between them, and to identify Being with Motion, would be to identify Stability with Motion through the mediation of Being, and so to make Motion and Stability one and the same thing.

(21) The species then being divided more generically, are characterized by sameness and difference. And then being divided, they are chacterized by the points generically indicated.

(1) But, on the other hand, [whereas] those things which only have the power of bringing forth by blending with another nature, are thus to be distinguished, this Space of Cosmos, with those that are in it, seems not to have been born, in that [the Cosmos] has in it undoubtedly all Nature’s potency. By “Space” I mean that in which are all things. For all these things could not have been had Space not been, to hold them all. Since for all things that there have been, must be provided Space. For neither could the qualities nor quantities, nor the positions, nor [yet] the operations, be distinguished of those things which are no where.

(6) Something besides a unity there must be or all would be indiscernibly buried, shapeless within that unbroken whole: none of the real beings would exist if that unity remained at halt within itself: the plurality of these beings, offspring of the unity, could not exist without their own nexts taking the outward path; these are the beings holding the rank of souls.

In the same way the outgoing process could not end with the souls, their issue stifled: every Kind must produce its next; it must unfold from some concentrated central principle as from a seed, and so advance to its term in the varied forms of sense. The prior in its being will remain unalterably in the native seat; but there is the lower phase, begotten to it by an ineffable faculty of its being, native to soul as it exists in the Supreme.

To this power we cannot impute any halt, any limit of jealous grudging; it must move for ever outward until the universe stands accomplished to the ultimate possibility. All, thus, is produced by an inexhaustible power giving its gift to the universe, no part of which it can endure to see without some share in its being.

There is, besides, no principle that can prevent anything from partaking, to the extent of its own individual receptivity in the Nature of Good. If therefore Matter has always existed, that existence is enough to ensure its participation in the being which, according to each receptivity, communicates the supreme good universally: if on the contrary, Matter has come into being as a necessary sequence of the causes preceding it, that origin would similarly prevent it standing apart from the scheme as though it were out of reach of the principle to whose grace it owes its existence.

In sum: The loveliness that is in the sense-realm is an index of the nobleness of the Intellectual sphere, displaying its power and its goodness alike: and all things are for ever linked; the one order Intellectual in its being, the other of sense; one self-existent, the other eternally taking its being by participation in that first, and to the full of its power reproducing the Intellectual nature.

(13) It has been remarked that the continuous is effectually distinguished from the discrete by their possessing the one a common, the other a separate, limit.

The same principle gives rise to the numerical distinction between odd and even; and it holds good that if there are differentiae found in both contraries, they are either to be abandoned to the objects numbered, or else to be considered as differentiae of the abstract numbers, and not of the numbers manifested in the sensible objects. If the numbers are logically separable from the objects, that is no reason why we should not think of them as sharing the same differentiae.

But how are we to differentiate the continuous, comprising as it does line, surface and solid? The line may be rated as of one dimension, the surface as of two dimensions, the solid as of three, if we are only making a calculation and do not suppose that we are dividing the continuous into its species; for it is an invariable rule that numbers, thus grouped as prior and posterior, cannot be brought into a common genus; there is no common basis in first, second and third dimensions. Yet there is a sense in which they would appear to be equal- namely, as pure measures of Quantity: of higher and lower dimensions, they are not however more or less quantitative.

Numbers have similarly a common property in their being numbers all; and the truth may well be, not that One creates two, and two creates three, but that all have a common source.

Suppose, however, that they are not derived from any source whatever, but merely exist; we at any rate conceive them as being derived, and so may be assumed to regard the smaller as taking priority over the greater: yet, even so, by the mere fact of their being numbers they are reducible to a single type.

What applies to numbers is equally true of magnitudes; though here we have to distinguish between line, surface and solid- the last also referred to as "body"- in the ground that, while all are magnitudes, they differ specifically.

It remains to enquire whether these species are themselves to be divided: the line into straight, circular, spiral; the surface into rectilinear and circular figures; the solid into the various solid figures- sphere and polyhedANSWER: whether these last should be subdivided, as by the geometers, into those contained by triangular and quadrilateral planes: and whether a further division of the latter should be performed.

(14) Whence Division furnishes the class of matter, seeking for the definition the simplicity of the name; and the definition of the artisan and maker, by composition and construction, presents the knowledge of the thing as it is; not of those things of which we have general notions.