Part 24

For space, there is no contrary, because strictly space does not belong to the genus of quantity. Even if space were part of quantity, "high" would not be the contrary of anything unless the universe contained also "low." The terms high and low, applied to parts, signify only higher and lower than something else. It is so also with right and left, which are relatives.

CLASSIFICATION OF SYLLABLES AND SPEECH.

Syllables and speech are quantitatives; they might be subjects in respect to quantity, but only so by accident. Indeed, the voice, by itself, is a movement,[386] it must therefore be reduced to movement and action.

DISCRETE QUANTITY QUITE DISTINCT FROM CONTINUOUS QUANTITY.

13. We have already explained that discrete quantity is clearly distinguished from continuous quantity, both by its own definition, and the general definition (for quantity).[387] We may add that numbers are distinguished from each other by being even and odd. If besides there be other differences amidst the even and odd numbers, these differences will have to be referred to the objects in which are the numbers, or to the numbers composed of unities, and not any more to those which exist in sense-beings. If reason separate sense-things from the numbers they contain, nothing hinders us then from attributing to these numbers the same differences (as to the numbers composed of unities).[388]

ELEMENTS OF CONTINUOUS QUANTITY.

What distinctions are admitted by continuous quantity? There is the line, the surface, and the solid; for extension may exist in one, two or three dimensions (and thus count the numerical elements of continuous size) instead of establishing species.[389] In numbers thus considered as anterior or posterior to each other, there is nothing in common, which would constitute a genus. Likewise in the first, second and third increases (of a line, surface, and solid) there is nothing in common; but as far as quantity is found, there is also equality (and inequality), although there be no extension which is quantitative more than any other.[390] However, one may have dimensions greater than another. It is therefore only in so far as they are all numbers, that numbers can have anything in common. Perhaps, indeed, it is not the monad that begets the pair, nor the pair that begets the triad, but it may be the same principle which begets all the numbers. If numbers be not derivative, but exist by themselves, we may, at least within our own thought, consider them as begotten (or, derivative). We conceive of the smaller number as the anterior, the greater as posterior. But numbers, as such, may all be reduced to unity.

STUDY OF GEOMETRICAL FIGURES.

The method of classification adopted for numbers may be applied to sizes, and thus distinguish the line, the surface, and the solid or body, because those are sizes which form different species. If besides each of these species were to be divided, lines might be subdivided into straight, curved and spiral; surfaces into straight and curved; solids into round or polyhedral bodies. Further, as geometers do, may come the triangle, the quadrilateral, and others.

STUDY OF THE STRAIGHT LINE.

14. But what about the straight line? Is it not a magnitude? Possibly; but if it be a magnitude, it is a qualified one.[391] It is even possible that straightness constitutes a difference of the (very nature of the) line, as line, for straightness refers solely to a line; and besides, we often deduce the differences of "Essence" from its qualities. That a straight line is a quantity added to a difference does not cause its being composed of the line, and of the property of straightness; for, were it thus composed, straightness would be its chief difference.

STUDY OF THE TRIANGLE.

Now let us consider the triangle, which is formed of three lines. Why should it not belong to quantity? Would it be so, because it is not constituted by three lines merely, but by three lines arranged in some particular manner? But a quadrilateral would also be constituted by four lines arranged in some particular manner. (But being arranged in some particular manner does not hinder a figure from being a quantity). The straight line, indeed, is arranged in some particular manner, and is none the less a quantity. Now if the straight line be not simply a quantity, why could this not also be said of a limited line? For the limit of the line is a point, and the point does not belong to any genus other than the line. Consequently, a limited surface is also a quantity, because it is limited by lines, which even more belong to quantity. If then the limited surface be contained in the genus of quantity, whether the surface be a triangle, a quadrilateral, a hexagon, or any other polygon, all figures whatever will belong to the genus of quantity. But if we assigned the triangle or quadrilateral to the genus of quality merely because we are speaking of some one definite triangle or quadrilateral, nothing would hinder one and the same thing from being subsumed under several categories. A triangle would then be a quantity so far as it was both a general and particular magnitude, and would be a quality by virtue of its possessing a particular form. The same might be predicated of the Triangle in itself because of its possessing a particular form; and so also with the sphere. By following this line of argument, geometry would be turned into a study of qualities, instead of that of quantities, which of course it is. The existing differences between magnitudes do not deprive them of their property of being magnitudes, just as the difference between essences does not affect their essentiality. Besides, every surface is limited, because an infinite surface is impossible. Further, when I consider a difference that pertains to essence, I call it an essential difference. So much the more, on considering figures, I am considering differences of magnitude. For if the differences were not of magnitude, of what would they be differences? If then they be differences of magnitude, the different magnitudes which are derived from differences of magnitude should be classified according to the species constituted by them (when considered in the light of being magnitudes).

GEOMETRY STUDIES QUANTITIES, NOT QUALITIES.

15. But how can you qualify the properties of quantity so as to call them equal or unequal?[392] Is it not usual to say of two triangles that they are similar? Could we not also predicate similarity of two magnitudes? Doubtless, for what is called similarity,[393] does not conflict with similarity or dissimilarity in the genus of quantity.[394] Here, indeed, the word "similarity" is applied to magnitudes in a sense other than to quality. Besides, if (Aristotle) said that the property characteristic of quantities is to enable them to be called equal or unequal, this does not conflict with predicating similarity of some of them. But as it has been said that the special characteristic of qualities is to admit of being called similar or dissimilar, we must, as has already been explained, understand similarity in a sense other than when it is applied to magnitudes. If similar magnitudes be identical, we must then consider the other properties of quantity and quality which might be present in them (so as clearly to contrast their differences). It may also be said that the term "similarity" applies to the genus of quantity so far as this contains differences (which distinguish from each other similar magnitudes).

DIFFERENCES WHICH COMPLETE THE BEING MUST BE PREFIXED TO THAT TO WHICH THEY REFER.

In general, the differences which complete a being should be classified along with that of which they are the differences, especially when a difference belongs to a single subject. If a difference complete the being of a subject, and do not complete the being of another, this difference should be classified along with the subject whose being it completes, leaving that whose being it does not complete for separate consideration. By this we do not mean completing the Being in general, but completing some particular being, so that the subject spoken of as a particular one admits no further essential addition. We therefore have the right to say that triangles, or that quadrilaterals, as well as surfaces and solids, are equal, and to predicate equality or inequality of quantitative entities. But we yet have to study whether quality only can be said to be similar or dissimilar.[395]

WHETHER QUALITY ONLY CAN BE CALLED SIMILAR OR DISSIMILAR.

When we were treating of things that were qualified, we had already explained that matter, united to quantity, and taken with other things, constitutes sense-being; that this "being" seems to be a composite of several things, that it is not properly a "whatness,"[396] but rather qualification (or, qualified thing). The ("seminal) reason," for instance that of fire, has more of a reference to "whatness," while the form that the reason begets is rather a qualification. Likewise, the ("seminal) reason" of man is a "whatness," whilst the form that this reason gives to the body, being only an image of reason, is rather a qualification. Thus if the Socrates that we see was the genuine Socrates, his mere portrait composed of no more than colors would also be called Socrates. Likewise, although this ("seminal) reason" of Socrates be that which constitutes the genuine Socrates, we nevertheless also apply the name of Socrates to the man that we see; yet the colors, or the figure of the Socrates we see, are only the image of those which are contained by his ("seminal) reason." Likewise, the reason of Socrates is itself only an image of the veritable reason (of the idea) of the man. This is our solution of the problem.[397]

THE VARIOUS TERMS EXPRESSING QUALITY.

16. When we separately consider each of the things which compose sense-being and when we wish to designate the quality which exists among them, we must not call it "whatness," any more than quantity or movement, but rather name it a characteristic, employing the expressions "such," "as," and "this kind." We are thus enabled to indicate beauty and ugliness, such as they are in the body. Indeed, sense-beauty is no more than a figure of speech,[343] in respect to intelligible beauty; it is likewise with quality, since black and white are also completely different (from their "reason," or their idea).

THE SEMINAL REASON HARMONIZES WITH ITS APPEARING ACTUALIZATION.

Is the content of ("seminal) reason" and of a particular reason, identical with what appears, or does it apply thereto only by a figure of speech?[343] Should it properly be classified among the intelligible, or the sense-objects? Sensual beauty of course evidently differs from intelligible beauty; but what of ugliness--in which classification does it belong? Must virtue be classified among intelligible or sensual qualities, or should we locate some in each class? (All this uncertainty is excusable, inasmuch) as it may be asked whether even the arts, which are "reasons," should be classified among sense-qualities? If these reasons be united to a matter, they must have matter as their very soul. But what is their condition here below, when united to some matter? These reasons are in a case similar to song accompanied by a lyre;[398] this song, being uttered by a sense-voice, is in relation with the strings of the lyre, while simultaneously being part of the art (which is one of these "seminal reasons"). Likewise, it might be said that virtues are actualizations, and not parts (of the soul). Are they sense-actualizations? (This seems probable), for although the beauty contained in the body be incorporeal, we still classify it among the things which refer to the body, and belong to it. As to arithmetic, and geometry, two different kinds must be distinguished: the first kind deals with visible objects, and must be classified among sense-objects; but the second kind deals with studies suitable to the soul, and should therefore be classified among intelligible entities. Plato[399] considers that music and astronomy are in the same condition.

MANY OTHER CONCEPTIONS BELONG AMONG SENSE-QUALITIES.

Thus the arts which relate to the body, which make use of the organs, and which consult the senses, are really dispositions of the soul, but only of the soul as applied to corporeal objects; and consequently, they should be classified among sense-qualities.[400] Here also belong practical virtues, such as are implied by civil duties, and which, instead of raising the soul to intelligible entities, fructify in the actions of political life, and refer to them, not as a necessity of our condition, but as an occupation preferable to everything else.[401] Among these qualities we shall have to classify the beauty contained in the ("seminal) reason," and, so much the more, black and white.

IN SPITE OF THIS CLASSIFICATION THE SOUL HERSELF REMAINS INCORPOREAL.

But is the soul herself a sense-being, if she be disposed in a particular way, and if she contain particular "reasons" (that is, faculties, virtues, sciences and arts, all of which refer to the body, and which have been classified as sense-qualities)?[402] It has already been explained that these "reasons" themselves are not corporeal; but that they have been classified among sense-qualities only because they referred to the body, and to the actions thereby produced. On the other hand, as sense-quality has been defined as the meeting of all the above enumerated entities, it is impossible to classify incorporeal Being in the same genus as the sensual being. As to the qualities of the soul, they are all doubtless incorporeal, but as they are experiences (or, sufferings, or, passions) which refer to terrestrial things, they must be classified in the genus of quality, just as the reasons of the individual soul. Of the soul we must therefore predicate experience, however dividing the latter in two elements, one of which would refer to the object to which it is applied, and the other to the subject in which it exists.[403] Though then these experiences cannot be considered as corporeal qualities, yet it must be admitted they relate to the body.[404] On the other hand, although we classify these experiences in the genus of quality, still the soul herself should not be reduced to the rank of corporeal being. Last, when we conceive of the soul as without experiences, and without the "reasons" above-mentioned, we are thereby classifying her along with the World from which she descends,[405] and we leave here below no intelligible being, of any kind whatever.

QUALITIES ARE CLASSIFIED AS CORPOREAL AND OF THE SOUL.

17. Qualities, therefore, should be classified as of the body, and of the soul.[406] Even though all the souls, as well as their immaterial qualities, be considered as existing on high, yet their inferior qualities must be divided according to the senses, referring these qualities either to sight, hearing, feeling, taste, or smell. Under sight, we will classify the differences of colors; under hearing, that of the sounds; and likewise, with the other senses. As to the sounds, inasmuch as they have but a single quality, they will have to be classified according to their being soft, harsh, agreeable, and the like.

DIFFERENCES OF BEING SHOULD BE DISTINGUISHED ACCORDING TO QUALITY.

It is by quality that we distinguish the differences which inhere in being, as well as the actualizations, the beautiful or ugly actions, and in general, all that is particular. Only very rarely do we discover in quantity differences which constitute species; so much is this the case, that it is generally divided by its characteristic qualities. We must therefore leave quantity aside, and that leads us to wonder how we may divide quality itself (since it is made use of to distinguish other things).[407]

DIFFERENCE OF QUALITY CANNOT BE DISTINGUISHED BY SENSATION.

What sort of differences, indeed, might we use to establish such divisions, and from what genus would we draw them? It seems absurd to classify quality by quality itself. This is just as if the difference of "beings" were to be called "beings." By what indeed could one distinguish white from black, and colors from tastes and sensations of touch? If we distinguish the difference of these qualities by the sense-organs, these differences would no longer exist in the subjects. How indeed could one and the same sense distinguish the difference of the qualities it perceives? Is it because certain things exercise an action that is constructive or destructive on the eyes, or the tongue? We would then have to ask what is the constructive or destructive element in the sensations thus excited? Yet, even were this answered, such an answer would not explain wherein these things differ.[407]

DIFFERENCE IN EFFECTS IS LIMITED TO THE INTELLIGIBLES.

A further possibility is that these things should be classified according to their effects, and that it is reasonable to do so with invisible entities, such as sciences; but this would not be applicable to sense-objects. When indeed we divide sciences by their effects, and when, in general, we classify them according to the powers of the soul, by concluding from the diversity of their effects that they differ, our mind grasps the difference of these powers, and it determines not only with what objects they deal, but it also defines their reason (or, essence). Let us admit that it is easy to distinguish arts according to their reasons, and according to the notions they include; but is it possible to divide corporeal qualities in that manner? Even when one studies the intelligible world, there is room for doubt as to how the different reasons distinguish themselves from each other; it is easy enough to see that white differs from black; but in what does it do so?

IT IS ABSURD TO DISTINGUISH BEING, QUALITIES AND DIFFERENCES BY THEMSELVES.

18. All the questions we have asked show that we doubtless must seek to discover the differences of the various (beings), so as to distinguish them from each other; but that it is as impossible as it is unreasonable to inquire what are the differences of the differences themselves.[408] Being of beings, quantities of quantities, qualities of qualities, differences of differences cannot be discovered; but we should, wherever possible, classify exterior objects, either according to their effects, or according to salient characteristics. When this is impossible, objects should be distinguished, as for instance dark from light green.

But how is white distinguished from black? Sensation or intelligence tell us that those things are different without informing us of their reason; either sensation, because its function is not to set forth the reason of things, but only to bring them somehow to our attention; or intelligence, because it discerns things that are simple by intuition, without having to resort to ratiocination, and limits itself to the statement that something is such or such. Besides, in each one of the operations of intelligence there is a difference (a special distinctive characteristic) which enables it to distinguish different things, without this difference (which is proper to each of the operations of intelligence) itself having need to be discerned by the help of some other difference.

SOME QUALITIES ARE DIFFERENCES.

Are all qualities differences, or not? Whiteness, colors, qualities perceived by touch and taste, may become differences between different objects, though they themselves be species. But how do the sciences of grammar or of music constitute differences? The science of grammar renders the mind grammatical, and the science of music renders the mind musical, especially if they be untaught; and these thus become specific differences. Besides, we have to consider whether a difference be drawn from the same genus (from which the considered things are drawn), or from some other genus. If it be drawn from the same genus, it fulfils, for the things of this genus, the same function as does a quality to the quality to which it serves as difference. Such are virtue and vice; virtue is a particular habit, and vice is also a particular habit; consequently, as habits are qualities, the differences of these habits (either of virtue or vice) will be qualities. It may perhaps be objected that a habit without difference is not a quality, and that it is the difference alone which constitutes the quality.[409] We will answer that it is (commonly) said that sweet is good, and that bitter is bad; this then implies a recognition of their difference by a habit (a manner of being), and not by a quality.

What if sweet be said to be "crude," or thick and bitter, thin or refined? The answer is that coarseness does not inform us of the nature of sweetness, but indicates a manner of being of what is sweet; and similarly, with what is refined.

THERE ARE DIFFERENCES WHICH ARE NOT QUALITIES.

There remains for us to examine if a difference of a quality never be a quality, as that of a being is not a being, nor that of a quantity, a quantity. Does five differ from three by two? No: five does not differ from three, it only exceeds it by two. How indeed could five differ from three by two, when five contains two? Likewise, a movement does not differ from a movement by a movement. As to virtue and vice, here is one whole opposed to another whole, and it is thus that the wholes are distinguished. If a distinction were drawn from the same genus, that is, from quality, instead of founding itself on another genus; as, for instance, if one said that such a vice referred to pleasures, some other to anger, some other to acquisitiveness, and if one were to admit that such a classification was good; it would evidently result that there are differences that are not qualities.

VARIOUS DERIVATIVES OF THE CATEGORY OF QUALITY.

19. As has been indicated above, the genus of quality contains the (beings) which are said to be qualified (qualitative entities), inasmuch as they contain some quality (as, for instance, the handsome man, so far as he is endowed with beauty).[410] These (beings) however do not properly belong to this genus, for otherwise there would here be two categories. It suffices to reduce them to the quality which supplies their name.

So non-whiteness, if it indicate some color other than white, is a quality; if it express merely a negation, or an enumeration, it is only a word, or a term which recalls the object; if it be a word, it constitutes a movement (so far as it is produced by the vocal organ); if it be a name or a term, it constitutes, so far as it is a significative, a relative. If things be classed not only by genera, if it be admitted that each assertion and expression proclaim a genus, our answer must be that some affirm things by their mere announcement, and that others deny them. It may perhaps be best not to include negations in the same genus as things themselves, since, to avoid mingling several genera, we often do not include affirmations.

As to privations, it may be remarked that if the things of which there are privations are qualities, then the privations themselves are qualities, as "toothless," or "blind."[411] But "naked" and (its contrary) "clothed" are neither of them qualities; they rather constitute habits, and thus belong among relatives.

Passion, at the moment it is felt, does not constitute a quality, but a movement; when it has been experienced, and has become durable, it forms a quality;[410] further, if the (being) which has experienced the passion have kept none of it, it will have to be described as having been moved, which amounts to the same thing as really being moved. However, in this case, the conception of time will have to be abstracted from that of movement; for we must not add the conception of the present to that of movement.[412]