The Politics of Aristotle

by Aristotle

  All these cases share a difficulty which occurs with regard to species of a genus, when one posits the universals, viz. whether it is the ideal animal or [25] something other than the ideal animal that is in animals. True, if the universal is not separable, this will present no difficulty; but if the 1 and the numbers are separable, as those who express these views say, it is not easy to solve the difficulty, if one may call the impossible ‘not easy’. For when we apprehend the unity in 2, or in general in [30] a number, do we apprehend a thing-in-itself or something else?

  Some, then, generate magnitudes from matter of this sort, others from the point—and the point is thought by them to be not 1 but something like 1—and from other matter like plurality, but not identical with it; about which principles none the less the same difficulties occur. For if the matter is one, line and plane and solid will [35] be the same; for from the same elements will come one and the same thing. But if the matters are more than one, and there is one for the line and a second for the [1085b1] plane and another for the solid, they either imply one another or not, so that the same results will follow even so; for either the plane will not contain a line or it will be a line.

  Again, how number can consist of the one and plurality, they make no attempt [5] to explain; at least as they state the case, the same objections arise as confront those who construct number out of the one and the indefinite dyad. For the one view generates number from the universally predicated plurality, and not from a particular plurality; and the other generates it from a particular plurality, but the first; for 2 is said to be a first plurality. Therefore there is practically no difference, [10] but the same difficulties will follow,—is it intermixture or position or fusion or generation? and so on. Above all one might press the question, if each unit is one, what does it come from? Certainly each is not the one-in-itself. It must, then, come from the one-in-itself and plurality, or a part of plurality. To say that the unit is a [15] plurality is impossible, for it is indivisible; and to generate it from a part of plurality involves many other objections; for each of the parts must be indivisible (or it will be a plurality and the unit will be divisible) and the elements will not be the one and plurality; for the single units do not come from plurality and the one. Again, the [20] holder of this view does nothing but produce another number; for his plurality of indivisibles is a number. Again, we must inquire, in view of this theory also, whether the number is infinite or finite. For there was at first, as it seems, a finite plurality, from which and from the one comes the finite number of units. And plurality in [25] itself is different from infinite plurality; what sort of plurality, then, is the element which co-operates with the one?

  One might inquire similarly about the point, i.e. the element out of which they make magnitudes. For surely this is not the one and only point; at any rate, then, let [30] them say out of what each of the other points is formed. Certainly not of some distance together with the point-in-itself. Nor again can parts of a distance be indivisible parts, as the parts of plurality out of which the units are said to be made are indivisible; for number consists of indivisibles, but magnitudes do not.

  [35] All these objections and others of the sort make it evident that number and magnitudes cannot exist apart from things. Again, the fact that the chief thinkers [1086a1] disagree about numbers is a sign that it is the incorrectness of the alleged facts themselves that brings confusion into the theories. For those who make the objects of mathematics alone exist apart from sensible things, seeing the difficulty about [5] the Forms and their fictitiousness, abandoned ideal number and posited mathematical. But those who wished to make the Forms at the same time numbers, but did not see, if one assumed these principles, how mathematical number was to exist apart from ideal, made ideal and mathematical number the same—in name, since in fact [10] mathematical number is destroyed; for they state hypotheses peculiar to themselves and not those of mathematics. But he who first supposed that the Forms exist and that the Forms are numbers and that the objects of mathematics exist, naturally separated the two. Therefore it turns out that all of them are right in some respect, but on the whole not right. And they themselves confirm this, for their statements [15] conflict. The cause is that their hypotheses and their principles are false. And it is hard to make a good case out of bad materials, according to Epicharmus: ‘as soon as ’tis said, ’tis seen to be wrong.’ But regarding numbers the questions we have raised and the conclusions we have reached are sufficient; for he who is already convinced [20] might be further convinced by a longer discussion, but one not yet convinced would not come any nearer to conviction.

  But regarding the first principles and the primary causes and elements, the views expressed by those who discuss only sensible substance have been partly [25] stated in the Physics, and partly do not belong to the present inquiry; but the views of those who say there are other substances besides the sensible must be discussed next after those we have been mentioning. Since, then, some say that the Ideas and the numbers are such substances, and that the elements of these are elements and principles of real things, we must inquire regarding these what they say and in what sense they say it.

  [30] Those who posit numbers only, and these mathematical, must be considered later; but as regards those who believe in the Ideas one might survey at the same time their way of thinking and the difficulties into which they fall. For they at the same time treat the Ideas as universal, and again as separable and individual. That [35] this is not possible has been shown before. The reason why those who say substances are universal combined these two views in one, is that they did not make them identical with sensible things. They thought that the sensible particulars were in a [1086b1] state of flux and none of them remained, but that the universal was apart from these and different. And Socrates gave the impulse to this theory, as we said before, by means of his definitions, but he did not separate them from the particulars; and in this he thought rightly, in not separating them. This is plain from the results; for [5] without the universal it is not possible to get knowledge, but the separation is the cause of the objections that arise with regard to the Ideas. His successors, treating it as necessary, if there are to be substances besides the sensible and transient substances, that they must be separable, had no others, but gave separate existence to these universally predicated substances, so that it followed that universals and [10] individuals were almost the same sort of thing. This in itself, then, would be one difficulty in the view we have mentioned.

  10 · Let us now mention a point which presents a certain difficulty both to those who believe in the Ideas and to those who do not, and which was stated at the [15] beginning among the problems. If we do not suppose substances to be separate, and in the way in which particular things are said to be separate, we shall destroy that sort of substance which we wish to maintain; but if we conceive substances to be separable, how are we to conceive their elements and their principles? [20]

  If they are individual and not universal, real things will be just of the same number as the elements, and the elements will not be knowable. For let the syllables in speech be substances, and their elements elements of substances; then there must be only one ba and one of each of the syllables, if they are not universal and the same [25] in form but each is one in number and a ‘this’ and not homonymous (and again they suppose each thing-in-itself to be one). And if the syllables are unique, so are the parts of which they consist; there will not, then, be more a’s than one, nor more than one of any of the other elements, on the same principle on which none of the syllables can exist in the plural number. But if this is so, there will not be other [30] things existing besides the elements, but only the elements. Again, the elements will not be even knowable; for they are not universal, and knowledge is of universals. This is clear both from demonstrations and from definitions; for we do not conclude that this triangle has its angles equal to two right angles, unless every triangle has [35] its angles equal to two right angles, nor that this
man is an animal, unless every man is an animal.

  But if the principles are universal either the substances composed of them are universal too, or non-substance will be prior to substance; for the universal is not a [1087a1] substance, and the element or principle is universal, and the element or principle is prior to the things of which it is the principle or element.

  All these difficulties follow naturally, when they make the Ideas out of elements and claim that there are separate unities apart from the substances which [5] have the same form. But if, e.g., in the case of the elements of speech, the a’s and the b’s may quite well be many and there need be no ideal a and ideal b besides the many, there may be, as far as this goes, an infinite number of similar syllables. The [10] statement that all knowledge is universal, so that the principles of things must also be universal and not separate substances, presents indeed, of all the points we have mentioned, the greatest difficulty, but yet the statement is in a sense true, although [15] in a sense it is not. For knowledge, like knowing, is spoken of in two ways—as potential and as actual. The potentiality, being, as matter, universal and indefinite, deals with the universal and indefinite; but the actuality, being definite, deals with a definite object,—being a ‘this’, it deals with a ‘this’. But per accidens sight sees [20] universal colour, because this individual colour which it sees is colour; and this individual a which the grammarian investigates is an a. For if the principles must be universal, what is derived from them must also be universal, as in demonstrations; and if this is so, there will be nothing capable of separate existence—i.e. no [25] substance. But evidently in a sense knowledge is universal, and in a sense it is not.

  BOOK XIV (N)

  1 · Regarding this kind of substance, what we have said must be taken as [30] sufficient. All philosophers make the first principles contraries: as in natural things, so also in the case of unchangeable substances. But since there cannot be anything prior to the first principle of all things, the principle cannot be the principle as being something else. To suggest this is like saying that the white is the first principle, not qua anything else but qua white, but yet that it is predicable of a subject, and is [35] white as being something else; for then that subject will be prior. But all things are generated from contraries as belonging to an underlying subject; a subject, then, [1087b1] must be present in the case of contraries, if anywhere. All contraries, then, are always predicable of a subject, and none can exist apart. But appearances suggest that there is nothing contrary to substance, and argument confirms this. No contrary, then, is the first principle of all things in the full sense; the first principle is something different.

  [5] But these thinkers make one of the contraries matter, some making the unequal—which they take to be the essence of plurality—matter for the one, which is the equal,1 and others making plurality matter for the one. (The former generate numbers out of the dyad of the unequal, i.e. of the great and small, and the other thinker we have referred to generates them out of plurality, while according to both it is generated by the substance of one.) For even the philosopher who says the [10] unequal and one are the elements, and the unequal is a dyad composed of the great and small, treats the unequal, or the great and the small, as being one, and does not draw the distinction that they are one in formula, but not in number. But they do not describe rightly even the principles which they call elements, for some name the [15] great and the small with the one and treat these three as elements of numbers, two being matter, one form; while others name the many and few, because the great and the small are more appropriate in their nature to magnitude than to number; and others name rather the universal character common to these—that which exceeds and that which is exceeded. None of these varieties of opinion makes any difference to speak of, in view of some of the consequences; they affect only the abstract objections, which these thinkers take care to avoid because their own demonstrations [20] are abstract,—with this exception, that if the exceeding and the exceeded are the principles, and not the great and the small, consistency requires that number should come from the elements before 2 does; for both are more universal than 2, as the exceeding and exceeded are more universal. But as it is, they say one of these [25] things but do not say the other. Others oppose the different and the other to the one, and others oppose plurality to the one. But if, as they claim, things consist of contraries, and to the one either there is nothing contrary, or if there must be something it is plurality, and the unequal is contrary to the equal and the different to the same and the other to the thing itself, those who oppose the one to plurality [30] have most claim to plausibility, but even their view is inadequate, for the one would on their view be a few; for plurality is opposed to fewness, and the many to the few.

  ‘One’ evidently means a measure. And in every case it is some underlying thing with a distinct nature of its own, e.g. in the scale a quarter-tone, in magnitude a finger or a foot or something of the sort, in rhythms a beat or a syllable; and [35] similarly in weight it is a definite weight; and in the same way in all cases, in qualities a quality, in quantities a quantity (and the measure is indivisible, in the [1088a1] former case in kind, and in the latter to the sense); which implies that the one is not, in any instance, in itself a substance. And this is reasonable; for the one means the measure of some plurality, and number means a measured plurality and a plurality [5] of measures. Thus it is natural that one is not a number; for the measure is not measures, but both the measure and the one are starting-points. The measure must always be something predicable of all alike, e.g. if the things are horses, the measure is horse, and if they are men, man. If they are a man, a horse, and a god, the [10] measure is perhaps living beings, and the number of them will be a number of living beings. If the things are man and white and walking, these will scarcely have a number, because all belong to a subject which is one and the same in number, yet the number of these will be a number of classes, or of some equivalent term.

  Those who treat the unequal as one thing, and the dyad as an indefinite [15] compound of great and small, say what is very far from being probable or possible. For these are modifications and accidents, rather than substrata, of numbers and magnitudes—the many and few of number, and the great and small of magnitude—like even and odd, smooth and rough, straight and curved. Again, apart from [20] this mistake, the great and the small, and the like, must be relative to something; but the relative is least of all things a real thing or substance, and is posterior to quality and quantity; and the relatives are accidents of quantity, as was said, but not [25] its matter, since there is something else both for relative in general and for its parts and kinds. For there is nothing either great or small, many or few, or, in general, relative, which is many or few, great or small, or relative without being so as something else. A sign that the relative is least of all a substance and a real thing is the fact that it alone has no proper generation or destruction or movement, as in [30] quantity there is increase and diminution, in quality alteration, in place locomotion, in substance simple generation and destruction. The relative has no proper change; for, without changing, a thing will be now greater and now less or equal, if that with [1088b1] which it is compared has changed in quantity. And the matter of each thing, and therefore of substance, must be that which is potentially of the nature in question; but the relative is neither potentially nor actually substance. It is strange, then, or rather impossible, to make non-substance an element in, and prior to, substance; for [5] all the categories are posterior. Again, the elements are not predicated of the things of which they are elements, but many and few are predicated both apart and together of number, and long and short of the line, and both broad and narrow apply to the plane. If there is a plurality, then, of which the one term, viz. few, is always predicated, e.g. 2 (which cannot be many for if it were many, 1 would be few), there [10] must be also one which is absolutely many, e.g. 10 is many (if there is no number which is greater than 10), or 10,000. How then, in view of
this, can number consist of few and many? Either both ought to be predicated of it, or neither; but according to the present account only the one or the other is predicated.

  2 · We must inquire generally, whether eternal things can consist of [15] elements. If they do, they will have matter; for everything that consists of elements is composite. Since, then, a thing must have come into being out of that of which it consists (and if it is eternal, then if it had come into being it would have done so in that way), and since everything comes to be what it comes to be out of that which is it potentially (for it could not have come to be out of that which had not this capacity, nor could it consist of such elements), and since the potential can be either [20] actual or not,—this being so, however everlasting number or anything else that has matter is, it must be capable of not existing, just like anything which is a single day or any number of years old; if this is capable of not existing, so is that which has lasted for a time so long that it has no limit. They cannot, then, be eternal, since that which is capable of not existing is not eternal, as we had occasion to show in another [25] context. If that which we are now saying is true universally—that no substance is eternal unless it is actuality, and if the elements are matter that underlies substance, no eternal substance can have elements present in it, of which it consists.

  There are some who describe the element which acts with the one as the [30] indefinite dyad, and object to the unequal, reasonably enough, because of the ensuing difficulties; but they have got rid only of those objections which inevitably arise from the treatment of the unequal, i.e. the relative, as an element; those which arise apart from this opinion must confront even these thinkers, whether it is ideal [35] number, or mathematical, that they construct out of those elements.