by Aristotle
11 · The question is naturally raised, what sort of parts belong to the form and what sort not to the form, but to the concrete thing. Yet if this is not plain it is not possible to define anything; for definition is of the universal and of the form. If then it is not evident which of the parts are of the nature of matter and which are [30] not, neither will the formula of the thing be evident. In the case of things which are found to occur in specifically different materials, as a circle may exist in bronze or stone or wood, it seems plain that these, the bronze or the stone, are no part of the essence of the circle, since it is found apart from them. Of things which are not seen to exist apart, there is no reason why the same may not be true, e.g. even if all circles [1036b1] that had ever been seen were of bronze (for none the less the bronze would be no part of the form); but it is hard to effect this severance in thought. E.g. the form of man is always found in flesh and bones and parts of this kind; are these then also [5] parts of the form and the formula? No, they are matter; but because man is not found also in other matters we are unable to effect the severance.
Since this is thought to be possible, but it is not clear when it is the case, some are in doubt even in the case of the circle and the triangle, thinking that it is not [10] right to define these by lines and by continuous space, but that all these are to the circle or the triangle as flesh or bones are to man, and bronze or stone to the statue; and they bring all things to numbers, and they say the formula of line is that of two. And of those who assert the Ideas some make two the line itself, and others make it [15] the form of the line; for in some cases they say the Form and that of which it is the Form are the same, e.g. two and the Form of two; but in the case of line they say this is no longer so.
It follows then that there is one Form for many things whose Form is evidently different (a conclusion which confronted the Pythagoreans also); and that it is possible to make one thing the very Form of all, and to hold that the others are not [20] Forms; but thus all things will be one.
Now we have stated that the question of definitions contains some difficulty, and why this is so. Therefore to bring all things thus to Forms and to eliminate the matter is useless labour; for some things surely are a particular form in a particular matter, or particular things in a particular state. And the comparison which [25] Socrates the younger used to make in the case of animal is not good; for it leads away from the truth, and makes one suppose that man can possibly exist without his parts, as the circle can without the bronze. But the case is not similar; for an animal is something perceptible, and it is not possible to define it without reference to movement—nor, therefore, without reference to the parts and to their being in a [30] certain state. For it is not a hand in any state that is a part of man, but the hand which can fulfil its work, which therefore must be alive; if it is not alive it is not a part.
Regarding the objects of mathematics, why are the formulae of the parts not parts of the formulae of the wholes, e.g. why are not the formulae of the semicircles parts of the formula of the circle? It cannot be said, ‘because these parts are perceptible things’; for they are not. But perhaps this makes no difference; for even some things which are not perceptible must have matter; for there is some matter in [1037a1] everything which is not an essence and a bare form but a ‘this’. The semicircles, then, will be parts, not of the universal circle, but of the individual circles, as has been said before; for while one kind of matter is perceptible, there is another which is intelligible.
It is clear also that the soul is the primary substance and the body is matter, [5] and man or animal is the compound of both taken universally; and Socrates or Coriscus, if even the soul of Socrates is Socrates, is taken in two ways (for some mean by such a term the soul, and others mean the concrete thing), but if he is simply this particular soul and this particular body, the individual is analogous to the universal.
Whether there is, apart from the matter of such substances, any other [10] substance, and one should look for some substance other than these, e.g. numbers or something of the sort, must be considered later. For it is for the sake of this that we are trying to determine the nature of perceptible substances, since in a sense the inquiry about perceptible substances is the work of natural science, i.e. of second [15] philosophy; for the natural scientist must not only know about the matter, but also about the substance in the sense of the formula, and even more than about the other. And in the case of definitions, how the elements in the formula are parts of the definition, and why the definition is one formula (for clearly the thing is one, but in virtue of what is the thing one, although it has parts?)—this must be considered [20] later.
What the essence is and in what sense it is independent, has been stated universally in a way which is true of every case, and also why the formula of the essence of some things contains the parts of the thing defined, while that of others does not; and we have stated that in the formula of the substance the material parts will not be present (for they are not even parts of the substance in that sense, but of [25] the concrete substance; but of this there is in a sense a formula, and in a sense there is not; for there is no formula of it with its matter, for this is indefinite, but there is a formula of it with reference to its primary substance—e.g. in the case of man the formula of the soul—, for the substance is the indwelling form, from which along with the matter the so-called concrete substance is derived; e.g. concavity is a form [30] of this sort, for from this and the nose arise snub nose and snubness; [‘nose’ will be found to be involved twice in these terms]);2 but in the concrete substance, e.g. a snub nose or Callias, the matter also will be present. And we have stated that the [1037b1] essence and the individual thing are in some cases the same; i.e. in the case of primary substances, e.g. curvature and the essence of curvature, if this is primary. (By a primary substance I mean one which does not imply the presence of something in something else, i.e. in a substrate which acts as matter.) But things [5] which are of the nature of matter or of wholes which include matter, are not the same as their essences, nor are accidental unities like that of Socrates and musical; for these are the same only by accident.
12 · Now let us treat first of definition, in so far as we have not treated of it [10] in the Analytics; for the problem stated in them is useful for our inquiries concerning substance. I mean this problem:—wherein consists the unity of that, the formula of which we call a definition, as for instance in the case of man, two-footed animal; for let this be the formula of man. Why, then, is this one, and not many, viz. animal and two-footed? For in the case of ‘man’ and ‘white’ there is a plurality [15] when one term does not belong to the other, but a unity when it does belong and the subject, man, has a certain attribute; for then a unity is produced and we have the white man. In the present case, on the other hand, one does not share in the other; the genus is not thought to share in its differentiae; for then the same thing would [20] share in contraries; for the differentiae by which the genus is divided are contrary. And even if the genus does share in them, the same argument applies, since the differentiae present in man are many, e.g. endowed with feet, two-footed, featherless. Why are these one and not many? Not because they are present in one thing; for on this principle a unity can be made out of any set of attributes. But surely all [25] the attributes in the definition must be one; for the definition is a single formula and a formula of substance, so that it must be a formula of some one thing; for substance means a ‘one’ and a ‘this’, as we maintain.
We must first inquire about definitions arising out of divisions. There is [30] nothing in the definition except the first-named genus and the differentiae. The other genera are the first genus and along with this the differentiae that are taken with it, e.g. the first may be animal, the next animal which is two-footed, and again animal which is two-footed and featherless, and similarly if the definition includes [1038a1] more terms. And in general it makes no difference whether it includes many or few terms,—nor, therefore, whet
her it includes few or simply two; and of the two the one is differentia and the other genus, e.g. in ‘two-footed animal’ ‘animal’ is genus, [5] and the other is differentia. If then the genus absolutely does not exist apart from the species which it as genus includes, or if it exists but exists as matter (for the voice is genus and matter, but its differentiae make the species, i.e. the letters, out of it), clearly the definition is the formula which comprises the differentiae.
But it is also necessary in division to take the differentia of the differentia; e.g. [10] endowed with feet is a differentia of animal; again we must know the differentia of animal endowed with feet qua endowed with feet. Therefore we must not say, if we are to speak rightly, that of that which is endowed with feet one part has feathers and one is featherless; if we say this we say it through incapacity; we must divide it into cloven-footed or not-cloven; for these are differentiae in the foot; cloven-footedness [15] is a form of footedness. And we always want to go on so till we come to the species that contain no differences. And then there will be as many kinds of foot as there are differentiae, and the kinds of animals endowed with feet will be equal in number to the differentiae. If then this is so, clearly the last differentia will be the substance of the thing and its definition, since it is not right to state the same things [20] more than once in our definitions; for it is superfluous. And this does happen; for when we say ‘animal which is endowed with feet, and two-footed’ we have said nothing other than ‘animal having feet, having two feet’; and if we divide this by the proper division, we shall be saying the same thing many times—as many times as there are differentiae.
If then a differentia of a differentia be taken at each step, one differentia—the [25] last—will be the form and the substance; but if we divide according to accidental qualities, e.g. if we were to divide that which is endowed with feet into the white and the black, there will be as many differentiae as there are processes of division. Therefore it is plain that the definition is the formula which contains the differentiae, or, according to the right method, the last of these. This would be [30] evident, if we were to change the order of such definitions, e.g. that of man, saying ‘animal which is two-footed and endowed with feet’; for ‘endowed with feet’ is superfluous when ‘two-footed’ has been said. But order is no part of the substance; for how are we to think the one element posterior and the other prior? Regarding the definitions, then, which arise out of divisions, let this much be taken as stated in [35] the first place as to their nature.
13 · Let us again return to the subject of our inquiry, which is substance. As [1038b1] the substrate and the essence and the compound of these are called substance, so also is the universal. About two of these we have spoken; about the essence and about the substrate, of which we have said that it underlies in two senses, either [5] being a ‘this’—which is the way in which an animal underlies its attributes—, or as the matter underlies the complete reality. The universal also is thought by some to be in the fullest sense a cause, and a principle; therefore let us attack the discussion of this point also. For it seems impossible that any universal term should be the name of a substance. For primary substance is that kind of substance which is peculiar to an individual, which does not belong to anything else; but the universal is [10] common, since that is called universal which naturally belongs to more than one thing. Of which individual then will this be the substance? Either of all or of none. But it cannot be the substance of all; and if it is to be the substance of one, this one will be the others also; for things whose substance is one and whose essence is one are themselves also one.
Further, substance means that which is not predicable of a subject, but the [15] universal is predicable of some subject always.
But perhaps the universal, while it cannot be substance in the way in which the essence is so, can be present in this, e.g. animal can be present in man and horse. Then clearly there is a formula of the universal. And it makes no difference even if [20] there is not a formula of everything that is in the substance; for none the less the universal will be the substance of something. Man is the substance of the individual man in whom it is present; therefore the same will happen again, for a substance, e.g. animal, must be the substance of that in which it is present as something peculiar to it. And further it is impossible and absurd that the ‘this’, i.e. the [25] substance, if it consists of parts, should not consist of substances nor of what is a ‘this’, but of quality; for that which is not substance, i.e. the quality, will then be prior to substance and to the ‘this’. Which is impossible; for neither in formula nor in time nor in coming to be can the affections be prior to the substance; for then they would be separable from it. Further, in Socrates there will be a substance in a [30] substance, so that he will be the substance of two things. And in general it follows, if man and such things are substances, that none of the elements in their formulae is the substance of anything, nor does it exist apart from the species or in anything else; I mean, for instance, that no animal exists apart from the particular animals, nor does any other of the elements present in formulae exist apart.
If, then, we view the matter from these standpoints, it is plain that no universal [1039a1] attribute is a substance, and this is plain also from the fact that no common predicate indicates a ‘this’, but rather a ‘such’. If not, many difficulties follow and especially the ‘third man’.
The conclusion is evident also from the following consideration—that a substance cannot consist of substances present in it actually (for things that are thus [5] actually two are never actually one, though if they are potentially two, they can be one, e.g. the double line consists of two halves—potentially; for the actualization of the halves divides them from one another; therefore if the substance is one, it will not consist of substances present in it); and according to the argument which [10] Democritus states rightly; he says one thing cannot come from two nor two from one; for he identifies his indivisible magnitudes with substances. It is clear therefore that the same will hold good of number, if number is a synthesis of units, as is said by some; for two is either not one, or there is no unit present in it actually.
The consequence of this view involves a difficulty. If no substance can consist [15] of universals because a universal indicates a ‘such’, not a ‘this’, and if no composite substance can be composed of actual substances, every substance would be incomposite, so that there would not even be a formula of any substance. But it is thought by all and has been previously stated that it is either only, or primarily, [20] substance that can be defined; yet now it seems that not even substance can. There cannot, then, be a definition of anything; or rather in a sense there can be, and in a sense there cannot. And what we say will be plainer from what follows.
14 · It is clear also from these very facts what consequences confront those [25] who say the Ideas are substances and can exist apart, and at the same time make the Form consist of the genus and the differentiae. For if the Forms exist and animal is present in man and horse, it is either one and the same in number, or different. (In formula it is clearly one; for he who states the formula unfolds the same formula in either case.) If there is a man-in-himself who is a ‘this’ and exists apart, the parts of [30] which he consists, e.g. animal and two-footed, must indicate a ‘this’ and be things existing apart and substances; therefore animal too must be of this sort.
Now if animal, which is in the horse and in man, is one and the same, as you are one and the same with yourself, how will the one in things that exist apart be [1039b1] one, and how will this animal escape being divided even from itself?
Further, if it is to share in two-footed and many-footed, an impossible conclusion follows; for contrary attributes will belong at the same time to it although it is one and a this. If it does not, what is the relation implied when one says the animal is two-footed or has feet? But perhaps these are put together and [5] are in contact, or are mixed. Yet all these are absurd.
But suppos
e the Form to be different in each species. Then there will be practically an infinite number of things whose substance is animal; for it is not by accident that man has animal for one of its elements. Further, animal-in-itself will be many. For the animal in each species will be the substance of the species; for it is not dependent on anything else; if it were, that other would be an element in man, i.e. [10] would be the genus of man. And further all the elements of which man is composed will be Ideas. Now nothing can be the Idea of one thing and the substance of another; this is impossible. Each, then, of the Ideas present in the species of animals will be the ideal animal. Further, from what will these Ideas be derived; how will they be derived from the ideal animal? Or how can an Idea of animal whose essence [15] is simply animal exist apart from the ideal animal? Further, in the case of sensible things both these consequences and others still more absurd follow. If, then, these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some maintain their existence.
15 · Since substance is of two kinds, the concrete thing and the formula (I [20] mean that one kind of substance is the formula taken with the matter, while another kind is the formula in its generality), substances in the former sense are capable of destruction (for they are capable also of generation), but there is no destruction of the formula in the sense that it is ever in course of being destroyed; for there is no generation of it (the being of house is not generated, but only the being of this [25] house), but without generation and destruction formulae are and are not; for it has been shown that no one produces nor makes these. For this reason, also, there is neither definition nor demonstration of sensible individual substances, because they have matter whose nature is such that they are capable both of being and of not being; for which reason all the individual instances of them are destructible. If then [30] demonstration is of necessary truths and definition involves knowledge, and if, just as knowledge cannot be sometimes knowledge and sometimes ignorance, but the state which varies thus is opinion, so too demonstration and definition cannot vary thus, but it is opinion that deals with that which can be otherwise than as it is, [1040a1] clearly there can neither be definition nor demonstration of sensible individuals. For perishing things are obscure to those who have knowledge of them, when they have passed from our perception; and though the formulae remain in the soul unchanged, [5] there will no longer be either definition or demonstration. Therefore when one of those who aim at definition defines any individual, he must recognize that his definition may always be overthrown; for it is not possible to define such things.