by Aristotle
Moreover, whether one counts them as quantities or does not, they have no [30] contrary. For how could there be any contrary to what cannot be grasped just in itself but only by reference to something else? Further, if large and small are to be contraries it will turn out that the same thing admits contraries at the same time, and that things are their own contraries. For the same thing turns out to be at the [35] same time both large and small—since in relation to this thing it is small but in relation to another this same thing is large; so the same thing turns out to be both large and small at the same time and thus to admit contraries at the same time. But [6a1] nothing seems to admit contraries at the same time. In the case of a substance, for example, while it seems to be able to receive contraries, yet it is certainly not at the same time ill and well nor is it at the same time pale and dark; nor does anything else admit contraries at the same time. It turns out also that things are their own [5] contraries. For if large is contrary to small, and the same thing is at the same time large and small, a thing would be its own contrary. But it is impossible for a thing to be its own contrary. Large, therefore, is not contrary to small, nor many to few. So [10] that even if someone says that these belong not to relatives but to quantity, it will still have no contrary.
But it is most of all with regard to place that there seems to be contrariety of a quantity. For people regard up as contrary to down—meaning by ‘down’ the region [15] towards the centre—because the centre is at the greatest distance from the limits of the world. And they probably derive from these their definition of the other contraries also; for they define as contraries those things in the same genus which are most distant from one another.
A quantity does not seem to admit of a more and a less. Four-foot for example: [20] one thing is not more four-foot than another. Or take number: we do not speak of a three as more three than a five, nor of one three as more three than another three. Nor yet is one time called more a time than another. Nor is there a single one, among those we listed, as to which a more and a less is spoken of. Hence a quantity [25] does not admit of a more and a less.
Most distinctive of a quantity is its being called both equal and unequal. For each of the quantities we spoke of is called both equal and unequal. For example, a body is called both equal and unequal, and a number is called both equal and [30] unequal, and so is a time; so also with the others we spoke of, each is called both equal and unequal. But anything else—whatever is not a quantity—is certainly not, it would seem, called equal and unequal. For example, a condition is certainly not called equal and unequal, but, rather, similar; and white is certainly not equal and [35] unequal, but similar. Thus most distinctive of a quantity would be its being called both equal and unequal.
7 · We call relatives all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else. For example, what is larger is called what it is than something else (it is called larger than something); and what is double is called what it is of something else (it is called [6b1] double of something); similarly with all other such cases. The following, too, and their like, are among relatives: state, condition, perception, knowledge, position. For each of these is called what it is (and not something different) of something else. A [5] state is called a state of something, knowledge knowledge of something, position position of something, and the rest similarly. All things then are relative which are called just what they are, of or than something else—or in some other way in relation to something else. Thus a mountain is called large in relation to something else (the mountain is called large in relation to something); and what is similar is called similar to something; and the others of this kind are in the same way spoken [10] of in relation to something.
Lying, standing, and sitting are particular positions; position is a relative. To-be-lying, to-be-standing, or to-be-sitting are themselves not positions, but they get their names paronymously from the aforesaid positions.
There is contrariety in relatives, e.g. virtue is contrary to vice (and each of [15] them is relative), and knowledge to ignorance. But there is not a contrary to every relative; there is no contrary to what is double or treble or anything like that.
Relatives seem also to admit of a more and a less. For a thing is called more [20] similar and less similar, and more unequal and less unequal; and each of these is relative, since what is similar is called similar to something and what is unequal unequal to something. But not all admit of a more and less; for what is double, or [25] anything like that, is not called more double or less double.
All relatives are spoken of in relation to correlatives that reciprocate. For example, the slave is called slave of a master and the master is called master of a slave; the double double of a half, and the half half of a double; the larger larger [30] than a smaller, and the smaller smaller than a larger; and so for the rest too. Sometimes, however, there will be a verbal difference, of ending. Thus knowledge is called knowledge of what is knowable, and what is knowable knowable by knowledge; perception perception of the perceptible, and the perceptible perceptible [35] by perception.3
Sometimes, indeed, they will not seem to reciprocate—if a mistake is made and that in relation to which something is spoken of is not given properly. For example, if a wing is given as of a bird, bird of a wing does not reciprocate; for it has not been given properly in the first place as wing of a bird. For it is not as being a [7a1] bird that a wing is said to be of it, but as being a winged, since many things that are not birds have wings. Thus if it is given properly there is reciprocation; for example, a wing is wing of a winged and a winged is winged with a wing. [5]
It may sometimes be necessary even to invent names, if no name exists in relation to which a thing would be given properly. For example, if a rudder is given as of a boat, that is not to give it properly (for it is not as being a boat that a rudder is said to be of it, since there are boats which have not got rudders); and so there is [10] not reciprocation—a boat is not called boat of a rudder. But perhaps it would be given more properly if given thus, that a rudder is rudder of (or somehow else related to) a ‘ruddered’ (since there is no established name); and now there is reciprocation, if it is given properly—a ruddered is ruddered by a rudder. Similarly [15] in other cases. For example, a head would be more properly given as of a headed than as of an animal, because it is not as being an animal that a thing has a head, since many animals have not got a head. This is perhaps the easiest way to lay hold of things for which there are no established names—if names derived from the original relatives are assigned to their reciprocating correlatives, as in the above [20] case ‘winged’ was derived from ‘wing’ and ‘ruddered’ from ‘rudder’.
All relatives, then, are spoken of in relation to correlatives that reciprocate, provided they are properly given. For, of course, if a relative is given as related to some chance thing and not to just that thing in relation to which it is spoken of, [25] there is not reciprocation. I mean that even with relatives that are admittedly spoken of in relation to correlatives that reciprocate and for which names exist, none reciprocates if a relative is given as related to something accidental and not to just that thing in relation to which it is spoken of. For example, if a slave is given as of—not a master, but—a man or a biped or anything else like that, there is not [30] reciprocation; for it has not been given properly.
Again, if that in relation to which a thing is spoken of is properly given, then, when all the other things that are accidental are stripped off and that alone is left to which it was properly given as related, it will always be spoken of in relation to that. [35] For example, if a slave is spoken of in relation to a master, then, when everything accidental to a master is stripped off—like being a biped, capable of knowledge, a man—and there is left only being a master, a slave will always be spoken of in relation to that. For a slave is called slave of a master. On the other hand, if that in [7b1] relation to which a thing is spoken of is
not properly given, then, when the other things are stripped off and that alone is left to which it was given as related, it will not be spoken of in relation to that. Suppose a slave is given as of a man and a wing [5] as of a bird, and strip off from man his being a master; a slave will no longer be spoken of in relation to a man, for if there is no master there is no slave either. Similarly, strip off from bird its being winged; a wing will no longer be a relative, for if there is nothing winged neither will there be a wing of anything.
[10] One must therefore give as correlative whatever it is properly spoken of in relation to; and if a name already exists it is easy to give this, but if it does not it may be necessary to invent a name. When correlatives are given thus it is clear that all relatives will be spoken of in relation to correlatives that reciprocate.
[15] Relatives seem to be simultaneous by nature; and in most cases this is true. For there is at the same time a double and a half, and when there is a half there is a double, and when there is a slave there is a master; and similarly with the others. [20] Also, each carries the other to destruction; for if there is not a double there is not a half, and if there is not a half there is not a double. So too with other such cases.
Yet it does not seem to be true of all relatives that they are simultaneous by nature. For the knowable would seem to be prior to knowledge. For as a rule it is of [25] actual things already existing that we acquire knowledge; in few cases, if any, could one find knowledge coming into existence at the same time as what is knowable. Moreover, destruction of the knowable carries knowledge to destruction, but knowledge does not carry the knowable to destruction. For if there is not a knowable [30] there is not knowledge—there will no longer be anything for knowledge to be of—but if there is not knowledge there is nothing to prevent there being a knowable. Take, for example, the squaring of the circle, supposing it to be knowable; knowledge of it does not yet exist but the knowable itself exists. Again, if animal is destroyed there is no knowledge, but there may be many knowables.
[35] The case of perception is similar to this; for the perceptible seems to be prior to perception. For the destruction of the perceptible carries perception to destruction, but perception does not carry the perceptible to destruction. For perceptions are to do with body and in body, and if the perceptible is destroyed, body too is destroyed (since body is itself a perceptible), and if there is not body, perception too is [8a1] destroyed; hence the perceptible carries perception to destruction. But perception does not carry the perceptible. For if animal is destroyed perception is destroyed, but there will be something perceptible, such as body, hot, sweet, bitter, and all the [5] other perceptibles. Moreover, perception comes into existence at the same time as what is capable of perceiving—an animal and perception come into existence at the same time—but the perceptible exists even before perception exists; fire and water and so on, of which an animal is itself made up, exist even before there exists an [10] animal at all, or perception. Hence the perceptible would seem to be prior to perception.
It is a problem whether (as one would think) no substance is spoken of as a relative, or whether this is possible with regard to some secondary substances. In the [15] case of primary substances it is true; neither wholes nor parts are spoken of in relation to anything. An individual man is not called someone’s individual man, nor an individual ox someone’s individual ox. Similarly with parts; an individual hand is not called someone’s individual hand (but someone’s hand), and an individual head [20] is not called someone’s individual head (but someone’s head). Similarly with secondary substances, at any rate most of them. For example, a man is not called someone’s man nor an ox someone’s ox nor a log someone’s log (but it is called someone’s property). With such cases, then, it is obvious that they are not relatives, [25] but with some secondary substances there is room for dispute. For example, a head is called someone’s head and a hand is called someone’s hand, and so on; so that these would seem to be relatives.
Now if the definition of relatives given above was adequate, it is either exceedingly difficult or impossible to reach the solution that no substance is spoken [30] of as a relative. But if it was not adequate, and if those things are relatives for which being is the same as being somehow related to something, then perhaps some answer may be found. The previous definition does, indeed, apply to all relatives, yet this—their being called what they are, of other things—is not what their being [35] relatives is.
It is clear from this that if someone knows any relative definitely he will also know definitely that in relation to which it is spoken of. This is obvious on the face of it. For if someone knows of a certain ‘this’ that it is a relative, and being for relatives is the same as being somehow related to something, he knows that also to which this [8b1] is somehow related. For if he does not in the least know that to which this is somehow related, neither will he know whether it is somehow related to something. The same point is clear also in particular cases. For example, if someone knows definitely of a certain ‘this’ that it is double he also, by the same token, knows [5] definitely what it is double of; for if he does not know it to be double anything definite neither does he know whether it is double at all. Similarly, if he knows of a certain ‘this’ that it is more beautiful, he must also, because of this, know definitely what it is more beautiful than. (He is not to know indefinitely that this is more [10] beautiful than an inferior thing. For that sort of thing is supposition, not knowledge. For he will no longer strictly know that it is more beautiful than an inferior thing, since it may so happen that there is nothing inferior to it.) It is plain, therefore, that anyone who knows any relative definitely must know definitely that also in relation [15] to which it is spoken of.
But as for a head or a hand or any such substance, it is possible to know it—what it itself is—definitely, without necessarily knowing definitely that in relation to which it is spoken of. For whose this head is, or whose the hand, it is not [20] necessary4 to know definitely. So these would not be relatives. And if they are not relatives it would be true to say that no substance is a relative.
It is perhaps hard to make firm statements on such questions without having examined them many times. Still, to have gone through the various difficulties is not unprofitable.
[25] 8 · By a quality I mean that in virtue of which things are said to be qualified somehow. But quality is one of the things spoken of in a number of ways.
One kind of quality let us call states and conditions. A state differs from a condition in being more stable and lasting longer. Such are the branches of [30] knowledge and the virtues. For knowledge seems to be something permanent and hard to change if one has even a moderate grasp of a branch of knowledge, unless a great change is brought about by illness or some other such thing. So also virtue; [35] justice, temperance, and the rest seem to be not easily changed. It is what are easily changed and quickly changing that we call conditions, e.g. hotness and chill and sickness and health and the like. For a man is in a certain condition in virtue of these but he changes quickly from hot to cold and from being healthy to being sick. [9a1] Similarly with the rest, unless indeed even one of these were eventually to become through length of time part of a man’s nature and irremediable or exceedingly hard to change—and then one would perhaps call this a state. It is obvious that by a state [5] people do mean what is more lasting and harder to change. For those who lack full mastery of a branch of knowledge and are easily changed are not said to be in a state of knowledge, though they are of course in some condition, a better or a worse, in regard to that knowledge. Thus a state differs from a condition in that the one is easily changed while the other lasts longer and is harder to change.
[10] States are also conditions but conditions are not necessarily states. For people in a state are, in virtue of this, also in some condition, but people in a condition are not in every case also in a state.
Another kind of quality is that in virtue of which we call people boxers or
[15] runners or healthy or sickly—anything, in short, which they are called in virtue of a natural capacity or incapacity. For it is not because one is in some condition that one is called anything of this sort, but because one has a natural capacity for doing something easily or for being unaffected. For example, people are called boxers or [20] runners not because they are in some condition but because they have a natural capacity to do something easily; they are called healthy because they have a natural capacity not to be affected easily by what befalls them, and sickly because they have an incapacity to be unaffected. Similarly with the hard and the soft: the hard is so [25] called because it has a capacity not to be divided easily, the soft because it has an incapacity for this same thing.
A third kind of quality consists of affective qualities and affections. Examples of such are sweetness, bitterness, sourness, and all their kin, and also hotness and [30] coldness and paleness and darkness. That these are qualities is obvious, for things that possess them are said to be qualified in virtue of them. Thus honey because it possesses sweetness is called sweet, and a body pale because it possesses paleness, and similarly with the others. They are called affective qualities not because the things that possess them have themselves been affected somehow—for honey is not [9b1] called sweet because it has been affected somehow nor is any other such thing. Similarly, hotness and coldness are not called affective qualities because the things that possess them have themselves been affected somehow, but it is because each of [5] the qualities mentioned is productive of an affection of the senses that they are called affective qualities. For sweetness produces a certain affection of taste, hotness one of touch, and the rest likewise.
Paleness and darkness, however, and other colourings are not called affective [10] qualities in the same way as those just mentioned, but because they themselves have been brought about by an affection. That many changes of colour do come about through an affection is clear; when ashamed one goes red, when frightened one turns pale, and so on. And so if somebody suffers by nature from some such [15] affection it is reasonable that he should have the corresponding colouring. For the very same bodily condition which occurs now when one is ashamed might occur also in virtue of a man’s natural make-up, so that the corresponding colouring too would come about by nature.