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  Quantity does not, it appears, admit of variation of degree. One thing cannot be two cubits long in a greater degree than another. (20) Similarly with regard to number: what is ‘three’ is not more truly three than what is ‘five’ is five; nor is one set of three more truly three than another set. Again, one period of time is not said to be more truly time than another. Nor is there any other kind of quantity, of all that have been mentioned, with regard to which variation of degree can be predicated. The category of quantity, therefore, (25) does not admit of variation of degree.

  The most distinctive mark of quantity is that equality and inequality are predicated of it. Each of the aforesaid quantities is said to be equal or unequal. For instance, one solid is said to be equal or unequal to another; number, too, and time can have these terms applied to them, as indeed can all those kinds of quantity that have been mentioned. (30)

  That which is not a quantity can by no means, it would seem, be termed equal or unequal to anything else. One particular disposition or one particular quality, such as whiteness, is by no means compared with another in terms of equality and inequality but rather in terms of similarity. Thus it is the distinctive mark of quantity that it can be called equal and unequal. (35)

  7 Those things are called relative, which, being either said to be of something else or related to something else, are explained by reference to that other thing. For instance, the word ‘superior’ is explained by reference to something else, for it is superiority over something else that is meant. Similarly, the expression ‘double’ has this external reference, for it is the double of something else that is meant. [6b] So it is with everything else of this kind. There are, moreover, other relatives, e. g. habit, disposition, perception, knowledge, and attitude. The significance of all these is explained by a reference to something else and in no other way. Thus, a habit is a habit of something, (5) knowledge is knowledge of something, attitude is the attitude of something. So it is with all other relatives that have been mentioned. Those terms, then, are called relative, the nature of which is explained by reference to something else, the preposition ‘of’ or some other preposition being used to indicate the relation. Thus, one mountain is called great in comparison with another; for the mountain claims this attribute by comparison with something. (10) Again, that which is called similar must be similar to something else, and all other such attributes have this external reference. It is to be noted that lying and standing and sitting are particular attitudes, but attitude is itself a relative term. To lie, to stand, to be seated, are not themselves attitudes, but take their name from the aforesaid attitudes.

  It is possible for relatives to have contraries. (15) Thus virtue has a contrary, vice, these both being relatives; knowledge, too, has a contrary, ignorance. But this is not the mark of all relatives; ‘double’ and ‘triple’ have no contrary, nor indeed has any such term.

  It also appears that relatives can admit of variation of degree. (20) For ‘like’ and ‘unlike’, ‘equal’ and ‘unequal’, have the modifications ‘more’ and ‘less’ applied to them, and each of these is relative in character: for the terms ‘like’ and ‘unequal’ bear a reference to something external. Yet, again, it is not every relative term that admits of variation of degree. (25) No term such as ‘double’ admits of this modification. All relatives have correlatives: by the term ‘slave’ we mean the slave of a master; by the term ‘master’, the master of a slave; by ‘double’, (30) the double of its half; by ‘half’, the half of its double; by ‘greater’, greater than that which is less; by ‘less’, less than that which is greater.

  So it is with every other relative term; but the case we use to express the correlation differs in some instances. Thus, by knowledge we mean knowledge of the knowable; by the knowable, that which is to be apprehended by knowledge; by perception, (35) perception of the perceptible; by the perceptible, that which is apprehended by perception.

  Sometimes, however, reciprocity of correlation does not appear to exist. This comes about when a blunder is made, and that to which the relative is related is not accurately stated. If a man states that a wing is necessarily relative to a bird, the connexion between these two will not be reciprocal, for it will not be possible to say that a bird is a bird by reason of its wings. The reason is that the original statement was inaccurate, for the wing is not said to be relative to the bird qua bird, since many creatures besides birds have wings, but qua winged creature. [7a] If, then, the statement is made accurate, the connexion will be reciprocal, for we can speak of a wing having reference necessarily to a winged creature, and of a winged creature as being such because of its wings.

  Occasionally, perhaps, it is necessary to coin words, (5) if no word exists by which a correlation can adequately be explained. If we define a rudder as necessarily having reference to a boat, our definition will not be appropriate, for the rudder does not have this reference to a boat qua boat, as there are boats which have no rudders. (10) Thus we cannot use the terms reciprocally, for the word ‘boat’ cannot be said to find its explanation in the word ‘rudder’. As there is no existing word, our definition would perhaps be more accurate if we coined some word like ‘ruddered’ as the correlative of ‘rudder’. If we express ourselves thus accurately, at any rate the terms are reciprocally connected, for the ‘ruddered’ thing is ‘ruddered’ in virtue of its rudder. So it is in all other cases. A head will be more accurately defined as the correlative of that which is ‘headed’, (15) than as that of an animal, for the animal does not have a head qua animal, since many animals have no head.

  Thus we may perhaps most easily comprehend that to which a thing is related; when a name does not exist, if, from that which has a name, we derive a new name, and apply it to that with which the first is reciprocally connected, as in the aforesaid instances, (20) when we derived the word ‘winged’ from ‘wing’ and ‘ruddered’ from ‘rudder’.

  All relatives, then, if properly defined, have a correlative. I add this condition because, if that to which they are related is stated at haphazard and not accurately, the two are not found to be interdependent. Let me state what I mean more clearly. (25) Even in the case of acknowledged correlatives, and where names exist for each, there will be no interdependence if one of the two is denoted, not by that name which expresses the correlative notion, but by one of irrelevant significance. The term ‘slave’, if defined as related, not to a master, but to a man, or a biped, or anything of that sort, is not reciprocally connected with that in relation to which it is defined, (30) for the statement is not exact. Further, if one thing is said to be correlative with another, and the terminology used is correct, then, though all irrelevant attributes should be removed, and only that one attribute left in virtue of which it was correctly stated to be correlative with that other, the stated correlation will still exist. If the correlative of ‘the slave’ is said to be ‘the master’, (35) then, though all irrelevant attributes of the said ‘master’, such as ‘biped’, ‘receptive of knowledge’, ‘human’, should be removed, and the attribute ‘master’ alone left, the stated correlation existing between him and the slave will remain the same, for it is of a master that a slave is said to be the slave. [7b] On the other hand, if, of two correlatives, one is not correctly termed, then, when all other attributes are removed and that alone is left in virtue of which it was stated to be correlative, the stated correlation will be found to have disappeared.

  For suppose the correlative of ‘the slave’ should be said to be ‘the man’, or the correlative of ‘the wing’ ‘the bird’; if the attribute ‘master’ be withdrawn from ‘the man’, (5) the correlation between ‘the man’ and ‘the slave’ will cease to exist, for if the man is not a master, the slave is not a slave. Similarly, if the attribute ‘winged’ be withdrawn from ‘the bird’, ‘the wing’ will no longer be relative; for if the so-called correlative is not winged, it follows that ‘the wing’ has no correlative.

  Thus it is essential that the correlated te
rms should be exactly designated; if there is a name existing, (10) the statement will be easy; if not, it is doubtless our duty to construct names. When the terminology is thus correct, it is evident that all correlatives are interdependent.

  Correlatives are thought to come into existence simultaneously. (15) This is for the most part true, as in the case of the double and the half. The existence of the half necessitates the existence of that of which it is a half. Similarly the existence of a master necessitates the existence of a slave, and that of a slave implies that of a master; these are merely instances of a general rule. Moreover, (20) they cancel one another; for if there is no double it follows that there is no half, and vice versa; this rule also applies to all such correlatives. Yet it does not appear to be true in all cases that correlatives come into existence simultaneously. The object of knowledge would appear to exist before knowledge itself, for it is usually the case that we acquire knowledge of objects already existing; it would be difficult, (25) if not impossible, to find a branch of knowledge the beginning of the existence of which was contemporaneous with that of its object.

  Again, while the object of knowledge, if it ceases to exist, cancels at the same time the knowledge which was its correlative, the converse of this is not true. It is true that if the object of knowledge does not exist there can be no knowledge: for there will no longer be anything to know. Yet it is equally true that, (30) if the knowledge of a certain object does not exist, the object may nevertheless quite well exist. Thus, in the case of the squaring of the circle, if indeed that process is an object of knowledge, though it itself exists as an object of knowledge, yet the knowledge of it has not yet come into existence. Again, if all animals ceased to exist, there would be no knowledge, but there might yet be many objects of knowledge.

  This is likewise the case with regard to perception: for the object of perception is, (35) it appears, prior to the act of perception. If the perceptible is annihilated, perception also will cease to exist; but the annihilation of perception does not cancel the existence of the perceptible. For perception implies a body perceived and a body in which perception takes place. Now if that which is perceptible is annihilated, it follows that the body is annihilated, for the body is a perceptible thing; and if the body does not exist, it follows that perception also ceases to exist. [8a] Thus the annihilation of the perceptible involves that of perception.

  But the annihilation of perception does not involve that of the perceptible. For if the animal is annihilated, it follows that perception also is annihilated, but perceptibles such as body, heat, sweetness, (5) bitterness, and so on, will remain.

  Again, perception is generated at the same time as the perceiving subject, for it comes into existence at the same time as the animal. But the perceptible surely exists before perception; for fire and water and such elements, out of which the animal is itself composed, (10) exist before the animal is an animal at all, and before perception. Thus it would seem that the perceptible exists before perception.

  It may be questioned whether it is true that no substance is relative, as seems to be the case, or whether exception is to be made in the case of certain secondary substances. With regard to primary substances, it is quite true that there is no such possibility, (15) for neither wholes nor parts of primary substances are relative. The individual man or ox is not defined with reference to something external. Similarly with the parts: a particular hand or head is not defined as a particular hand or head of a particular person, (20) but as the hand or head of a particular person. It is true also, for the most part at least, in the case of secondary substances; the species ‘man’ and the species ‘ox’ are not defined with reference to anything outside themselves. Wood, again, is only relative in so far as it is some one’s property, not in so far as it is wood. It is plain, then, (25) that in the cases mentioned substance is not relative. But with regard to some secondary substances there is a difference of opinion; thus, such terms as ‘head’ and ‘hand’ are defined with reference to that of which the things indicated are a part, and so it comes about that these appear to have a relative character. (30) Indeed, if our definition of that which is relative was complete, it is very difficult, if not impossible, to prove that no substance is relative. If, however, our definition was not complete, if those things only are properly called relative in the case of which relation to an external object is a necessary condition of existence, perhaps some explanation of the dilemma may be found.

  The former definition does indeed apply to all relatives, but the fact that a thing is explained with reference to something else does not make it essentially relative.

  From this it is plain that, (35) if a man definitely apprehends a relative thing, he will also definitely apprehend that to which it is relative. Indeed this is self-evident: for if a man knows that some particular thing is relative, assuming that we call that a relative in the case of which relation to something is a necessary condition of existence, he knows that also to which it is related. [8b] For if he does not know at all that to which it is related, he will not know whether or not it is relative. This is clear, moreover, in particular instances. (5) If a man knows definitely that such and such a thing is ‘double’, he will also forthwith know definitely that of which it is the double. For if there is nothing definite of which he knows it to be the double, he does not know at all that it is double. Again, if he knows that a thing is more beautiful, it follows necessarily that he will forthwith definitely know that also than which it is more beautiful. He will not merely know indefinitely that it is more beautiful than something which is less beautiful, (10) for this would be supposition, not knowledge. For if he does not know definitely that than which it is more beautiful, he can no longer claim to know definitely that it is more beautiful than something else which is less beautiful: for it might be that nothing was less beautiful. It is, therefore, evident that if a man apprehends some relative thing definitely, he necessarily knows that also definitely to which it is related.

  Now the head, (15) the hand, and such things are substances, and it is possible to know their essential character definitely, but it does not necessarily follow that we should know that to which they are related. It is not possible to know forthwith whose head or hand is meant. Thus these are not relatives, and, this being the case, (20) it would be true to say that no substance is relative in character. It is perhaps a difficult matter, in such cases, to make a positive statement without more exhaustive examination, but to have raised questions with regard to details is not without advantage.

  8 By ‘quality’ I mean that in virtue of which people are said to be such and such. (25)

  Quality is a term that is used in many senses. One sort of quality let us call ‘habit’ or ‘disposition’. Habit differs from disposition in being more lasting and more firmly established. The various kinds of knowledge and of virtue are habits, for knowledge, even when acquired only in a moderate degree, is, it is agreed, (30) abiding in its character and difficult to displace, unless some great mental upheaval takes place, through disease or any such cause. The virtues, also, such as justice, self-restraint, and so on, are not easily dislodged or dismissed, so as to give place to vice.

  By a disposition, on the other hand, we mean a condition that is easily changed and quickly gives place to its opposite. (35) Thus, heat, cold, disease, health, and so on are dispositions. For a man is disposed in one way or another with reference to these, but quickly changes, becoming cold instead of warm, ill instead of well. [9a] So it is with all other dispositions also, unless through lapse of time a disposition has itself become inveterate and almost impossible to dislodge: in which case we should perhaps go so far as to call it a habit.

  It is evident that men incline to call those conditions habits which are of a more or less permanent type and difficult to displace; for those who are not retentive of knowledge, but volatile, (5) are not said to have such and such a ‘habit’ as regards knowledge, yet they are disposed, we may say, either better or
worse, towards knowledge. Thus habit differs from disposition in this, that while the latter is ephemeral, the former is permanent and difficult to alter.

  Habits are at the same time dispositions, but dispositions are not necessarily habits. (10) For those who have some specific habit may be said also, in virtue of that habit, to be thus or thus disposed; but those who are disposed in some specific way have not in all cases the corresponding habit.

  Another sort of quality is that in virtue of which, for example, we call men good boxers or runners, or healthy or sickly: in fact it includes all those terms which refer to inborn capacity or incapacity. (15) Such things are not predicated of a person in virtue of his disposition, but in virtue of his inborn capacity or incapacity to do something with ease or to avoid defeat of any kind. Persons are called good boxers or good runners, not in virtue of such and such a disposition, (20) but in virtue of an inborn capacity to accomplish something with ease. Men are called healthy in virtue of the inborn capacity of easy resistance to those unhealthy influences that may ordinarily arise; unhealthy, in virtue of the lack of this capacity. (25) Similarly with regard to softness and hardness. Hardness is predicated of a thing because it has that capacity of resistance which enables it to withstand disintegration; softness, again, is predicated of a thing by reason of the lack of that capacity.

  A third class within this category is that of affective qualities and affections. Sweetness, bitterness, sourness, are examples of this sort of quality, (30) together with all that is akin to these; heat, moreover, and cold, whiteness, and blackness are affective qualities. It is evident that these are qualities, for those things that possess them are themselves said to be such and such by reason of their presence. Honey is called sweet because it contains sweetness; the body is called white because it contains whiteness; and so in all other cases.