Things are called “relative” (a) In the sense that “the double” is relative to the half, and “the triple” to the third; and in general the “many times greater” to the “many times smaller,” and that which exceeds to the thing exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing heated or cut; and in general the active to the passive. (c) In the sense that the measurable is relative to the measure, and the knowable to knowledge, and the sensible to sensation. (a) In the first sense they are said to be numerically relative; either simply, or in a definite relation to numbers or to 1. E.g., “the double” in relation to 1 is a definite number; the “many times as great” is in a numerical relation to 1, but not in a definite relation such as this or that; 1021athe relation of that which is 1.5 times something else to that something is a definite numerical relation to a number; and that which is (n+1)/n times something else is in an indefinite relation to a number, just as “the many times as great” is in an indefinite relation to 1. The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is “so much” plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the “so much.” Thus not only are all these things said to be relative in respect of number, but also the “equal” and “like” and “same,” though in another way: for all these terms are used in respect of “one”. Things are “the same” whose essence is one; “like” whose quality is one; “equal” whose quantity is one. Now “one” is the starting-point and standard of number; and so all these relations involve number, though not all in the same way. (b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere)¹; they have no actualizations in respect of motion. Of things potentially relative, some are further relative in respect of particular times; as, e.g., that which has made or will make is relative to that which has been or will be made. It is in this way that a father is called father of a son; the one has acted, and the other has been acted upon, in a particular way. Again, some things are relative in virtue of a privation of their potentiality; such is “the impossible” and all similar terms, e.g. “the invisible.” Thus relative terms which involve number and potentiality are all relative because their very essence contains a reference to something else; but not because something else is related to their essence. But (c) that which is measurable or knowable or thinkable is called relative because something else is related to its essence. For “thinkable” signifies that there is a thought which thinks it; but thought is not relative to that of which it is the thought (for then the same thing would have been said twice). And similarly sight is the sight of something; not of that of which it is the sight, although this is of course true—it is relative to some color or other similar thing. To describe it in the other way—“the sight of the object of sight”—would be to say the same thing twice. 1021bThings, then, which are called relative of their own nature are so called, some in these senses, and others because the classes which contain them are of this kind. E.g., medicine is reckoned as relative because its genus, science, is thought to be a relative thing. Further, there are the properties in virtue of which the things which possess them are called relative; e.g., “equality” is relative because “the equal” is relative, and “similarity” because “the similar” is relative. Other things are accidentally relative; e.g., a man is relative because he happens to be “double” something else, and “double” is a relative term; or “white” is relative if the same thing happens to be white as well as double.

“Perfect” 〈or “complete”〉 means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are “perfect” when they have no deficiency in respect of the form of their peculiar excellence. And thus by an extension of the meaning we use the term in a bad connection, and speak of a “perfect” humbug and a “perfect” thief; since indeed we call them “good”— e.g. a “good” thief and a “good” humbug. (c) And goodness is a kind of perfection. For each thing, and every substance, is perfect when, and only when, in respect of the form of its peculiar excellence, it lacks no particle of its natural magnitude. (d) Things which have attained their end, if their end is good, are called “perfect”; for they are perfect in virtue of having attained the end. Hence, since the end is an ultimate thing, we extend the meaning of the term to bad senses, and speak of perishing “perfectly” or being “perfectly” destroyed, when the destruction or calamity falls short in no respect but reaches its extremity. Hence, by an extension of the meaning, death is called an “end,” because they are both ultimate things. And the ultimate object of action is also an end. Things, then, which are called “perfect” in themselves are so called in all these senses; either because in respect of excellence they have no deficiency and cannot be surpassed, and because no part of them can be found outside them; or because, in general, they are unsurpassed in each particular class, and have no part outside. 1022aAll other things are so called in virtue of these, because they either produce or possess something of this kind, or conform to it, or are referred in some way or other to things which are perfect in the primary sense.

“Limit” means: (a) The furthest part of each thing, and the first point outside which no part of a thing can be found, and the first point within which all parts are contained. (b) Any form of magnitude or of something possessing magnitude. (c) The end of each thing. (This end is that to which motion and action proceed, and not the end from which. But sometimes it is both the end from which and the end to which, i.e. the final cause.) (d) The reality or essence of each thing; for this is the limit of our knowledge of it, and if it is a limit of the knowledge, it is also a limit of the thing. Thus it is obvious that “limit” has not only as many senses as “beginning” but even more; because the beginning is a kind of limit, but not every limit is a beginning.

“That in virtue of which” has various meanings. (a) The form or essence of each individual thing; e.g., that in virtue of which a man is good is “goodness itself.” (b) The immediate substrate in which a thing is naturally produced; as, e.g., color is produced in the surface of things. Thus “that in virtue of which” in the primary sense is the form , and in the secondary sense, as it were, the matter of each thing, and the immediate substrate. And in general “that in virtue of which” will exist in the same number of senses as “cause.” For we say indifferently “in virtue of what has he come?” or “for what reason has he come?” and “in virtue of what has he inferred or inferred falsely?” or “what is the cause of his inference or false inference?” (And further, there is the positional sense of καθ’ ὅ, “in which he stands,” or “in which he walks”; all these examples denote place or position.) Hence “in virtue of itself” must also have various meanings. It denotes (a) The essence of each particular; e.g., Callias is in virtue of himself Callias and the essence of Callias. (b) Everything contained in the definition; e.g., Callias is in virtue of himself an animal, because “animal” is present in the definition, since Callias is a kind of animal. (c) Any attribute which a thing has received directly in itself or in any of its parts; e.g., the surface is white in virtue of itself; and man lives in virtue of himself, because the soul is a part of the man, and life is directly contained in it. (d) That which has no other cause. Man has many causes: “animal,” “twofooted,” etc.; but nevertheless man is in virtue of himself man. (e) All things which belong to a thing alone and qua alone; and hence that which is separate is “in virtue of itself.” ²