“Things are ‘relative’
- as double to half, and treble to a third, and in general that which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded;
- as that which can heat to that which can be heated, and that which can cut to that which can be cut, and in general the active to the passive
- as the measurable to the measure, and the knowable to knowledge, and the perceptible to perception.
- Relative terms of the first kind are numerically related either indefinitely or definitely, to numbers themselves or to 1.
E.g. the double is in a definite numerical relation to 1, and that which is ‘many times as great’ is in a numerical, but not a definite, relation to 1, i.e. not in this or in that numerical relation to it; the relation of that which is half as big again as something else to that something is a definite numerical relation to a number; that which is n+I/n times something else is in an indefinite relation to that something, as that which is ‘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 always commensurate, and ’number’ is not predicated of that which is not commensurate, but that which exceeds is, in relation to that which is exceeded, so much and something more; and this something is indefinite; for it can, indifferently, be either equal or not equal to that which is exceeded.
All these relations, then, are numerically expressed and are determinations of number, and so in another way are the equal and the like and the same. For all refer to unity. Those things are the same whose substance is one; those are like whose quality is one; those are equal whose quantity is one; and 1 is the beginning and measure of number, so that all these relations imply number, though not in the same way.
- Things that are active or passive imply an active or a passive potency and the actualizations of the potentialities;
e.g. that which is capable of heating is related to that which is capable of being heated, because it can heat it, and, again, that which heats is related to that which is heated and that which cuts to that which is cut, in the sense that they actually do these things. But numerical relations are not actualized except in the sense which has been elsewhere stated; actualizations in the sense of movement they have not. Of relations which imply potency some further imply particular periods of time, e.g. that which has made is relative to that which has been made, and that which will make to that which will be made.
For it is in this way that a father is called the father of his son; for the one has acted and the other has been acted on in a certain way. Further, some relative terms imply privation of potency, i.e. ‘incapable’ and terms of this sort, e.g. ‘invisible’.
“Relative terms which imply number or potency, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else involves a reference to it; but
- that which is measurable or knowable or thinkable is called relative because something else involves a reference to it.
For ’that which is thinkable’ implies that the thought of it is possible, but the thought is not relative to ’that of which it is the thought’; for we should then have said the same thing twice. Similarly sight is the sight of something, not ‘of that of which it is the sight’ (though of course it is true to say this); in fact it is relative to colour or to something else of the sort. But according to the other way of speaking the same thing would be said twice,-’the sight is of that of which it is.’
Things that are by their own nature called relative are called so sometimes in these senses, sometimes if the classes that include them are of this sort; e.g. medicine is a relative term because its genus, science, is thought to be a relative term. Further, there are the properties in virtue of which the things that have them are called relative, e.g. equality is relative because the equal is, and likeness because the like is.
Other things are relative by accident; e.g. a man is relative because he happens to be double of something and double is a relative term; or the white is relative, if the same thing happens to be double and white.