Section 12

Now let us first deal with definition, in so far as it has not been dealt with in the Analytics; for the problem stated there 1 has a bearing upon our discussion of substance. The problem I mean is this: what constitutes the unity of the thing of which we say that the formula is a definition? E.g., in the case of man, two-footed animal; for let us take this as the formula of man.

Why, then, is this a unity and not a plurality, animal and two-footed? For in the case of man and white we have a plurality when the latter does not refer to the former, but a unity when it does refer to it, and the subject, man, has an attribute; for then they become a unity and we have the white man.

But in the case before us one term does not partake of the other; the genus is not considered to partake of its differentiae, for then the same thing would be partaking simultaneously of contraries, since the differentiae by which the genus is distinguished are contrary. And even if it does partake of them, the same argument applies, since the differentiae are many; e.g. terrestrial, two-footed, wingless.

Why is it that these are a unity and not a plurality? Not because they are present in one genus, for in that case all the differentiae of the genus will form a unity. But all the elements in the definition must form a unity, because the definition is a kind of formula which is one and defines substance, so that it must be a formula of one particular thing; because the substance denotes one thing and an individual, as we say.

We must first 2 examine definitions which are reached by the process of division.

For there is nothing else in the definition but the primary genus and the differentiae; the other genera consist of the primary genus together with the differentiae which are taken with it. E.g., the primary genus is animal; the next below it, two-footed animal; and again, two-footed wingless animal; and similarly also if the expression contains more terms still.

In general it does not matter whether it contains many or few terms, nor, therefore, whether it contains few or two. Of the two one is differentia and the other genus; e.g., in two-footed animal animal is genus, and the other term differentia.

If, then, the genus absolutely does not exist apart from the species which it includes, or if it exists, but only as matter (for speech is genus and matter, and the differentiae make the species, i.e. the letters, out of it), obviously the definition is the formula composed of the differentiae.

But further we must also divide by the differentia of the differentia. E.g., having feet is a differentia of animal; then in turn we must discover the differentia of animal having feet qua having feet. Accordingly we should not say that of that which has feet one kind is winged and another wingless, (that is if we are to speak correctly; if we say this it will be through incapability), but only that one kind is cloven-footed and another not; because these are differentiae of foot, since cloven-footedness is a kind of footedness.

And thus we tend always to progress until we come to the species which contain no differentiae. At this point there will be just as many species of foot as there are differentiae, and the kinds of animals having feet will be equal in number to the differentiae. Then, if this is so, obviously the ultimate differentia will be the substance and definition of the thing, since we need not state the same things more than once in definitions, because this is superfluous.

However, it does happen; for when we say footed two-footed animal we have simply said animal having feet, having two feet. And if we divide this by its proper division, we shall be stating the same thing several times, as many times as there are differentiae.

If, then, we keep on taking a differentia of a differentia, one of them, the last, will be the form and the substance. But if we proceed with reference to accidental qualities—e.g. if we divide that which has feet into white and black—there will be as many differentiae as there are divisions. It is therefore obvious that the definition is the formula derived from the differentiae, and strictly speaking from the last of them.

This will be clear if we change the order of such definitions, e.g. that of man, saying two-footed footed animal; for footed is superfluous when we have already said two-footed. But there is no question of order in the substance; for how are we to think of one part as posterior and the other prior?

With regard, then, to definitions by division, let this suffice as a preliminary statement of their nature.