But before definitions, and demonstrations, and divisions, it must be propounded in what ways the question is stated; and equivocal terms are to be treated; and synomyms stated accurately according to their significations.
Then it is to be inquired whether the proposition belongs to those points, which are considered in relation to others, or is taken by itself. Further, If it is, what it is, what happens to it; or thus, also, if it is, what it is, why it is. And to the consideration of these points, the knowledge of Particulars and Universals, and the Antecedents and the Differences, and their divisions, contribute.
Now, Induction aims at generalization and definition; and the divisions are the species, and what a thing is, and the individual. The contemplation of the How adduces the assumption of what is peculiar; and doubts bring the particular differences and the demonstrations, and otherwise augment the speculation and its consequences; and the result of the whole is scientific knowledge and truth.
Again, the summation resulting from Division becomes Definition. For Definition is adopted before division and after: before, when it is admitted or stated; after, when it is demonstrated. And by Sensation the Universal is summed up from the Particular. For the starting point of Induction is Sensation; and the end is the Universal.
Induction, accordingly, shows not what a thing is, but that it is, or is not. Division shows what it is; and Definition similarly with Division teaches the essence and what a thing is, but not if it is; while Demonstration explains the three points, if it is, what it is, and why it is.
There are also Definitions which contain the Cause. And since it may be known when we see, when we see the Cause; and Causes are four -- the matter, the moving power, the species, the end; Definition will be fourfold.
Accordingly we must first take the genus, in which are the points that are nearest those above; and after this the next difference. And the succession of differences, when cut and divided, completes the "What it is." There is no necessity for expressing all the differences of each thing, but those which form the species.
Geometrical analysis and synthesis are similar to logical division and definition; and by division we get back to what is simple and more elementary. We divide, therefore, the genus of what is proposed for consideration into the species contained in it; as, in the case of man, we divide animal, which is the genus, into the species that appear in it, the mortal, and the immortal. And thus, by continually dividing those genera that seem to be compound into the simpler species, we arrive at the point which is the subject of investigation, and which is incapable of further division.
For, after dividing "the animal" into mortal and immortal, then into terrestrial and aquatic; and the terrestrial again into those who fly and those who walk; and so dividing the species which is nearest to what is sought, which also contains what is sought, we arrive by division at the simplest species, which contains nothing else, but what is sought alone.
For again we divide that which walks into rational and irrational; and then selecting from the species, apprehended by division, those next to man, and combining them into one formula, we state the definition of a man, who is an animal, mortal, terrestrial, walking, rational.
Whence Division furnishes the class of matter, seeking for the definition the simplicity of the name; and the definition of the artisan and maker, by composition and construction, presents the knowledge of the thing as it is; not of those things of which we have general notions. To these notions we say that explanatory expressions belong. For to these notions, also, divisions are applicable.
Now one Division divides that which is divided into species, as a genus; and another into parts, as a whole; and another into accidents.
The division, then, of a whole into the parts, is, for the most part, conceived with reference to magnitude; that into the accidents can never be entirely explicated, if, necessarily, essence is inherent in each of the existences.
Whence both these divisions are to be rejected, and only the division of the genus into species is approved, by which both the identity that is in the genus is characterized, and the diversity which subsists in the specific differences.
The species is always contemplated in a part. On the other hand, however, if a thing is part of another, it will not be also a species. For the hand is a part of a man, but it is not a species. And the genus exists in the species. For [the genus] is both in man and the ox. But the whole is not in the parts. For the man is not in his feet. Wherefore also the species is more important than the part; and whatever things are predicated of the genus will be all predicated of the species.
It is best, then, to divide the genus into two, if not into three species. The species then being divided more generically, are characterized by sameness and difference. And then being divided, they are characterized by the points generically indicated.
For each of the species is either an essence; as when we say, Some substances are corporeal and some incorporeal; or how much, or what relation, or where, or when, or doing, or suffering.
One, therefore, will give the definition of whatever he possesses the knowledge of; as one can by no means be acquainted with that which he cannot embrace and define in speech. And in consequence of ignorance of the definition, the result is, that many disputes and deceptions arise. For if he that knows the thing has the knowledge of it in his mind, and can explain by words what he conceives; and if the explanation of the thought is definition; then he that knows the thing must of necessity be able also to give the definition.
Now in definitions, difference is assumed, which, in the definition, occupies the place of sign. The faculty of laughing, accordingly, being added to the definition of man, makes the whole -- a rational, mortal, terrestrial, walking, laughing animal. For the things added by way of difference to the definition are the signs of the properties of things; but do not show the nature of the things themselves. Now they say that the difference is the assigning of what is peculiar; and as that which has the difference differs from all the rest, that which belongs to it alone, and is predicated conversely of the thing, must in definitions be assumed by the first genus as principal and fundamental.
Accordingly, in the larger definitions the number of the species that are discovered are in the ten Categories; and in the least, the principal points of the nearest species being taken, mark the essence and nature of the thing. But the least consists of three, the genus and two essentially necessary species. And this is done for the sake of brevity.
We say, then, Man is the laughing animal. And we must assume that which pre-eminently happens to what is defined, or its peculiar virtue, or its peculiar function, and the like.
Accordingly, while the definition is explanatory of the essence of the thing, it is incapable of accurately comprehending its nature. By means of the principal species, the definition makes an exposition of the essence, and almost has the essence in the quality.