Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Division is “an expression distributing some thing by its members, or a term by its various significations,” as when I say: “Of animal, one is rational and another irrational”; “canis signifies a constellation and signifies an animal.”

Because division is ordered to making manifest, by distribution, the confusion of what is divided, just as definition is ordered to making manifest its quiddity, three conditions are required for a good division. First, each member must be inferior, that is, smaller than what is divided, for every whole is greater than its part. Second, all the dividing members together must exhaust or equal the whole divided, because in a whole there is nothing other than all its parts together. Third, the dividing members must have some opposition between them, at least formal opposition, because if they had no opposition, they would have no distinction but rather identity, and thus would not be different members. All these conditions can be seen in this division: Of animals, one is rational and another irrational; and in this one: Of goods, one is honorable, another useful, another pleasant.

Some add a fourth condition: that division be made into only two dividing members, or at least as few as possible. But although it is true that every division can be reduced to two members if it is stated by contradictories, as in “Of goods, one is honorable and another is not honorable,” this is not always necessary for a good division. Rather, when some genus is distributed into species immediately subordinate to it on an equal footing, it may be divided into those species. But if it is not divided into several species immediately and equally subordinate to it, division should be made into two members, or as few as possible, and then distributed into other subordinate members. Thus substance would not be well divided into man, plant, and angel, but in a certain order into corporeal and spiritual; corporeal into living and nonliving, and so on.

There are many species or modes of division. For just as a whole, which division distributes, is said in many ways, so too is division. There is an essential whole, an integral whole, a universal whole, and a potential whole, and thus the species of division can be multiplied.

To enable you to grasp them all briefly, make two lines or orders. One line consists of divisions per se, the other of divisions per accidens, or accidental divisions. In the division per se, include five species, which are gathered in this way. Whatever is divided is either a vocal sound signifying with respect to its significations, or the thing signified. If the former, it is a division of the name; if the latter, a division of the thing. A thing that is a whole can be compared either with the parts by which it is integrated, the parts by which it is essentially constituted, or the parts subordinated to it. If division is made in the first way, it is partition, by which something is divided into its integral parts, as when you say: “The human body is divided into head, chest, and feet”; “The universe is divided into angels, corruptible bodies, and incorruptible bodies.” If in the second way, it is an essential division into its constituents, as when you say: “Of man, one part is soul, another body”; or, “Of man, one extreme is animal, the other rational.” If in the third way, division is either into parts subordinated to the whole according to predication or according to power. If according to predication, it is division of a genus into species, because the genus is predicated of the species as of its inferiors. Division of a genus by differences also belongs here; indeed, it seems to be the same division, because the genus is not divided into differences, but by differences into species. It is explained better when made by differences, as in: “Of animals, one is rational, another irrational.” This is the most proper and quidditative division, since it concerns those things into which and by which a genus is essentially contracted, and in which the divided item is predicated of the dividing members. If division is made into parts subordinated to the whole that are related as powers, it is division of a potential whole, as when you say: “Of soul, one power is intellective, another appetitive”; “Of prudence, one power is judicative, another deliberative, another imperative.” This division is according to the different functions or powers of a thing.

In the line of divisions per accidens, although divisions can be multiplied infinitely, because no certain rule is given for things that are accidental, nevertheless three are more frequent. First is division of a subject into accidents, as: “Of animals, one is white, another black.” Second, conversely, division of an accident into subjects, as: “Of white things, one is snow, another milk.” Third, division of an accident into accidents, as: “Of white things, one is sweet, another bitter,” and so on.

There are three rules of division, or topics for arguing, which are derived from the conditions of a good division. First: From the divided whole to its division, and conversely, the consequence holds affirmatively or negatively. This is clear because they are mutually convertible. Second: From the divided whole together with the negation of one member, if the division has two members, or of several members, if it is multiple, to the positing of the remaining member, the consequence is good; for example: “A horse is an animal and is not rational; therefore it is irrational.” Third: When the members are really opposed, the consequence from positing one member to denying the other holds good. This is clear because opposites cannot exist together, at least naturally and in themselves.