Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

We will resolve questions concerning division by means of questions rather than arguments. Is this the quidditative and proper definition of division: “a discourse, namely, that distributes a thing or a name through its parts”? We answer affirmatively. It is given through what is proper and quidditative to division. “Discourse” is put in place of the genus, or as the matter, by which we also understand a complex term. Like definition, division can have the role of a predicate in a categorical proposition and therefore the role of a complex term, and it can belong to the first operation. “Distributing” means “by distributing and manifesting”; this explains the specific and differentiating character of the mode of knowing proper to division, since by distributing and distinguishing the parts it manifests the confusion of the whole. For both definition and division manifest something through parts: definition manifests constitutive parts, while division manifests quasi-quantitative parts. Definition regards the totality of quiddity, whereas division regards the totality of quantity or distribution. Having parts belongs to quiddity and quantity, though in different ways. Thus definition explains what is defined through parts by constituting it, not by distributing it; division distributes and removes the confusion of what is divided through distribution and, as it were, enumeration of the parts. “A thing or a name” is said to indicate the twofold division of a name and of a thing, which we treated in the text.

Second, you will ask whether logical division treats and distributes only a logical whole, or also extends to physical, metaphysical, nominal, real, and other divisions.

For the resolution, note that there is a logical whole, that is, a predicable or universal in relation to its inferiors; a physical whole, that is, a composite of matter and form or of integral parts; a metaphysical whole, that is, a composite of genus and specific difference; a potential whole, that is, something consisting of diverse powers or potential parts; and an accidental whole, that is, something consisting of many accidents. Some therefore say that it belongs only to dialectic to teach the division of a logical whole.

We must say, however, that in all these divisions one can consider the matter in which division is exercised, or the form, namely, the technique or manner of manifesting and carrying out division. As to its matter, not all divisions belong to logic, since many are physical or metaphysical. Thus, materially, it belongs per se to logic only to consider division of the logical whole, namely, a universal or predicable, into subjective parts, as a genus into species, a species into individuals, and so forth. But as to the form, or technique or manner of dividing—which is the second intention of division—it belongs to logic to treat every division, because whether physical or metaphysical, such division is a mode of knowing and is performed in a methodical way. Physical or metaphysical definition likewise belongs to logic, since logic treats the technique and intention of all definitions.

Third, you will ask whether division can be given by negative or contradictory terms, for example: “An animal is either a man or a non-man.”

Some deny this, both because such a division gives us no information—the negative member gives no information but merely negates—and because the divided thing is understood in each member and shared by the dividing members. But “non-man” is broader than animal and does not share the notion of animal.

Nevertheless, it must be said that the proposed division is methodical and conforms to logical rules. It is proved because in a good division the members must be opposed to one another; otherwise they would not be separated by differences, but would either be identical or disparate. They need not, however, be relatively or contrarily opposed; therefore they can be contradictorily opposed. This is confirmed: “A man is either seeing or blind,” “air is either dark or bright,” and “an animal is either rational or irrational” are good divisions, one member of each being negative or privative, yet they are commonly accepted. Therefore the proposed division is good.

To the reasons for doubt we reply that the negative member is not taken absolutely, but as falling upon and restricted to the divided item; thus it is not broader than what is divided. Hence when I say, “An animal is either a man or a non-man,” “non-man” is not understood absolutely and in its whole extension, but as an animal that is not a man; thus it is no broader than animal as such. Likewise, in “irrational,” animal is understood, not “irrational” absolutely as it is found in a stone. In this way the negative member, as applied to this divided thing, gives information and manifests something, namely, every irrational animal, every brute animal, and so on.

Objection: A genus is rightly divided by differences, as animal into rational and irrational; yet the genus is not predicated of the differences. Therefore the divided thing should not be understood in the dividing members.

We reply that a genus is not divided into differences, but divided by differences into species; the genus is predicated of the species. Thus, when animal is divided into rational and irrational, what is understood is: “One animal is rational, another animal is irrational,” and these are species.

You will object: In partition, by which a thing is divided into integral parts, the divided thing cannot be predicated of the dividing members, since the divided thing is a whole and the dividing items are parts, and a whole is not predicated of a part. In accidental division, too, an accident is not predicated of the subjects themselves, nor the subject of the accidents, since they are not identical. Therefore.

We reply that in the first case the divided item is not predicated of each part; rather, each part shares something of the whole, not by predication but by dependence on it. In the second case the divided item is predicated of the dividing members, namely, of subjects accidentally; there the accident is identified with the subject and conversely, because the accident is signified concretely. Thus it does not signify the form alone, but something having the form, and what has the form is identified with the subject. Hence St. Thomas says, ST I, q. 13, a. 12, body, that man and white are the same in subject but differ in account, that is, in form and quiddity.

Fourth, you will ask whether analogical division is included in this mode of knowing.

Some deny it, saying that in analogical division there is no divided item in which the dividing members agree, except for a name, and there are no differences by which the division is made.

NEVERTHELESS, THE ANSWER MUST BE AFFIRMATIVE, because analogical division is methodical and belongs to a mode of knowing: its dividing members are really distinct from one another, as God and creature, accident and substance, yet they agree in something one—not simply or by univocal unity, but proportionally and analogically. Although the analogical item has no differences, it has modes by which it can be divided. This suffices for a methodical way of dividing, since division requires some order in its execution, and this belongs to logic.

Finally, you will ask whether something can be divided by several essential divisions, or whether every division must be adequate, so that it completely exhausts what is divided and leaves no room for another division.

THE ANSWER IS that when something is divided according to that by which it is ultimately and indivisibly constituted in its essence, it admits only one essential division. But if several formal aspects concur, each of which can be participated in a different way, it can then be divided by several essential divisions, though they are inadequate. Thus St. Thomas, ST I-II, q. 95, a. 4, takes different divisions of human law from the different principles from which it proceeds and the different ends it regards. Sins, too, are divided in species into carnal and spiritual, and according as they are against God or neighbor. See also the cited place and ST I-II, q. 72, aa. 2 and 4, and our later treatment of divisions of propositions.