Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

We shall briefly settle this matter, discussing what pertains to division more by way of questions than arguments.

First, then, you will ask whether this is a proper and quidditative definition: “Division is an expression distributing a thing or a name through its parts.”

WE REPLY that it is proper and quidditative in the same way as the definition of definition and of a mode of knowing. It is given through what is proper and quidditative to division. For “expression” is posited in place of the genus, or matter; by “expression” we understand an expression that is a mode of knowing. This is required by the phrase “distributing,” which means the same as manifesting by distribution. “Distributing through parts” explains division’s proper difference, because by distributing and distinguishing the parts it manifests the confusion of some whole. Note here that both definition and division manifest something through parts, but definition manifests constitutive parts, while division manifests parts that are, as it were, quantitative, because definition regards the totality of quiddity, whereas division regards the totality of quantity or distribution.

“A thing” is said to indicate the twofold division, one of a name and the other of a thing, which we discussed in the text.

Second, you will ask whether logical division considers only a logical whole and its division, or embraces all divisions, whether physical or metaphysical, of a name or of a thing, and so on.

Some think that it belongs to dialectic alone to set out the division of a logical whole—that is, of a predicable or universal into its inferiors. For there is a physical whole consisting of matter and form or of integral parts; a metaphysical whole consisting of metaphysical parts, genus and difference; a potestative whole consisting of different powers or potential parts; an accidental whole consisting of many accidents; and finally a logical and universal whole consisting of subjective parts of which it is predicated. Only this last seems to belong to logic.

FOR MY PART, I SAY that in all these divisions we can consider either the art and method of manifesting a division and proceeding in it, so that the intellect makes it aptly and without error, or the matter itself in which the division is made and exercised. If we consider the matter, not all divisions belong to logic, since many are physical or metaphysical divisions, or partitions of quantity, distinguished from logical division. In this respect it is true that, on the side of the matter divided, it belongs per se to logic only to consider the division of a logical or predicable whole into subjective parts, as genus into species, species into individuals, and so on. But if we speak of the art and method of dividing, which is the second intention of division, then it belongs to logic to treat every division. For even when something is divided by an accidental or physical division, that division is a mode of knowing and is made artfully; therefore it belongs to logic, just as physical, metaphysical, and descriptive definition belong to logic because it treats the art and intention involved in all of them.

Third, you will ask whether a division can be given through negative or contradictory terms, so that one member of the division is negative and the other positive.

Some deny this, first because such a division makes nothing known to us: the negative member of the division makes nothing known but purely denies, as if you said, “Animal is divided into human being and nonhuman being”; by “nonhuman” nothing is made known to me. They also argue that the divided thing must be understood in each member of the division, since the divided thing is participated in by the dividers. But “nonhuman” does not participate in the account of animal, since nonhuman extends more broadly than animal.

NEVERTHELESS, the stated division is artful and conforms to logical rules. In a good division the members must be opposed to one another; otherwise, if they were not opposed, they would not be separated by differences but would either be the same or unrelated. They need not always be relatively or contrarily opposed, however; they can therefore be contradictorily opposed. This is confirmed because a division can be made by privative terms, as when you say, “One human being sees, another is blind”; “one part of the air is dark, another bright.” Therefore division can also be made through negative terms, since privation formally is a kind of negation. It is clear that everyone commonly admits this division: “Animal is divided into rational and irrational”; yet “irrational” is negative or privative with respect to “rational.”

Accordingly, since the divided thing itself is communicated to the members of the division, a negative member is always understood as falling on that divided thing—not absolutely, but restricted to it—and thus it does not extend more broadly than what is divided. When I say, “Animal is divided into human and nonhuman,” “nonhuman” is not understood absolutely and in its full breadth, but as the animal that is not human. An animal that is not human does not extend more broadly than animal as such. Likewise, in “Animal is divided into rational and irrational,” what is understood is “animal that is irrational,” not “irrational” absolutely, as it is also found in a stone. In this way the negative term too makes something known insofar as it is conjoined to the divided thing. For “nonhuman animal” or “irrational animal” makes known to me every brute animal absolutely and confusedly, and that is a kind of knowledge.

IF YOU SAY: Genus is rightly divided by differences, as “animal is divided into rational and irrational,” and yet genus is not predicated of differences; therefore the divided thing should not be understood in the members of the division.

We reply that genus is not divided into differences, but is divided by differences into species, as St. Thomas says in Metaphysics III, lecture 8,¹ and Book X, lecture 10.² Genus is predicated of species. Thus, when “animal” is divided into rational and irrational, what is understood is “one is a rational animal, another an irrational animal,” which are species.

YOU WILL OBJECT: In a partition by which a thing is divided into integral parts, the divided thing cannot be predicated of the dividers, since the whole is not predicated of its parts. The same applies to accidental division, in which an accident is not predicated of its subjects, nor a subject of its accidents, because they are not identified.

We reply that the divided thing is predicated of the dividers when it is divided into subjective parts, whether essentially or accidentally. When it is divided into integral or potestative parts, the divided thing cannot be predicated of each part; rather, each part participates in something of the whole, not by predication but by dependence on it. In accidental division, however, the divided thing is predicated of the dividers, namely, of the subjects accidentally; there the accident is identified with the subject, or conversely, because the accident is signified concretely and thus does not signify only the form but something having the form. What has the form is identified with the subject. For this reason St. Thomas said in Summa theologiae I, q. 13, a. 12, that a human being and a white thing 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. It seems not, because the members dividing an analogate are primarily diverse, not different from one another; therefore they do not presuppose some divided thing in which they agree, except perhaps in name, as equivocal things do. In that case it would be a division of a name, not of a thing. Likewise, an analogate is not divided according to different concepts, since, for example, a lower concept dividing being does not add anything to being. For if it added something, that addition would be being, but this is already supposed to be included in being. Therefore there is only a division according to different explanations of the same concept, which is properly not a division but a different explanation of the same thing.

NEVERTHELESS, WE REPLY that analogical division is artful, belongs to logic, and pertains to a mode of knowing, because its members are really distinct from one another, as God and creature, accident and substance. They also have an agreement and are one—not absolutely and simply, but as is explained more fully in Logic q. 13 and 14. They therefore have agreement in something real that is one proportionally, and have simple difference among themselves; this suffices for an artful mode of dividing, because making a division requires some ordering.

To the reason for doubt we say that the members of a division are called primarily diverse because they do not agree in some genus or become contracted through differences added to a genus. This does not prevent them from truly dividing a higher account, as it were by contracting and dividing it through different modes and explanations, though not through added differences, as will be said in the cited places in Logic. This suffices for them to agree in some concept according to a proportional unity and to differ absolutely according to different concepts. They agree not merely in name but in the thing conceived—for example, in being, which is one proportionally but not simply, as will be said there.

Finally, you will ask whether every division must be essentially adequate, so as to exhaust the whole divided thing, or whether something can be divided essentially by several divisions.

This will be discussed below when we treat the divisions of a proposition.³ FOR NOW, WE SAY that when something is divided according to that by which it is constituted in its essence ultimately and indivisibly, it admits only one essential division. But if several formalities concur, each of which can be participated in a different way, there is no obstacle to its being divided essentially by several inadequate essential divisions. On this rule see St. Thomas, Summa theologiae I–II, q. 95, a. 4, treating the division of human law, which takes different divisions from the different principles from which it proceeds and the different ends it regards. Sins are also divided in species into carnal and spiritual sins, and according to whether they are against God or neighbor, as is said in Summa theologiae I–II, q. 72, aa. 2 and 4.