Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Since difference is convertible with the species it constitutes, and is predicated of individuals through the species, while species is universal, and since difference is said of the species equally and convertibly, it must be universal just as the species is. THE DIFFICULTY, however, is whether it is formally universal because it regards the species, or because of its formal relation to the individuals of that species.

There may also be a doubt concerning the inferiors of difference itself: which things are directly and per se inferiors of difference? For some are inferiors immediately under the difference itself, while others are immediately under the species and mediately under the difference. For example, “rational” can be predicated of Peter and Paul as inferiors of “human being”; it can also be predicated of this and that rational thing as inferiors immediately under it.

WE THEREFORE INQUIRE with respect to which inferiors difference is constituted as the third predicable.

I ANSWER AND SAY, FIRST: Difference is not formally a logical universal by its relation to the species, but to inferiors, although it concomitantly has an order to the species as a universal with which it is convertible.

THE REASON is clear, because the formality of universality is taken from the order to its correlative. The correlative of a universal formally is its inferiors: for a universal is related to many as a superior and as something contractible to inferiors. It is clear, however, that the difference of a species is neither superior to nor contractible by that species, since it is equal to it. Therefore it cannot be formally universal with respect to the species or be superior to it.

This is confirmed because something is universal and superior with respect to another when, upon being communicated to that other, it is contracted by it; and something is contracted to another when through contraction it loses universality and abstraction. But by being communicated to a species, difference does not become singular or lose its universality; rather, it preserves it. Therefore with respect to the species it is neither contractible nor superior. Hence one cannot say that it is predicated of the species as a superior universal, for it is not predicated of it as something higher, but as an equal of an equal. This equality therefore presupposes universality concomitantly, as the second part of the conclusion says; it does not formally constitute universality. For example, someone is not formally called a king because he is equal to the king; rather, because he has a kingdom and rules others, he is equal to the king.

IF IT IS SAID that difference is not formally universal by its order to the species because the species is not an inferior, but that it is universal radically, because by regarding the species and being convertible with it, it consequently regards the individuals contained under the species.

THE OBJECTION IS: The root of universality is the same as the foundation of universality, which is unity abstracted from many and an aptitude for many. But unity abstracted from many and an aptitude for them do not have their root in a relation to the species, because this relation is one of convertibility and equality, not superiority to those many things. Therefore difference is not radically universal because it regards the species, but because it is abstracted from and apt for those many things, which are its inferiors.

I SAY, SECOND: As the third predicable, difference does not regard this and that difference as its inferiors—for example, rational and this or that rational thing—but the inferiors contained under the species it constitutes. For example, rational regards Peter and Paul as its inferiors.

THE REASON is clear, because the predicability of the third predicable is “in answer to what sort.” Therefore only those things should be constituted as its inferiors with respect to which difference functions as a superior and as “in answer to what sort,” and can be predicated as “in answer to what sort.” But it does not function in this way with respect to this and that difference, although it does with respect to the individuals of the species. For when I say “this rational thing is rational,” the predication is not “in answer to what sort,” since no difference of this rational thing is predicated of it; rather, its whole and complete nature, whatever it may be, complete or incomplete, is predicated. Therefore this does not predicate a quality of it, but its quiddity, although it is not per se a genus or species, as we said above in the question on genus¹, since it is not contracted by other differences, which would entail an infinite regress. With respect to the inferiors of its species, however, difference is predicated as the account that qualifies their nature and functions as a superior. Therefore these are the inferiors of difference insofar as it is the third predicable.

THE ARGUMENTS ARE RESOLVED.

First it is argued against the first conclusion: “A human being is rational” is a predication of the third predicable; therefore, with respect to human being there is a universality of predicability just as there is predicability. But human being is not conceived there as an individual, but as a species.

The antecedent is certain, because this predication cannot pertain to any other predicable than the third.

This is confirmed because the third predicable has the species as its immediate correlative and through the species regards the individual contained under it; therefore it is called universal more by its order to the species than by its order to the individual.

The consequence is proved because a relation is more denominated by its order to an immediate correlative than by its order to a mediate one. The antecedent is proved because the third predicable formally, insofar as it is such, regards its correlative as “in answer to what sort,” but it does not immediately regard individuals, only the nature of individuals, which is the species; otherwise it would not be an essential quality if it did not immediately qualify the essence. Therefore its immediate correlative is the species itself, or the constituted essence; for that is an immediate correlative which is immediately constituted and qualified by difference.

THE ANSWER IS that the predication “A human being is rational” belongs to the third predicable in a material and metaphysical sense, not formally and logically. For what is predicated of human being is the reality that is the third predicable, but not under the formality and relation of the third predicable or third universal; thus it is more a third predicate than a third predicable. Nevertheless, it concomitantly retains there the universality of the third predicable, which it exercises not with respect to the species but with respect to individuals. This is like genus when it is predicated of an individual, as “Peter is an animal”: there it retains the account of genus, though it is not genus by its order to that individual, but by its order to the species. And when a proper attribute is predicated of specific nature, as “A human being is capable of laughter,” it does not exercise the account of a universal, although it predicates a nature receptive of the fourth predicable by its order to individuals.

To the confirmation, the antecedent is denied. As for its proof, the species is said to be immediately constituted by difference, and in the account of what is constituted it immediately regards difference as a metaphysical difference, not in the account of a universal or logical difference; in that latter account, its immediate correlative is its inferiors. But because difference regards them as predicable “in answer to what sort,” the order to the specific nature as constituted in this way by difference must be presupposed, so that it grounds predicability “in answer to what sort.” It is no contradiction for difference to have one relation to the species as constituted and another as a universal with respect to inferiors. Just as difference regards genus as contracting it and as comparing with it to constitute a species, so it regards the thing constituted by the relation of a constituent; that relation is nevertheless one of reason, because genus, difference, and species are not really distinct. The relation of difference to its inferiors as “in answer to what sort” is a relation of superior to inferiors, which nevertheless presupposes its relation to the species as constituted.

Second it is argued: Difference as the third predicable regards the species and individuals by the same relation or intention; but this relation, insofar as it touches individuals, is universal; therefore it is universal also insofar as it touches the species.

The consequence is clear, and the minor was granted above. The major is proved: First, in regarding the species, difference regards all things contained under it, since whatever is said universally is said of everything contained under it. Again, difference is predicated of the species and individuals under the same concept and predication; therefore it is under the same intention and relation.

This is confirmed because difference is predicated of the species equally and convertibly with it; therefore it is universal, since a species, being universal in itself, can be equaled only by a universal.

THE ANSWER IS: The antecedent is distinguished. If taken as the relation of difference as constituent to the species as constituted, difference regards the species and individuals by the same relation, because it constitutes the same thing in individuals as in the species, namely, nature. But if taken as the relation of difference as a universal and predicable formally and logically, it regards individuals and the species by different relations: it regards individuals as superior and the species as equal.

As for the proof, in regarding the species, difference also regards the individuals under the account of constitution by the same relation, but under the account of superiority and equality by different relations, although one is connected with the other. Thus its predication of individuals is universal, but its predication of the species is not.

To the confirmation, it is said that by being equal to the species difference does indeed have universality, but not with respect to the species to which it is equal; rather, it is universal with respect to individuals, to which it is not equal but superior.