Commentaria in Primam Partem Summae Theologiae

A clear title. – In the body, a single conclusion, responsive to the question in the affirmative: One is opposed to many in different ways.

It is proved. The one, the principle of number, is opposed to number as a measure to what is measured; but the one converted with being is opposed as the undivided to the divided. Therefore. – The antecedent, in its first part, is proved from Book X of the Metaphysics: because measure belongs first to the one, and number is a measured multitude. The second part is evident. The consequence, moreover, is clear: because one opposition is relative and the other privative.

II. Note here that, although the text intends to speak of different unities and multitudes, from this doctrine you will nevertheless be able to draw most excellently the conclusion that the same unity, taken in different ways—namely as the principle of number and as an undivided thing—is opposed in different ways to the same multitude taken in different ways, namely under the aspect of number and under the aspect of a divided thing. And thus this distinction will sometimes be a distinction of things and sometimes a distinction of reasons. And when it is a distinction of reasons, it belongs both to each unity and to each multitude: since one, convertible with being (ens), is the principle of transcendent number, while one in the category of quantity is the undivided.

III. In response to the second, a difficulty arises as to how it is verified that multitude is composed of unities, not according to what they have of indivision, but according to what they have of entity. For this is manifestly impossible in transcendent multitude, of which the text speaks. For either the discourse is about multitude as multitude is; or about many things. Not about many things, as is clear from the force of the argument and the reply, when it is said that multitude is a heterogeneous whole. But concerning multitude itself, it is evident that it is not composed of one things, but of unities: otherwise transcendent multitude, as multitude is, would be substance, being composed as it were from the substances of things.

IV. To this it is said that both one and many, taken transcendentally, can be understood in two ways: in one way, substantially; in another way, completively, or formally. If they are understood in the first way, it is evident that multitude is composed of things that are one, and that it is a substance, or a real being: and thus the text¹ seems to be interpreted according to the plain sense of the letter. – And if it is objected: therefore he does not speak of multitude formally, it will be said that he speaks of multitude formally with respect to what it really is.

Speaking, however, more deeply and more formally, it seems to me that what must be said is that this is a discourse on unity and multitude formally and universally: and that by those words, unities according to that which they have of entity, the text does not mean the thing which is one; rather, it means the very nature of unity, insofar as it exercises the act of being. That this may be perceived more clearly, let us begin from one in the genus of quantity. Unity can be taken from the genus of quantity in two ways. In one way, as it is not a number, which is to be undivided in itself, just as number is divided into several unities. And thus it is clear that it does not compose number; just as neither does not-house compose a house. In another way, as it is in itself such an entity, say an accident: and thus it composes number. Transcendental unity likewise can be taken in two ways. First, as it is undivided, which is to be not a multitude: and thus it is impossible for it to compose a multitude, for the reason given. In another way, according to that which it is, that is, according to the very negation of division, but insofar as it has the character of being: and thus it composes a multitude taken formally and completively. So that this distinction, contracted to one and many transcendentally, is not a distinction of privation from a positive subject; rather, it is a distinction of a privative act from a positive act. So that indivision itself, insofar as it exercises an act of privation, does not compose; and this same thing, insofar as it has the character of a certain entity, composes a multitude, which, according to truth, is formally a negative being, more than one is. – And that this is the meaning of the text is evident not only from its formal sense, but also from the reply to the fourth objection, where it is said that divided things do not have the character of multitude, unless each of the things divided has the character of one. For here it clearly appeared that multitude arises formally from unities taken formally: and consequently from negations, since he had taught in the preceding article that only a negation is added formally.

V. In response to the fourth, a doubt arises as to how these words are verified: division is prior to unity, not simply, but according to the manner of our apprehension. For it seems that division is prior to unity simply. Since a habit is naturally prior to its privation, and division is related to unity as habit to privation: therefore. – Nor can it be said that division is not truly a habit by which unity is privated in itself, but is a habit according to our way of understanding; for one would have to assign, at least circumlocutorily, what that habit is by which unity is privated in itself. Nor would it be easy to devise this. For that habit in itself is either something positive or negative. If positive, then something positive beyond being (ens) would be prior to unity, which is impossible. If negative, then some negation is prior to unity; and if this is not unfitting, why is it unfitting that division, which is a negation, be prior to unity?

VI. To this it is said that the labor is in equivocation. For both propositions are true: both that division is prior to unity simply, that is, in itself, in intelligible being (since division is a negation, which is a being of reason): and that division is posterior to unity simply, that is, according to simple being, which is being in the nature of things; for intelligible being is only being in a certain respect.

The first proposition is proved from what has been said. For it is not intelligible that affirmation should not be prior to negation. Now to be one is to be this and not to be not-this: wherein it is evident that the negation of the other extreme of contradiction is included in the intelligibility of unity. The extremes of contradiction, therefore, whose very opposition is division, naturally precede unity. For first there is man, and in that same prior there is not-man, in the order of intelligible being: and thus there is division. Then man is man and is not not-man, which is to be one, that is, undivided. For it is not divided in itself, so as to be man and not-man. In respect of the privation of such division, each thing is and is called one: if one is a privative name according to truth, as we suppose. Nor is it unfitting that the negation of division be prior to the negation of unity: although it is impossible that the positing of division in reality precede the positing of unity.

The second proposition is evident in itself. For it is not necessary, in order that man be and be understood as one, that the negation of man be in some nature, say bovine or celestial. For if man alone existed, he would nevertheless be one: just as, before the creation of the world, God was one, and not-God was in no thing; but once other things were created, the division of God from not-God was posited in the nature of things. Concerning which division the text says that it is not prior simply, as is clear from the end of the response, where it is said: second we apprehend that this being is not that being, and thus we apprehend division. What could be clearer? In saying this being is not that being, he expressed division in the nature of things. And on account of the same division he said that we define simples from composites. He therefore subordinated division, both real and positive, to unity formally: but not contradictory division in intelligible being.