Disputationes metaphysicae

1. In this matter Aristotle, Metaphysics IV, c. 2, indicates that one and many are opposed privatively. But in Book X, c. 1, he thinks that they are opposed neither relatively, because one is not said in relation to another; nor contradictorily, because neither is a mere negation, for neither can truly be said both of things which are not and of things which are; nor merely privatively, because neither consists in privation alone, but expresses something positive; nor finally merely contrarily, because they formally include some negation; whence he concludes that they are opposed in a certain way contrarily and in a certain way privatively. St. Thomas, however, I, q. 11, a. 2, thinks that this opposition approaches more to privative, because one (he says) is opposed to many as the undivided to the divided.

2. In order, however, that this may be explained more fully, it is to be considered that many can be compared to one in two ways: first, as they are many; secondly, as they are in some way one; in which way we said that multitude is a member dividing being in that partition by which it is divided into one and many. Wherefore, speaking formally of multitude as it is a member of that division, it differs from one simply so called as the imperfect from the perfect, and so they are as it were two disparate and distinct notions. Just as, if we consider number under the notion of one discrete quantity, or suppose that it has one formal notion as such, it will be distinguished from unity as a certain formal notion distinct from the formal notion of one, as two disparate natures or species are wont to be distinguished, or as the line is distinguished from the point. But considering multitude as it is multitude and a mere aggregation of several, we can then consider either only that which is positive in unity and multitude, and so they are related after the manner of whole and part, because multitude results in this way from unities; or we can consider the included negation, and so each includes some negation; for multitude, by expressing many positive beings, includes this negation, that one is not the other, which can be called the negation of identity; but one expresses the negation of division. And so they seem to be mutually opposed privatively according to diverse notions; for one includes the negation of division, which is of the notion of multitude; but multitude includes the negation of identity or real conjunction, which is of the notion of unity. Yet, because multitude includes unity and requires indivision in the individual unities of which multitude itself consists, but one conversely does not include multitude, nor the division which is of the notion of multitude, but rather removes it, therefore one is simply said to be opposed to multitude after the manner of privation, rather than conversely.

3. Whence, although St. Thomas, above, ad 2, says that unities compose multitude according to what they have of entity, not according to what they have of indivision, which he repeats in other places, as De potentia, q. 9, a. 7, ad 10 and 14, this nevertheless seems to be understood with proportion, namely of multitude in so far as it is something positive. But if all the things which multitude includes are considered, it seems it must be said otherwise; for, as the same St. Thomas says, I, q. 11, a. 2, ad 4, and in the said question of De potentia, a. 7, ad 15, in the understanding of multitude is included being divided from another, and that each of them is one in itself: for however much (he says) things are understood as divided, multitude will not be understood unless each of the divided things is understood to be one, and consequently undivided; it follows, therefore, that one composes multitude as regards all the things which are of its notion, not only by reason of the positive but also by reason of the negation which one expresses, because it is of the notion of multitude not only that one thing is not another, but also that each is undivided in itself, because otherwise they would not compose a certain and determinate multitude. Nor do I sufficiently understand what Cajetan means on the aforesaid solution ad 2 of St. Thomas, saying that multitude formally arises from unities formally, and consequently from negations, and nevertheless that the indivision of unity does not concur to compose multitude in so far as it exercises the privation of division, but in so far as it has the notion of being. For what is it for a privation to have the notion of being? For if this is said only by reason of the entity in which it is founded, it is repugnant to his former saying and to the reason given by us; but if the negation is said to have the notion of being in so far as it can be conceived after the manner of being, then the division is irrelevant, because it has this only by extrinsic denomination, and so the negation is rather only a being of reason than having the notion of real being, of which Cajetan speaks.

4. Finally, one and many can be compared in the notion of measure and measured, and in this way they can have a relative opposition, whether that be a real relation or one of reason, which seems more so, because this notion of measure seems to consist only in a certain extrinsic denomination, and to be founded more in our apprehension and use and mode of knowing than in some relation or relationship which is in the thing. Whence St. Thomas, in the said a. 2, attributes this opposition of measure and measured to quantitative unity with respect to number, which is in quantity, not to transcendental unity and multitude; which I do not see why it could have been said, except in order to human use or according to a certain denomination resulting thence; for, if the things themselves are considered according to themselves, transcendental one keeps the same proportion to its multitude as numerical or quantitative one to its number, because it is its principle and composes it, whence it can also be measured by it.