Disputationes metaphysicae

1. The Thomists speak in this matter in a diverse way of unity and multitude, of division and indivision. For they say that unity is by its nature prior to multitude, which is certain and self-evident; both because, speaking per se, one is independent of multitude in every genus; for one does not depend on many, but many on one, nor is one defined through many, but multitude is defined through unity; and also because one is the principle and composes multitude; whence also as regards the consequence of subsisting they are not convertible; for, if there is multitude, it is necessary that there be unity, but not conversely.

2. Of division and indivision, however, some say that division is by its nature prior to indivision and unity. So Soncinas teaches, Metaphysics IV, q. 23, ad 6, and Metaphysics X, q. 4; and Javellus there, q. 6; but Cajetan, I, q. 11, a. 2, around ad 4, uses a scarcely intelligible distinction; for he says that division is prior to unity simply according to itself, yet in intelligible being, and that it is posterior to unity simply, that is, according to being simply, which is to be in the nature of things. The former part he proves, because affirmation is prior to negation; but to be one is to be this, and not to be not-this; therefore division between those contradictory extremes naturally precedes unity; but the second he proves, because the negation of one being from another, which is a real negation, is posterior to unity; from which reasons the sense of the former distinction proposed by Cajetan is understood; for by negation in intelligible being he seems to understand the division of being from non-being, and of each being from such non-being, which others call a negation of reason only; but by negation according to the being of the thing he understands the division of one being from another, which is wont to be called a real negation. But, as is evident from what has been said above, the division which unity per se primarily denies is neither of these, but is the negation of the real division of the being itself in itself, and it is about this division that it is inquired whether it is prior or posterior to indivision.

3. And it seems to me indeed that division of this kind is in no way prior according to the thing to one or to the indivision included in it; for, if we compare these two generally and in their whole breadth, it is prior that some being be undivided in itself than that there be some division of one being from another or of some being in itself; but if we compare them in individual beings, each by its nature has indivision in itself prior to division. What division, then, or in what subject, is said to be or is according to itself prior to indivision or unity? Next, there is no reason which persuades the contrary, because, although indivision is opposed to division after the manner of privation, it is not therefore necessary that division be prior: first indeed, because, although in things which are properly and rigorously privatively opposed the habit is by its nature prior to the negation, because such a privation is only in a subject apt by nature, which by its nature regards the habit prior to the privation, nevertheless in privation broadly taken and improper, such as is the indivision of one, as has been explained, it is not necessary that the habit be prior to the negation; as, although immaterial privatively taken expresses a negation, it is simply prior that there be the immaterial in things than the material, because it does not express a privation properly so called and in a subject apt by nature which of itself would postulate first to be material rather than immaterial; and in man, for example, it is prior in the order of generation that he lack teeth than that he have them, which lack, although for the time of infancy it does not have the most proper notion of privation, nevertheless approaches it more than the negation of division which the indivision of one expresses; therefore much less is it necessary that in the present case division be by its nature prior to indivision. And therefore St. Thomas, I, q. 11, a. 2, ad 4, rightly taught that division is prior to unity not simply, but according to the notion of our apprehension.

4. Comparing these two, then, according to themselves and by their nature, as unity is prior to multitude, so indivision is prior to division; but as regards us division is said to be prior to indivision, because, since indivision is known as a negation, it is necessary that that of which it is the negation be apprehended first, because as regards us affirmation always precedes negation; this, however, will have to be understood of indivision taken formally for the negation, or for the foundation of the negation, according to the various modes of explaining the indivision of one which we treated above. And Aristotle speaks in the same way, Book X, text 6, of one or its indivision with respect to multitude; for he says that multitude is prior in reason on account of sense, in which last word he sufficiently declares that he speaks of priority as regards us; and so St. Thomas expounded it there, lect. 4. And he declares that this is to be understood of multitude by reason of division only; for, if multitude is taken according to the whole of what is of its notion, then even as regards us multitude is posterior, because it is nothing other (he says) than an aggregation of unities. Whence, although things which are divided are many, they nevertheless do not have the notion of many except after it is attributed to this and that that it is one.