On the contrary, Things which are opposed in idea, are themselves opposed to each other. But the idea of "one" consists in indivisibility; and the idea of "multitude" contains division. Therefore "one" and "many" are opposed to each other.
I answer that, "One" is opposed to "many," but in various ways. The "one" which is the principle of number is opposed to "multitude" which is number, as the measure is to the thing measured. For "one" implies the idea of a primary measure; and number is "multitude" measured by "one," as is clear from Metaph. x. But the "one" which convertible with "being" is opposed to "multitude" by way of privation; as the undivided is to the thing divided.
Reply to Objection 1: No privation entirely takes away the being of a thing, inasmuch as privation means "negation in the subject," according to the Philosopher (Categor. viii). Nevertheless every privation takes away some being; and so in being, by reason of its universality, the privation of being has its foundation in being; which is not the case in privations of special forms, as of sight, or of whiteness and the like. And what applies to being applies also to one and to good, which are convertible with being, for the privation of good is founded in some good; likewise the removal of unity is founded in some one thing. Hence it happens that multitude is some one thing; and evil is some good thing, and non-being is some kind of being. Nevertheless, opposite is not predicated of opposite; forasmuch as one is absolute, and the other is relative; for what is relative being (as a potentiality) is non-being absolutely, i.e. actually; or what is absolute being in the genus of substance is non-being relatively as regards some accidental being. In the same way, what is relatively good is absolutely bad, or vice versa; likewise what is absolutely "one" is relatively "many," and vice versa.
Reply to Objection 2: A "whole" is twofold. In one sense it is homogeneous, composed of like parts; in another sense it is heterogeneous, composed of dissimilar parts. Now in every homogeneous whole, the whole is made up of parts having the form of the whole; as, for instance, every part of water is water; and such is the constitution of a continuous thing made up of its parts. In every heterogeneous whole, however, every part is wanting in the form belonging to the whole; as, for instance, no part of a house is a house, nor is any part of a man a man. Now multitude is such a kind of a whole. Therefore inasmuch as its part has not the form of the multitude, the latter is composed of unities, as a house is composed of not houses; not, indeed, as if unities constituted multitude so far as they are undivided, in which way they are opposed to multitude; but so far as they have being, as also the parts of a house make up the house by the fact that they are beings, not by the fact that they are not houses.
Reply to Objection 3: "Many" is taken in two ways: absolutely, and in that sense it is opposed to "one"; in another way as importing some kind of excess, in which sense it is opposed to "few"; hence in the first sense two are many but not in the second sense.
Reply to Objection 4: "One" is opposed to "many" privatively, inasmuch as the idea of "many" involves division. Hence division must be prior to unity, not absolutely in itself, but according to our way of apprehension. For we apprehend simple things by compound things; and hence we define a point to be, "what has no part," or "the beginning of a line." "Multitude" also, in idea, follows on "one"; because we do not understand divided things to convey the idea of multitude except by the fact that we attribute unity to every part. Hence "one" is placed in the definition of "multitude"; but "multitude" is not placed in the definition of "one." But division comes to be understood from the very negation of being: so what first comes to mind is being; secondly, that this being is not that being, and thus we apprehend division as a consequence; thirdly, comes the notion of one; fourthly, the notion of multitude.
Whether God is one?
Objection 1: It seems that God is not one. For it is written "For there be many gods and many lords" (1 Cor. 8:5).
Objection 2: Further, "One," as the principle of number, cannot be predicated of God, since quantity is not predicated of God; likewise, neither can "one" which is convertible with "being" be predicated of God, because it imports privation, and every privation is an imperfection, which cannot apply to God. Therefore God is not one.
On the contrary, It is written "Hear, O Israel, the Lord our God is one Lord" (Dt. 6:4).
I answer that, It can be shown from these three sources that God is one. First from His simplicity. For it is manifest that the reason why any singular thing is "this particular thing" is because it cannot be communicated to many: since that whereby Socrates is a man, can be communicated to many; whereas, what makes him this particular man, is only communicable to one. Therefore, if Socrates were a man by what makes him to be this particular man, as there cannot be many Socrates, so there could not in that way be many men. Now this belongs to God alone; for God Himself is His own nature, as was shown above ( Question [3], Article [3]). Therefore, in the very same way God is God, and He is this God. Impossible is it therefore that many Gods should exist.
Secondly, this is proved from the infinity of His perfection. For it was shown above ( Question [4], Article [2]) that God comprehends in Himself the whole perfection of being. If then many gods existed, they would necessarily differ from each other. Something therefore would belong to one which did not belong to another. And if this were a privation, one of them would not be absolutely perfect; but if a perfection, one of them would be without it. So it is impossible for many gods to exist. Hence also the ancient philosophers, constrained as it were by truth, when they asserted an infinite principle, asserted likewise that there was only one such principle.
Thirdly, this is shown from the unity of the world. For all things that exist are seen to be ordered to each other since some serve others. But things that are diverse do not harmonize in the same order, unless they are ordered thereto by one. For many are reduced into one order by one better than by many: because one is the "per se" cause of one, and many are only the accidental cause of one, inasmuch as they are in some way one. Since therefore what is first is most perfect, and is so "per se" and not accidentally, it must be that the first which reduces all into one order should be only one. And this one is God.
Reply to Objection 1: Gods are called many by the error of some who worshipped many deities, thinking as they did that the planets and other stars were gods, and also the separate parts of the world. Hence the Apostle adds: "Our God is one," etc.
Reply to Objection 2: "One" which is the principle of number is not predicated of God, but only of material things. For "one" the principle of number belongs to the "genus" of mathematics, which are material in being, and abstracted from matter only in idea. But "one" which is convertible with being is a metaphysical entity and does not depend on matter in its being. And although in God there is no privation, still, according to the mode of our apprehension, He is known to us by way only of privation and remotion. Thus there is no reason why a certain kind of privation should not be predicated of God; for instance, that He is incorporeal and infinite; and in the same way it is said of God that He is one.
Whether God is supremely one?
Objection 1: It seems that God is not supremely "one." For "one" is so called from the privation of division. But privation cannot be greater or less. Therefore God is not more "one" than other things which are called "one."
Objection 2: Further,
