Summa Theologica, by St. Thomas Aquinas, [1947], at sacred-texts.com
After the foregoing, we consider the divine unity; concerning which there are four points of inquiry:
(1) Whether "one" adds anything to "being"?
(2) Whether "one" and "many" are opposed to each other?
(3) Whether God is one?
(4) Whether He is in the highest degree one?
Objection 1: It seems that "one" adds something to "being." For everything is in a determinate genus by addition to being, which penetrates all "genera." But "one" is a determinate genus, for it is the principle of number, which is a species of quantity. Therefore "one" adds something to "being."
Objection 2: Further, what divides a thing common to all, is an addition to it. But "being" is divided by "one" and by "many." Therefore "one" is an addition to "being."
Objection 3: Further, if "one" is not an addition to "being," "one" and "being" must have the same meaning. But it would be nugatory to call "being" by the name of "being"; therefore it would be equally so to call being "one." Now this is false. Therefore "one" is an addition to "being."
On the contrary, Dionysius says (Div. Nom. 5, ult.): "Nothing which exists is not in some way one," which would be false if "one" were an addition to "being," in the sense of limiting it. Therefore "one" is not an addition to "being."
I answer that, "One" does not add any reality to "being"; but is only a negation of division; for "one" means undivided "being." This is the very reason why "one" is the same as "being." Now every being is either simple or compound. But what is simple is undivided, both actually and potentially. Whereas what is compound, has not being whilst its parts are divided, but after they make up and compose it. Hence it is manifest that the being of anything consists in undivision; and hence it is that everything guards its unity as it guards its being.
Reply to Objection 1: Some, thinking that the "one" convertible with "being" is the same as the "one" which is the principle of number, were divided into contrary opinions. Pythagoras and Plato, seeing that the "one" convertible with "being" did not add any reality to "being," but signified the substance of "being" as undivided, thought that the same applied to the "one" which is the principle of number. And because number is composed of unities, they thought that numbers were the substances of all things. Avicenna, however, on the contrary, considering that "one" which is the principle of number, added a reality to the substance of "being" (otherwise number made of unities would not be a species of quantity), thought that the "one" convertible with "being" added a reality to the substance of beings; as "white" to "man." This, however, is manifestly false, inasmuch as each thing is "one" by its substance. For if a thing were "one" by anything else but by its substance, since this again would be "one," supposing it were again "one" by another thing, we should be driven on to infinity. Hence we must adhere to the former statement; therefore we must say that the "one" which is convertible with "being," does not add a reality to being; but that the "one" which is the principle of number, does add a reality to "being," belonging to the genus of quantity.
Reply to Objection 2: There is nothing to prevent a thing which in one way is divided, from being another way undivided; as what is divided in number, may be undivided in species; thus it may be that a thing is in one way "one," and in another way "many." Still, if it is absolutely undivided, either because it is so according to what belongs to its essence, though it may be divided as regards what is outside its essence, as what is one in subject may have many accidents; or because it is undivided actually, and divided potentially, as what is "one" in the whole, and is "many" in parts; in such a case a thing will be "one" absolutely and "many" accidentally. On the other hand, if it be undivided accidentally, and divided absolutely, as if it were divided in essence and undivided in idea or in principle or cause, it will be "many" absolutely and "one" accidentally; as what are "many" in number and "one" in species or "one" in principle. Hence in that way, being is divided by "one" and by "many"; as it were by "one" absolutely and by "many" accidentally. For multitude itself would not be contained under "being," unless it were in some way contained under "one." Thus Dionysius says (Div. Nom. cap. ult.) that "there is no kind of multitude that is not in a way one. But what are many in their parts, are one in their whole; and what are many in accidents, are one in subject; and what are many in number, are one in species; and what are many in species, are one in genus; and what are many in processions, are one in principle."
Reply to Objection 3: It does not follow that it is nugatory to say "being" is "one"; forasmuch as "one" adds an idea to "being."
Objection 1: It seems that "one" and "many" are not mutually opposed. For no opposite thing is predicated of its opposite. But every "multitude" is in a certain way "one," as appears from the preceding article. Therefore "one" is not opposed to "multitude."
Objection 2: Further, no opposite thing is constituted by its opposite. But "multitude" is constituted by "one." Therefore it is not opposed to "multitude."
Objection 3: Further, "one" is opposed to "one." But the idea of "few" is opposed to "many." Therefore "one" is not opposed to "many."
Objection 4: Further, if "one" is opposed to "multitude," it is opposed as the undivided is to the divided; and is thus opposed to it as privation is to habit. But this appears to be incongruous; because it would follow that "one" comes after "multitude," and is defined by it; whereas, on the contrary, "multitude" is defined by "one." Hence there would be a vicious circle in the definition; which is inadmissible. Therefore "one" and "many" are not opposed.
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.
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 (Q[3], A[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 (Q[4], A[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.
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, nothing seems to be more indivisible than what is actually and potentially indivisible; such as a point and unity. But a thing is said to be more "one" according as it is indivisible. Therefore God is not more "one" than unity is "one" and a point is "one."
Objection 3: Further, what is essentially good is supremely good. Therefore what is essentially "one" is supremely "one." But every being is essentially "one," as the Philosopher says (Metaph. iv). Therefore every being is supremely "one"; and therefore God is not "one" more than any other being is "one."
On the contrary, Bernard says (De Consid. v): "Among all things called one, the unity of the Divine Trinity holds the first place."
I answer that, Since "one" is an undivided being, if anything is supremely "one" it must be supremely being, and supremely undivided. Now both of these belong to God. For He is supremely being, inasmuch as His being is not determined by any nature to which it is adjoined; since He is being itself, subsistent, absolutely undetermined. But He is supremely undivided inasmuch as He is divided neither actually nor potentially, by any mode of division; since He is altogether simple, as was shown above (Q[3], A[7]). Hence it is manifest that God is "one" in the supreme degree.
Reply to Objection 1: Although privation considered in itself is not susceptive of more or less, still according as its opposite is subject to more or less, privation also can be considered itself in the light of more and less. Therefore according as a thing is more divided, or is divisible, either less or not at all, in the degree it is called more, or less, or supremely, "one."
Reply to Objection 2: A point and unity which is the principle of number, are not supremely being, inasmuch as they have being only in some subject. Hence neither of them can be supremely "one." For as a subject cannot be supremely "one," because of the difference within it of accident and subject, so neither can an accident.
Reply to Objection 3: Although every being is "one" by its substance, still every such substance is not equally the cause of unity; for the substance of some things is compound and of others simple.