Thomas Aquinas - Summa Theologica, Part I (Prima Pars)

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 Obj. 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 Obj. 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 Obj. 3: It does not follow that it is nugatory to say "being" is "one"; forasmuch as "one" adds an idea to "being." _______________________

SECOND ARTICLE [I, Q. 11, Art. 2]

Whether "One" and "Many" Are Opposed to Each Other?

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."

Obj. 2: Further, no opposite thing is constituted by its opposite. But multitude is constituted by one. Therefore it is not opposed to "multitude."

Obj. 3: Further, "one" is opposed to "one." But the idea of "few" is opposed to "many." Therefore "one" is not opposed to "many."

Obj. 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 is convertible with being is opposed to multitude by way of privation; as the undivided is to the thing divided.

Reply Obj. 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 Obj. 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.