Whether "one" adds anything to "being"?

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."