Thomas Aquinas, Summa Theologiae

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."

Articulus 1

Argumentum 1

Ad primum sic proceditur. Videtur quod unum addat aliquid supra ens. Omne enim quod est in aliquo genere determinato, se habet ex additione ad ens, quod circuit omnia genera. Sed unum est in genere determinato, est enim principium numeri, qui est species quantitatis.

Ergo unum addit aliquid supra ens.

Argumentum 2

Praeterea, quod dividit aliquod commune, se habet ex additione ad illud. Sed ens dividitur per unum et multa.

Ergo unum addit aliquid supra ens.

Argumentum 3

Praeterea, si unum non addit supra ens, idem esset dicere unum et ens. Sed nugatorie dicitur ens ens. Ergo nugatio esset dicere ens unum, quod falsum est.

Addit igitur unum supra ens.

Sed Contra

Sed contra est quod dicit dionysius, ult. Cap. De div. Nom., nihil est existentium non participans uno, quod non esset, si unum adderet supra ens quod contraheret ipsum.

Ergo unum non habet se ex additione ad ens.

Corpus

Respondeo dicendum quod unum non addit supra ens rem aliquam, sed tantum negationem divisionis, unum enim nihil aliud significat quam ens indivisum. Et ex hoc ipso apparet quod unum convertitur cum ente. Nam omne ens aut est simplex, aut compositum. Quod autem est simplex, est indivisum et actu et potentia. Quod autem est compositum, non habet esse quandiu partes eius sunt divisae, sed postquam constituunt et componunt ipsum compositum. Unde manifestum est quod esse cuiuslibet rei consistit in indivisione. Et inde est quod unumquodque, sicut custodit suum esse, ita custodit suam unitatem.

Ad 1

Ad primum igitur dicendum quod quidam, putantes idem esse unum quod convertitur cum ente, et quod est principium numeri, divisi sunt in contrarias positiones.

Pythagoras enim et Plato, videntes quod unum quod convertitur cum ente, non addit aliquam rem supra ens, sed significat substantiam entis prout est indivisa, existimaverunt sic se habere de uno quod est principium numeri.

Et quia numerus componitur ex unitatibus, crediderunt quod numeri essent substantiae omnium rerum.

E contrario autem Avicenna, considerans quod unum quod est principium numeri, addit aliquam rem supra substantiam entis (alias numerus ex unitatibus compositus non esset species quantitatis), credidit quod unum quod convertitur cum ente, addat rem aliquam supra substantiam entis, sicut album supra hominem.

Sed hoc manifeste falsum est, quia quaelibet res est una per suam substantiam. Si enim per aliquid aliud esset una quaelibet res, cum illud iterum sit unum, si esset iterum unum per aliquid aliud, esset abire in infinitum. Unde standum est in primo. Sic igitur dicendum est quod unum quod convertitur cum ente, non addit aliquam rem supra ens, sed unum quod est principium numeri, addit aliquid supra ens, ad genus quantitatis pertinens.

Ad 2

Ad secundum dicendum quod nihil prohibet id quod est uno modo divisum, esse alio modo indivisum; sicut quod est divisum numero, est indivisum secundum speciem, et sic contingit aliquid esse uno modo unum, alio modo multa. Sed tamen si sit indivisum simpliciter; vel quia est indivisum secundum id quod pertinet ad essentiam rei, licet sit divisum quantum ad ea quae sunt extra essentiam rei, sicut quod est unum subiecto et multa secundum accidentia; vel quia est indivisum in actu, et divisum in potentia, sicut quod est unum toto et multa secundum partes, huiusmodi erit unum simpliciter, et multa secundum quid. Si vero aliquid e converso sit indivisum secundum quid, et divisum simpliciter; utpote quia est divisum secundum essentiam, et indivisum secundum rationem, vel secundum principium sive causam, erit multa simpliciter, et unum secundum quid; ut quae sunt multa numero et unum specie, vel unum principio. Sic igitur ens dividitur per unum et multa, quasi per unum simpliciter, et multa secundum quid. Nam et ipsa multitudo non contineretur sub ente, nisi contineretur aliquo modo sub uno.

Dicit enim dionysius, ult. Cap. De div. Nom., quod non est multitudo non participans uno, sed quae sunt multa partibus, sunt unum toto; et quae sunt multa accidentibus, sunt unum subiecto; et quae sunt multa numero, sunt unum specie; et quae sunt speciebus multa, sunt unum genere; et quae sunt multa processibus, sunt unum principio.

Ad 3

Ad tertium dicendum quod ideo non est nugatio cum dicitur ens unum, quia unum addit aliquid secundum rationem supra ens.