Thomas Aquinas, Summa Theologiae

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.

Articulus 2

Argumentum 1

Ad secundum sic proceditur. Videtur quod unum et multa non opponantur. Nullum enim oppositum praedicatur de suo opposito.

Sed omnis multitudo est quodammodo unum, ut ex praedictis patet.

Ergo unum non opponitur multitudini.

Argumentum 2

Praeterea, nullum oppositum constituitur ex suo opposito. Sed unum constituit multitudinem.

Ergo non opponitur multitudini.

Argumentum 3

Praeterea, unum uni est oppositum. Sed multo opponitur paucum.

Ergo non opponitur ei unum.

Argumentum 4

Praeterea, si unum opponitur multitudini, opponitur ei sicut indivisum diviso, et sic opponetur ei ut privatio habitui.

Hoc autem videtur inconveniens, quia sequeretur quod unum sit posterius multitudine, et definiatur per eam; cum tamen multitudo definiatur per unum. Unde erit circulus in definitione, quod est inconveniens.

Non ergo unum et multa sunt opposita.

Sed Contra

Sed contra, quorum rationes sunt oppositae, ipsa sunt opposita.

Sed ratio unius consistit in indivisibilitate, ratio vero multitudinis divisionem continet.

Ergo unum et multa sunt opposita.

Corpus

Respondeo dicendum quod unum opponitur multis, sed diversimode.

Nam unum quod est principium numeri, opponitur multitudini quae est numerus, ut mensura mensurato, unum enim habet rationem primae mensurae, et numerus est multitudo mensurata per unum, ut patet ex X metaphys..

Unum vero quod convertitur cum ente, opponitur multitudini per modum privationis, ut indivisum diviso.

Ad 1

Ad primum ergo dicendum quod nulla privatio tollit totaliter esse, quia privatio est negatio in subiecto, secundum philosophum.

Sed tamen omnis privatio tollit aliquod esse. Et ideo in ente, ratione suae communitatis, accidit quod privatio entis fundatur in ente, quod non accidit in privationibus formarum specialium, ut visus vel albedinis, vel alicuius huiusmodi. Et sicut est de ente, ita est de uno et bono, quae convertuntur cum ente, nam privatio boni fundatur in aliquo bono, et similiter remotio unitatis fundatur in aliquo uno. Et exinde contingit quod multitudo est quoddam unum, et malum est quoddam bonum, et non ens est quoddam ens. Non tamen oppositum praedicatur de opposito, quia alterum horum est simpliciter, et alterum secundum quid.

Quod enim secundum quid est ens, ut in potentia, est non ens simpliciter, idest actu, vel quod est ens simpliciter in genere substantiae, est non ens secundum quid, quantum ad aliquod esse accidentale. Similiter ergo quod est bonum secundum quid, est malum simpliciter; vel e converso. Et similiter quod est unum simpliciter, est multa secundum quid; et e converso.

Ad 2

Ad secundum dicendum quod duplex est totum, quoddam homogeneum, quod componitur ex similibus partibus; quoddam vero heterogeneum, quod componitur ex dissimilibus partibus. In quolibet autem toto homogeneo, totum constituitur ex partibus habentibus formam totius, sicut quaelibet pars aquae est aqua, et talis est constitutio continui ex suis partibus. In quolibet autem toto heterogeneo, quaelibet pars caret forma totius, nulla enim pars domus est domus, nec aliqua pars hominis est homo.

Et tale totum est multitudo. Inquantum ergo pars eius non habet formam multitudinis, componitur multitudo ex unitatibus, sicut domus ex non domibus, non quod unitates constituant multitudinem secundum id quod habent de ratione indivisionis, prout opponuntur multitudini; sed secundum hoc quod habent de entitate, sicut et partes domus constituunt domum per hoc quod sunt quaedam corpora, non per hoc quod sunt non domus.

Ad 3

Ad tertium dicendum quod multum accipitur dupliciter. Uno modo, absolute, et sic opponitur uni. Alio modo, secundum quod importat excessum quendam, et sic opponitur pauco. Unde primo modo duo sunt multa; non autem secundo.

Ad 4

Ad quartum dicendum quod unum opponitur privative multis, inquantum in ratione multorum est quod sint divisa. Unde oportet quod divisio sit prius unitate, non simpliciter, sed secundum rationem nostrae apprehensionis. Apprehendimus enim simplicia per composita, unde definimus punctum, cuius pars non est, vel principium lineae. Sed multitudo, etiam secundum rationem, consequenter se habet ad unum, quia divisa non intelligimus habere rationem multitudinis, nisi per hoc quod utrique divisorum attribuimus unitatem. Unde unum ponitur in definitione multitudinis, non autem multitudo in definitione unius. Sed divisio cadit in intellectu ex ipsa negatione entis. Ita quod primo cadit in intellectu ens; secundo, quod hoc ens non est illud ens, et sic secundo apprehendimus divisionem; tertio, unum; quarto, multitudinem.