PROPOSITION XXXII.
Division is prior, not in order of nature but in order of cognition, to Indivision, and, therefore, to Unity.
I. THE FIRST MEMBER of this Proposition, in which it is asserted that 'Division is not prior in order of nature to Indivision,' is equally self-evident; for, how can there be division, unless there is something to divide? And that something must be undivided, prior to its division.
II. But THE SECOND MEMBER, which declares that 'division is prior in order of cognition to Indivision and, therefore, to Unity,' requires much more careful examination, especially since it introduces us to the whole question touching the genetic order of these Transcendental concepts.
It will be well that the Angelic Doctor should lead the way. He says in one place, 'According to the Philosopher' (in the tenth Book of his Metaphysics), 'Multitude is prior to Unity in sensile perception, as a whole is prior to its parts, and the Composite to the Simple,' (i.e. in sensile perception, because all things material and sensible are composite and integral wholes); 'but Unity is prior to Multitude in order of nature and of cognition. . . Division is the cause of Multitude, and is conceptually prior to Multitude. Now, Unity has a privative signification in relation to Division, since it is undivided Entity; but not as regards Multitude. Hence, Division is prior in order of cognition to Unity, while Multitude is posterior. The following is the explanation: -- For that which first comes into the mind is, Being; and the next is, the negation of Being. Now, from these two results, in the third place, the concept of Division (for, from the fact that something is understood to be Being, and that it is apprehended not to be this Being; the concept ensues, that it is divided from this Being). Then there follows, in the fourth place, the concept of the nature of Unity; forasmuch, that is, as this Being is understood not to be divided in itself. Then, in the fifth place, follows the concept of Multitude; forasmuch, that is, as this Being is apprehended as divided from the other, and each of Them as in itself one. For, however much certain things may be apprehended as divided, Multitude will not be apprehended, unless each of the divided entities be apprehended as one.'{1} He speaks much in the same way in another place. 'Division,' he remarks, 'is prior to Unity; not simply, but according to the nature of our apprehension. For we apprehend things simple by means of things composite: hence, we define a point to be a thing which has no part, or the beginning of a line. But Multitude conceptually comes after Unity; because we do not conceive things divided to have the nature of multitude, save for the reason that we attribute unity to each of the things divided. Hence, Unity has a place in the definition of Multitude; but not Multitude in the definition of Unity. But Division occurs in the intellect from the mere negation of Being, so that Being is first conceived; secondly, that this Being is not that Being. Thus, in the second place, we apprehend Division; in the third, Unity; in the fourth place, Multitude.'{2}
These declarations of St. Thomas give rise to a difficulty, which shall be examined presently. Meanwhile, let us elaborate his doctrine touching the genetic order of the Transcendentals at present under consideration. The concept which first comes into the mind, is that of Being. There is no room for doubt here; consequently, all the Doctors of the School are of accord. But now comes the puzzle. For Unity expresses Indivision, or the negation of division; consequently, the concept of Unity presupposes the concept of Division, viz, of that of which it is itself the negation. But it seems impossible, at first sight, to understand Division; unless there be divided things, i.e. more things than one. So then, according to the theory proposed, it would be impossible to intue the Unity, i.e. of God; unless there were some other Being besides Himself. Yet such a conclusion is hardly consonant with right reason; and, consequently, the theory must be rejected. The easiest answer to this difficulty will be found in a careful analysis of these primary concepts. If the mind conceives Being, it will hardly be disputed that it can consequently conceive not-Being, or the negation of Being, which will form a sort of ideal outside to Being. Contrasting this ideal outside with Being previously conceived, the mind perceives that Being is not Not-Being. It may make a difficult subject somewhat easier of comprehension, if it be represented under a symbolical form. Therefore, let it stand thus: -- First A; then not-A. The mind consequently conceives that A is not Not-A. Therefore A is all A; or better, All A is A. Therefore A is undivided in itself. Thus the division between Being and its negation is sufficient for the genesis of the essential idea of Unity, without any intervention of plurality. But Unity also expresses, by consequence, that The One is distinct from all others. How is this evolved in intellectual consciousness? To pursue the question under a symbolical form: -- A is not Not-A, which is the same as to say, that it is wholly A. Therefore A is not x, assuming x as the expression of indefinite otherness to A. Posit B; that is, some definite being. B is evidently x, and, consequently, it is not A. Therefore, A is not B. And now to escape from the symbols, -- it appears that the formal concept of Unity is generated by the division of Being from Not-Being. In the formal concept of Unity is virtually included the separation of that being, which is one, from all other conceivable being, supposing that such being should be. If such a being is, the virtual division becomes ipso facto actual. If that plurality of distinct beings really is, sufficient material for the concept of Multitude has been provided.{3}
It now only remains to explain an apparent difficulty in the exposition of the Angelic Doctor, which, however, will cost little trouble, after the analysis just given. St. Thomas, then, asserts that the idea of Unity arises from a previous divisive judgment, that This Being is not that other; thereby, as it would seem, presupposing Multitude in the concept of Unity. But he is evidently considering Unity in its adequate, and not in its formal, signification; for at the same time he gives for a sufficient foundation of the concept, the division of Being from not-Being. Consequently, he seems to mean, that the idea of One is consequent on the judgment, that Being is not otherness from Being; for it is manifest, as may be seen above, that for the actual separation of one Being (not, observe, the aptitudinal) from another, it is necessary that there should be more Beings than one. There is, however, another solution which is perhaps preferable, because more satisfactory. The words of St. Thomas, ex hoc enim quod aliquid intelligitur ens, et intelligitur non esse hoc ens, sequitur in intellectu quod sit divisum ab eo, may be translated, For from the fact that something is understood to be Being, and that this (whatever it may be) is understood not to be Being, it follows conceptually that the former is divided from the latter. This rendering is more in accordance with the immediate context.
{1} 'Secundum Philosophum (in x. Met.) multitudo est prior uno secundum sensum, sicut totum partibus et compositum simplici; sed unum est prius multitudine naturaliter et secundum rationem. . . . Divisio est causa multitudinis, et est prior secundum intellectum quam multitudo. Unum autem dicitur privative respectu divisionis, cum sit ens indivisum, non autem respectu multitudinis. Unde divisio est prior secundum rationem quam unum; sed multitudo posterior. Quod sic patet. Primum enim quod in intellectum cadit, est ens; secundum vero est negatio entis; ex his autem duobus sequitur tertio intellectus divisionis (ex hoc enim quod aliquid intelligitur ens, et intelligitur non esse hoc ens, sequitur in intellectu quod sit divisum ab eo). Quarto autem sequitur in intellectu ratio unius, prout scil. intelligitur hoc ens non esse in se divisum. Quinto autem sequitur intellectus multitudinis, prout scil. hoc ens intelligitur divisum ab alio, et utrumque ipsorum esse in se unum. Quantumcumque enim aliqua intelligantur divisa, non intelligetur multitude, nisi quodlibet divisorum intelligatur esse unum.' De Potentia, Q. ix, a. 7, ad 15m.
{2} 'Unde oportet quod divisio sit prius unitate, non simpliciter sed secundum rationem nostrae apprehensionis. Apprehendimus enim simplicia per composita; unde definimus punctum, cujus 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 prima cadit in intellectu ens; secundo, quod hoc ens non sit illud ens. Et sic secundo apprehendimus divisionem; tertio unum; quarto multitudinem.' 520 xi, 2, ad 4m.
{3} 'Sic igitur patet quod pluralitatis vel divisionis ratio prima sive principium est ex affirmatione et negatione, ut talis ordo originis pluralitatis intelligatur; quod prima sint intelligenda ens at non ens, ex quibus ipsa prima divisa constituuntur, et per hoc sunt plura. Unde sicut primum ens, in quantum indivisum est, statim invenitur unum; ita post divisionem entis et non entis statim invenitur pluralitas primarum simpilcium. Quamvis autem divisia praecedat pluralitatem primarum, non tamen diversitas; quia divisia non requirit utrumque condivisorum esse, cum divisio sit per affirmationem et negationem; sed diversitas requirit utrumque esse ens, unde praesupponit pluralitatem. Unde nulla modo potest esse quod pluralitatis primarum causa sit diversitas, nisi diversitas pro divisione sumatur.' Opuso. LX (aliter LXIII), in Boetii L. de Trinitate, Q. iv, a. I, c.