PROPOSITION XXX.

Unity is an adequate Attribute of Being.

This Proposition is at once so evident and maintained with such unanimity by Philosophers of every School, that it may be regarded as axiomatic. No one, indeed, can fail to see, that every Being or Thing is one, by the mere fact that it is a Being. The Angelic Doctor shall be spokesman for the whole School. In passages already quoted in the two preceding Theses, he thrice refers to the mutual convertibility of Being and One, as to an indisputable fact; while, in another work, he states that Everything is in so far forth Being, as it is One; wherefore, Being and One are convertible.'^{1} So much is plain; so plain indeed, that it would only suffer by addition of proof.

But this doctrine, indisputable as it is, gives rise to a consider able difficulty; and an opportunity is offered of discussing it in the present Proposition, 'which has been introduced mainly on this account. For, according to the Philosopher, whose assertion has been accepted generally by the School, One is opposed to Many, Unity to Multitude; and these two divide Being. But it is impossible that one member of a division should be convertible with the divided Whole. Consequently, Unity cannot be an adequate Attribute of Being.

Now, in the first place, it concerns us to remark that Many, purely as such, is not Being but beings and, therefore, can form no member of a division of which Being is the divided Whole. Wherefore, Many can only be included under Being, in so far forth as it puts on the form of unity. Now, this unity of Many may be fourfold. For either it is purely conceptual, or it arises from contiguity, accumulation, conglomeration, or it owes its origin to physical mixture and combination, or it is the result of physical and entitative union. Again, the unity arising out of contiguity, accumulation, or conglomeration, may be either fortuitous and unordered, or with design and ordered. Thus there are, in all, five kinds of Unity which Many may exhibit. An apposite instance of conceptual unity is to be found in the very notion of Multitude; for, whether the Many included he determinate or indeterminate in number, they are gathered together by the mind into a sort of logical unity. In a heap of stones, the unity of the concept arises from contiguity; and accumulation, from conglomeration, in fossiliferous strata. But these are, so to say, fortuitous. The bricks, stones, mortar, timber, &c., which compose a house, are one, by a contiguity and accumulation which are ordered and designed. Nearly the same may be said of such concepts as an Army, a State, a Society, a Committee, &c.; or, to add a significant word which would include them all, a Union. Wine and water, nay wine itself in the present condition of the trade, are examples of physical mixture. So are soda-water and poplins for dresses. Instances of physical and entitative union of many are the limbs of a body, a red rose, where there is conjunction of accident and substance; the union of oxygen and hydrogen in water, the union between soul and body.

Now, throughout each and all of these categories of multitude, there is unity of some sort; there is, therefore, proportionally Being. Hence, since Many, as such, cannot come under the category of Being, but beings; it follows, that Many can only be said to divide Being, inasmuch as it is conceived as Multitude, i.e., as in some way or other collected into one. Therefore, it cannot contradivide Being with unity as the other member of division; but only divides Being, after precisely the same proportion as it divides Unity. Consequently, it offers no hindrance to the adequation of Unity with Being.

Thus, then, the difficulty is solved, and the truth of the present Proposition is established. Nevertheless, as the doctrine touching the relation of Multitude to Being and Unity has not as yet been exhaustively treated, it may be well to subjoin some further observations.

It is easy to perceive that Multitude, which is only conceptually gathered together into one, is purely logical Being and, therefore, only logically one. So likewise, in the case of union by contiguity and accumulation, whether fortuitous or designed, there is really not Being, but beings; not One, but ones. Under such form of constitution, therefore, Multitude is only Being and One, by an act of the intellect which has something of a real foundation for its concept. Such multitudes, consequently, are justly called entities of reason or conceptual entities, as distinguished from real Beings. Hence, Multitude, in both these cases, is conceptual, not real; and cannot in any sense be said to divide real Being, which is the adequate object of Metaphysics. So soon, however, as there is real physical union, there is also real Being. Considered under this point of view, Multitude is twofold. For its multiplicity is either actual or merely virtual. If it is actual, then its Being and its unity are accidental; in other words, it is Being and One in a way, hut it is simply manifold. If it is virtual merely, it is simply Being and simply One, and manifold in a way. Accordingly, mixtures, Substance taken together with its informing Accident, are Being and One by accident, while they are simply Multitude; whereas, integral parts of an existing whole, -- oxygen and hydrogen in water, -- soul and body in a living animal, -- are simply Being and One, while they are manifold by accident. In other words, virtual multitude is really Being, really One; and real actual Multitude is virtually Being, virtually One.

Two questions suggest themselves, in view of the doctrine here propounded, which shall be considered under the form of Corollaries.

COROLLARY I.

Of what nature, it may he asked, is this Division of Unity and Being by these Forms of Multitude? Is Being or Unity (for they are convertible) predicated of these two primary determinations, -- viz., Being, One, simply, and Being, One, by accident, -- univocally, equivocally, or analogously? In order to give an exhaustive answer to this question, it will be necessary to recall to mind the different kinds of Multitude already enumerated; omitting, of course, the first whose unity is purely conceptual. They shall now, however, with the Angelic Doctor for a guide, be represented, not under the form of their multiplicity, hut under their form of unity. 'In three ways,' he writes, 'a certain unity is constituted out of two or more. First of all, out of two (or more) which remain integral and perfect. But this cannot be effected, save in the case of component elements whose form is either collocation, or order, or shape. Thus, out of many stones brought together without any order, a heap is made by mere collocation; but, out of stones and timber disposed in some definite order and likewise reduced to a certain shape, a house is made. . . . Secondly, a sort of unity is made out of perfect (components), but transmuted; as a composite is made out of simple elements. . . . Thirdly, it is made out of certain (components), not commingled or transmuted, but imperfect; as man is made of soul and body, and in like manner one body is made up of different members.'^{2} It is plain, then, that to ask whether the division of Being into One and Many is univocal, equivocal, or analogous; if it mean any thing, is identical with the question, whether the division of Unity into simply One and One in a Way (secundum quid) is univocal, equivocal, or analogous. Now, no general answer can be given to this question, on account of the different forms of unity which constitute the afore-mentioned classes of composite Unity. Each must be considered separately. Wherefore,

I. Between simple unity (which is Transcendental) and that unity of composition which arises from fortuitous adjacency or aggregation, there is, at the most, a distant analogy of proportion; for the Forms in each are simply distinct.

II. The same may be said of that unity of composition which arises from designed or orderly aggregation. For, in such cases, the Unity is not entitative or natural, but conceptual only.

III. Where the Unity is the result of natural commixture, while the Matter and substantial Form of the commixed remain unchanged; the analogy approaches to that of attribution of the second class. For, though the two or more entities which are mingled together preserve their integral unity; yet there is a real, physical, quantitative, union between them, which is sometimes qualitative also, as in the instance of hot negus.

IV. Much more plainly is this analogy of proportion seen to exist in the case of Substance informed by its accidents; since, although Accident has an Entity and, therefore, Unity of its own, as distinct from the Substance which it informs; nevertheless, it is of its essence to be inherent in its Subject.

V. With regard to natural transformations or transmutations, and the conjunction of imperfect substances which mutually complete each other, it may be said, that they are univocally one, for they are only potentially many, and, constitute severally one real Entity.

Hence it may be inferred, that the last three classes are included either univocally or analogously under Transcendental Unity, while the former two are excluded.

COROLLARY II.

The second question which awaits solution is this. How are Unity and Multiplicity opposed? What sort of opposition, in other words, exists between the two? The answer to this inquiry will depend upon the point of view under which Multiplicity is regarded. For it may be considered either formally, i.e. as exhibiting some form of unity; or materially, i.e. precisely as many, or more than one. If it be regarded formally, Multiplicity is opposed to Unity either as disparate or as the imperfect to the perfect: -- as disparate, where there is no physical union; as the imperfect to the perfect, where such union subsists. If the question regards Multitude or Multiplicity, simply as being many, it may be understood in two ways. For it may be understood of Many either positively or negatively; because Many may be regarded in either of these two ways. If the question is understood positively, viz., of Many as simply so many distinct entities; then it is opposed to One, as a whole is opposed to its part. If it be taken negatively, i.e. with regard to the negation included in Unity and the negation included in Multiplicity; then they are opposed privatively. For unity expresses the negation of division, which division within itself is of the essence of Multitude; while Multitude expresses the negation of identity which is of the essence of Unity.

But here arises a difficulty, which has occasioned what seems like a serious misunderstanding of the teaching of St. Thomas in this matter. It has been already stated in the explanation of the word Multitude given at the commencement of this Chapter, that, according to St. Thomas, Multitude supposes the Unity or Indivision of each of its constituents. The same Doctor asserts as much, if possible, more unequivocally, in a passage which will appear later on. Yet, on the other hand, he says in another place, 'There is a twofold Whole; one homogeneous, which is made up of parts that are similar; the other heterogeneous, which is made up of parts that are dissimilar. . . Now, in every heterogeneous whole, each part is destitute of the form of the Whole; for there is no part of the houses (for instance) 'which is the house, and no part of man which is man. And such a whole is Multitude. Forasmuch, then, as no part of it has the form of Multitude; Multitude is composed of unities, as a house is composed of things which are not houses. Not that Unities constitute Multitude by reason of that attribute of indivision which is theirs and by which they are opposed to Multitude, but by reason of their Entity; just as the parts of a house constitute a house, in that they are material substances, not because they are not house.'^{3} Similarly, in another place he says, 'Unity does not constitute multitude by virtue of its privativeness ' (i.e. of division), 'but by virtue of its entity.'^{4} Therefore it would seem, according to the tenor of these passages, as though St. Thomas was at variance with his own previous declaration, that Multitude supposed indivision in its components. This apparent discrepancy will, however, disappear, if we examine the matter with attention. There are three ways, as Suarez reminds us, of regarding Multitude, which are familiar to us already in the previous discussions on Unity. We may consider Multitude formally, or materially, i.e. as to its material part; and this latter under a double aspect, i.e. as inclusive, first, of its positive, secondly, of its negative element. Let us commence by looking at Multitude in its adequate acceptation. It includes the Many which are, as it were, its material, and their union, which is its formal part. It may, therefore, be described as the union of two or more entities. Now, the two or more entities, as such, constitute the material part, considered under its positive aspect; and the existence of two or more entities answers to the idea of Plurality. But Plurality necessarily presupposes Distinction, or the negation of identity in regard of the several entities; and this is the material part according to its negative element. This Distinction, then, or negation of identity, presupposes the unity and identity of each separate entity with itself. Wherefore, Unity, or indivision of Being, is an essential prerequisite of Many; i.e. the many cannot be, unless each constituent of the many is one and undivided in itself. But this Plurality is reduced to Unity by Union, which is the formal part of Multitude. Now, in the process of uniting the Many into One, the Indivision of each member in itself can play no part; if anything, it would rather be in the way. For this union requires that the several members should part, as it were, with their autonomy, so as to become members one of another and thus to constitute a whole. That which in each member promotes this union, is its Entity which, forasmuch as it is finite, can be perfected by conjunction; and thus, the union causes each entity to forget the distinctiveness of its own Being, in order to form a part in the constitution of a new Entity. Here its power of cohesion comes into play; not the repelling force of its unity. Thus, to adopt the illustration of St. Thomas, it is not because bricks are not timber, nor timber mortar, nor any of these a house, that they can combine to form a house; but because each is an Entity capable of conjunction with the other, and so, of contributing its part to the constitution of a house. In like manner, it is not because the soul of man is undivided in itself and distinct from the body, or because the body, in its turn, is undivided in itself and distinct from the soul, (though both these are necessarily presupposed, as has been seen), that they together constitute man; but it is because of the imperfect entity of both, which seeks mutual conjunction for the required perfection of each.

Multitude or Multiplicity, then, has a sort of composite Indivision proper to itself; for it cannot lose a part, without ceasing to be the same Multiplicity which it was before. Therefore, its composite entity is incapable of division, and it is identical with itself. But this Unity is not entitative or essential, but composite and accidental; with the exception of transformations and the union of imperfect substances, such as soul and body, which are not included here, because they come under the category of Transcendental Unity. Consequently, it still remains true, that Unity and Multitude are privatively opposed. For Unity includes negation of division within itself absolutely and completely; whereas it is of the essence of Multitude, that it should be divided within itself for the reason that materially it is Many, and, therefore, is deprived of intrinsic indivision. On the other hand, Multitude essentially postulates negation of oneness in its constituents, of which negation Unity is essentially deprived. Accordingly, St. Thomas observes -- 'There is a twofold Unity; one of which is convertible with Being, and adds nothing to Being, over and above, save Indivision. And this Unity excludes (privat) Multitude, inasmuch as Multitude is caused by division. Not that it excludes extrinsic Multitude of which One constitutes part; but intrinsic Multitude, which is opposed to Unity. For it is not because a thing is said to he one, that therefore the existence of anything outside it, with which it may constitute Multitude, is denied; but what is denied is, its own division into many.'^{5} From these principles the Angelic Doctor deduces elsewhere another distinction between Unity and Multitude. For, 'In Multitude,' he observes, 'there is negation, in that one thing is distinguished from another by negation. Hence, in Multitude there is real negation or privation, in that one thing is said not to be another. And it is such a distinction by negation, that the negation contained in the nature of Unity negatives. Wherefore, I remark that the negation in which the nature of Unity is completed, is only a conceptual negation; for every relation of Being to negation and Not-Being is only conceptual. Hence, the relation of Being to Not-Being is only conceptual; and in like manner the privation, by which Not-Being is denied of Being, is only conceptual, as being the privation 'of a privation, or the negation of a negation.'^{6} One slight difficulty yet remains, whose solution will bring this Corollary to a close.

It has been maintained that Substance, as informed by its accidents, transformations of substances most probably, and certainly union of imperfect substances, are included among entities which are transcendentally one. But if so, Unity does not necessarily express Indivision; for such entities are, clearly enough, divisible in themselves. Thus, in a red rose there is the entity of the rose and the entity of redness; and these are physically separable from each other. Similarly, in a man there is soul and body, which are also really separable; and in water there are oxygen and hydrogen, which in like manner are distinct entities. But these three represent their respective classes.

The answer is as follows. First of all, as to substances informed by their accidents, it must be granted that the substances, distinct from their accidents, are complete entities; which is the reason why their inclusion under simple unity and simple being is less certain. But, on the other hand, it must be remembered that Accident is not simple being, but, as St. Thomas describes it, Being of Being. It is of its nature to postulate inhesion in some Subject, and, consequently, its entity is not naturally separable from that Subject. As to water, the oxygen and hydrogen are only potentially there, not actually; and when these are again evolved by chemical decomposition, the one entity of water ceases to be, and the two entities of oxygen and hydrogen take its place. Water, therefore, as water, is entitatively undivided. Much the same may be said of all substantial transformations. As regards imperfect substances, they are not complete entities, but Beings halved, so to speak; as they are essentially constituted to form one complete substance, by a substantial union that gives due perfection to each. This holds good equally in the case of integral parts, or members, that go to the formation of an organized whole.

{1} 'Unumquodque, in quantum est unum, in tantum est ens; unde ens et unum convertuntur.' Quol. vi, Q. I, a. I, c.

{2} 'Tripliciter aliquid unum ex duobus vel pluribus constituitur. Uno modo, ex duobus integris perfectis remanentibus; quod quidem fieri non potest, nisi in iis quorum forma est compositio, vel ordo, vel figura; sicut ex multis lapidibus absque aliquo ordine adunatis, per solam compositionem fit acervus; ex lapidibus autem et lignis secundum aliquem ordinem dispositis, et etiam ad aliquam figuram redactis, fit domus. . . . Alio modo fit aliquid unum ex perfectis, sed transmutatis, sicut ex elementis fit mixtum. . . . Tertio modo aliquid fit ex aliquibus non permixtis vel permutatis, sed imperfectis; sicut ex anima et corpore fit homo; et similiter ex diversis membris unum corpus constituitur.' 3ae ii, I, c.

{3} 'Duplex est totum; quoddam homogeneum, quod componitur ex similibus partibus; quoddam vero heterogeneum, quod componitur ex dissimilibus 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. In quantum ergo pars ejus 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 domes.' 1ae xi, 2, ad 2m.

{4} 'Unum non constituit multitudinem ex parte privationis, sed ex parte illa qua ponit ens.' De Potentia, Q. ix, a. 7, ad 10m.

{5} 'Duplex est unum; quoddam scil. quod convertitur cum ente, quod nihil addit supra ens nisi indivisionem. Et hoc unum privat multitudinem, in quantum multitudo ex divisione causatur; non quidem multitudinem extrinsecam quam unum constituit sicut pars, sed multitudinem intrinsecam quae unitati opponitur. Non enim ex hoc quod aliquid dicitur esse unum, negatur quin aliquid sit extra ipsum quod cum eo constituat multitudinem; sed negatur divisio ipsius in multa.' De Potentia, Q. iii, a. 16, ad 3m. Cf. 1ae xi, 2, ad 4m.

{6} 'In multitudine negatio est, secundum quod una res distinguitur ab alia per negationem. Unde in multitudine est negatlo vel privatio realis, secundum quod una res non dicitur esse alia. Et hujusmodi distinctionem per negationem negat negatio importata in ratione unitatis. IJnde dico, quod negatio ista in qua perficitur ratio unitatis, non est nisi negatio rationis tantum. Omnis enim respectus qui est entis ad negationem, vel ad non ens, non est nisi rationis. Unde relatio qua refertur ens ad non ens, non est nisi tantum in ratione. Et similiter privatio, qua de ente negatur non ens, est in ratione tantum, Ut privatio privationis, vel negatio negationis.' in I Sentt. d. xxiv, Q. I,a. 3, ad 1m.