PROPOSITION XXXIII.

Transcendental Unity is neither convertible nor identical with Quantitative Unity; though this latter in itself absolutely is a special determination of the former.

PROLEGOMENON.

Numeric Unity has received two meanings. By some it is identified with Quantitative Unity; by others, with Individual Unity. The question involved in this diversity of acceptation will offer itself for consideration, later on, under the Category of Quantity; and does not concern us now. The object at present is to show, that Transcendental Unity is neither convertible nor identical with Numeric Unity; whether this latter be understood to stand for Quantitative or, on the other hand, Individual Unity. The present Proposition undertakes to distinguish it from Quantitative; the succeeding, from Individual Unity. It would almost seem, so far as one can form a judgment on a matter so obscure, as though the prominence of Number in the Pythagorean Metaphysics were due to this identification of Transcendental with Quantitative Unity. St. Thomas accuses Avicenna more than once of this confusion of the two, and maintains against him the doctrine which it is the purpose of these two Theses to establish.^{1}

I. THE FIRST MEMBER of the Proposition, viz, that Transcendental is not convertible or identical with Quantitative Unity, is so self-evident as scarcely to require proof. For, if all Unity were Quantitative, one of two things must follow; either that there is no other Being but material Being, or that no Being which is immaterial is one.

II. THE SECOND MEMBER, which declares that Quantitative Unity in itself absolutely is a special determination of Transcendental Unity, needs declaration.

Quantity, (we presume now what will afterwards be discussed, viz. that Quantity has a distinct entity of its own, apart from the substance or Subject which it informs), may be considered under three aspects; first, as it is in itself; secondly, in its relation to the subject which it informs; thirdly, in its relation to the entire composite, that is, to the substance as informed by itself, out of which union arises an integral whole. The present question concerns the Unity which it has, or bestows, under these several aspects. These points shall be separately discussed, in the order which has been already adopted.

a. The first point, then, is to determine the nature of the Unity which Quantity, in itself and absolutely considered, possesses. Some have maintained that it is of a character altogether distinct from Transcendental Unity; and that it adds something positive to Quantity, by virtue of which it becomes the principle of number. But this opinion is singular, and rests on no solid foundation. Let it suffice to say, with St. Thomas and most of the Doctors, that the Unity of Quantity itself is simply Transcendental Unity, determined to this particular Category; for, like real Being, Unity also is determined to the tea Categories. In other words, Quantitative Unity, thus considered, is Transcendental Unity in Quantity. Hence, Quantitative bears to Transcendental Unity the relation of the contained to the containing, of the determined to the undetermined. So then, Quantitative is Transcendental Unity, yet is not convertible with, but a special determination ot it; since Transcendental Unity is to be found in the other Categories, as well as in that of Quantity, and beyond all the Categories, besides. Such is the doctrine of St. Thomas, as it is given in the following passage: 'Since Division is the cause of Multitude, and Indivision of Unity; one must form one's judgment of the One and the Many, according to the nature of the division. Now, there is a certain division which entirely transcends the Category of Quantity; one, that is, which arises out of a sort of formal opposition that has nothing to do with quantity. Hence, the Multitude which follows upon this division, and the Unity which consists in privation of this division, must necessarily be of wider universality and extension than the Category of Quantity.'^{2}

b. The next point is, to determine the nature of that Unity which Quantity, as a form, confers on the Substance which it informs. A little consideration will suffice to show that the Unity, thus conferred on Substance, is purely adventitious and extrinsic. For Substance of its own proper nature has its own Entity and its own Transcendental Unity, which is incapable of any alienation or change by accidental addition of whatever sort. Further confirmation is derived from the fact, that the same continuous Quantity may give an extrinsic and accidental Unity to two Substances, whose Entity and Transcendental Unity remain severally intact and mutually distinct. Thus, to adopt the example of Suarez, a stick may be cut from the hedge, and the said stick may be partly living, partly dead. In such case, there are two substantial forms and, consequently, two distinct Substances in different parts of the stick. Yet it is called one stick (i.e. it is sensibly one), because of the adventitious Unity which it has received from its information by one continuous Quantity. The Unity, then, which Quantity gives to Substance is entirely distinct from the entitative Unity of this latter. But it may be asked, What is the nature of this Unity which Quantity gives to its subject? Is it mere Indivision, or does it include something positive which has been added? The Unity which Quantity communicates is its own Transcendental Unity. So far is plain enough. Now, it has been shown that Transcendental Unity includes, in its formal concept, the Being of which Division is denied. Therefore, every determination of Transcendental Unity must include, in its formal concept, the determined Being which is undivided. Consequently, Quantity bestows its Unity on Substance by bestowing itself. Indeed, there is no other imaginable way in which it could do so. But what is that positive perfection which Quantity adds to material Substance? This is a question which will be discussed in its proper place. Suffice it now to say, that Quantity gives to material Substance its local extension and the localization of part outside part. From what has been said it will appear, that the Transcendental Unity of Quantity and the Transcendental Unity of Substance are essentially differentiated by their separate determination; so that the former cannot be imbibed into the latter by virtue of its communication, but, remaining Transcendental in Quantity, is extrinsic and accidental to Substance.

c. The third point is, What sort of Unity results to the whole Composite, as such, from the information of material Substance by Quantity? The answer has already been implicitly given, in a previous discussion a few pages back. In accordance with the more probable and more received opinion, it must be said, that such Unity is Transcendental. For there is real physical conjunction and mutual completion between material Substance and its Quantity, which results in the constitution of a real new Entity that is undivided in itself. Nevertheless, this newly constituted Entity must be included under the category of Being by accident, and of Unity by accident; for the reason that the Quantity, even as component part of the quantified Substance, claims no place in the Essence of the composite, but remains an Accident supervening. Accident does not enter into the definition of Substance; although Substance, after a sort, enters into the definition of Accident.

DIFFICULTIES.

I. It is objected against the second member of this Proposition that Quantitative Unity, absolutely regarded, is not the mere determination of Transcendental Unity to a certain Category, but is specifically distinct. For it is of the nature of Transcendental Unity to add nothing to the Entity of which it is the Attribute, save Indivision. But Quantitative Unity adds to Quantity something positive; by virtue of which it becomes the principle of Number, and is invested with the faculties of a measure. Unless this be admitted, there seems to be no sufficient reason why Number should be limited to the Category of Quantity; since Transcendental Unity in all the Categories would supply a sufficient basis for numeration. Then, as to measure, unless Quantitative Unity adds something positive to Quantity; there is no reason why that Unity should be a measure, rather than any other Unity.

ANSWER. There is no necessity for the introduction of anything positive into Quantitative Unity, beyond that inclusion of the Entity itself which has been shown to enter into the common concept of Transcendental Unity; and for this reason. Almost the only difference discoverable between Transcendental and Numerical Unity is to be found in this, that the latter is limited to Quantitative Being, not the former. Hence the determination of Being to Quantified Being is sufficient reason of itself for the determination of Unity to Quantified or Numerical Unity. It must be observed, however, that this answer, equally with the objection, supposes the identification of Numerical with Quantified Unity. Then, as to its functions as a Measure, it must be remarked, first of all, that Measure is not Unity, but a consequent of Unity. Then, (to answer the argument directly), the conclusion is just; but it has no relevance. For it is freely admitted that Transcendental Unity is just as much the Measure of Multitude, as Quantitative Unity is the Measure of Number. If an appeal be made to common usage, and it should be contended that Measure is limited to Quantified Being; it suffices to reply, that this arises from the practical necessities of life and the derivation of our ideas from sensible perfection; while, on the other hand, it is most true, in the highest of senses, that God is the Supreme Measure of all things.

II. Again: it has been objected that Transcendental Unity expresses Indivisibility. But it is of the nature of Quantity, and therefore of Quantitative Unity, that it should be capable of division. Therefore, Quantitative Unity cannot be a mere determination of Transcendental Unity.

ANSWER. The reply to this objection is given by a simple denial of the Major. It is quite untrue that Transcendental Unity consists in the indivisibility of Being. If this were so; no composite Being could be entitatively One. Moreover, it has been sufficiently shown that Unity is actual indivision of Being; and equally belongs to Being that is capable, as to Being that is incapable, of Division.

III. A third objection has been brought against the same member of the Proposition; and it is this. There must be something more added, by the informing Quantity, to a Substance than the mere actual division which is the Transcendental Unity of that Quantity. For, suppose some material Substance informed by a definite continuous Quantity. Then, let that Substance be divided.

The Quantity remains the same as before; but, nevertheless, the Substance, still under the information of its Quantity, loses its Unity and becomes two Substances. Hence it is plain, that Quantity gives to Substance a Unity which is quite distinct from its own Transcendental Unity.

ANSWER. This argument is based upon a false assumption; and the false assumption is due to an amphibology. For 'the same Quantity' may express identity of measure, or entitative identity. In the instance adduced there may be identity of measure, but most certainly there is not identity of Being. But why? The answer to this question necessitates a careful analysis of the concepts which more immediately enter into the question, What is meant by continuous Quantity? Continuous Quantity is that which is united within one common limit. Within that limit there is unbroken continuity; but the continuity stops at the limit. Now, if Transcendental Unity adds nothing to Being but actual Indivision; it is manifest that the Transcendental Unity of continuous Quantity will consist in undivided continuity within the one common limit. If that continuity be broken, Quantitative Unity is broken. Now, to apply this brief analysis to the example brought forward in the objection. If that Substance be divided, informed as it is by its own special Quantity, the continuity of its Quantity is broken. The quantity no longer remains continuous under one common limit, but is divided off under two limits. Thus the quantity loses its Transcendental Unity, and becomes many, --not quantity, but quantities which are to any distance separable from each other. Therefore, the entitative Unity of Quantity does not remain, and cannot, therefore, be the same. To take an illustration: There is a worm crawling before our feet. It is one Substance and one continuous Quantity, whose limit gives the animal its sensible configuration. Now cut it in two. There are two distinct living Substances; but there are also two distinct continuous Quantities under two limits, which give to the two animals respectively, their external form. So separate are they now, that one may remain in England, and the other find its way to China. Thus, after the operation, the previous Substance (i.e. the worm) has lost its Transcendental Unity, and has become two Entities and two Unities. The continuous Quantity which informed it has lost its Transcendental Unity, as well as Entity; and has become two Entities, two Unities. Consequently, the Unity which it conferred on the Substance of the worm has ceased, and is replaced by two Unities, extraneous and accidental to the substantial Essence of the two worms.

{1} See 1ae xi, 1, ad 1m; in I Sentt. d. xxiv, Q. i, a. 3, o; De Potent. Q. ix, a. 7, o; besides passages already quoted, where the opposite opinion is maintained.

{2} 'Cum divisio multitudinem causet, indivisio vero unitatem, oportet secundum rationem divisionis de uno et multo judicium sumi. Est autem quaedam divisio quae omnino genus quantitatis excedit, quae scil. est per aliquam oppositionem formalem, quae nullam quantitatem concernit. Unde oportet quod multitudo hanc divisionem consequens et unum quod hanc divisionem privat, sint majoris communitatis et ambitus quam genus quantitatis.' De Potentia, Q. ix, a. 7, c, v. fi.