27. Kinds of Unity.—(a) The unity we have been describing has been called transcendental, to distinguish it from predicamental unity—the unity which is proper to a special category of being, namely, quantity, and which, accordingly, is also called quantitative or mathematical unity. While the former is common to all being, with which it is really identical, and to which it adds nothing real, the latter belongs and is applicable, properly speaking, only to the mode of being which is corporeal, [pg 117] which exists only as affected by quantity, as occupying space, as capable of measurement; and therefore, also, this latter unity adds something real to the being which it affects, namely, the attribute of quantity, of which unity is the measure and the generating principle.[136] For quantity, as we shall see, is a mode of being really distinct from the corporeal substance which it affects. The quantity has its own transcendental unity; so has the substance which it quantifies; so has the composite whole, the quantified body, but this latter transcendental unity, like the composite being with which it is identical, is not a unum per se but only a unum per accidens (cf. b, infra).
We derive our notion of quantitative or mathematical unity, which is the principle of counting and the standard of measuring, from dividing mentally the continuous quantity or magnitude which is one of the immediate data of sense experience. Now the distinction between this unit and transcendental unity supposes not merely that quantity is really distinct from the corporeal substance, but also that the human mind is capable of conceiving as real certain modes of being other than the corporeal, modes to which quantitative concepts and processes, such as counting and measuring, are not properly applicable, as they are to corporeal reality, but only in an analogical or transferred sense ([2]). The notion of transcendental unity, therefore, bears the same relation to that of quantitative unity, as the notion of being in general bears to that of quantified or corporeal being.
(b) Transcendental unity may be either essential (or substantial, “unum per se,” “unum simpliciter”), or accidental (“unum per accidens,” “unum secundum quid”). The former characterizes a being which has nothing in it beyond what is essential to it as such, e.g. the unity of any substance: and this unity is twofold—(1) unity of simplicity and (2) unity of composition—according as the substance is essentially simple (such as the human soul or a pure spirit) or essentially composite (such as man, or any corporeal substance: since every such substance is composed essentially of a formative and an indeterminate principle).[137]
Accidental unity is the unity of a being whose constituent factors or contents are not really united in such a way as to form one essence, whether simple or composite. It is threefold: (1) collective unity, or unity of aggregation, as of a heap of stones or a crowd of men; (2) artificial unity, as of a house or a picture; and (3) natural or physical unity, as of any existing substance with its connatural accidents, e.g. a living organism with its size, shape, qualities, etc., or the human soul with its faculties.[138]
(c) Transcendental unity may be either individual (singular, numerical, concrete, real) or universal (specific, generic, abstract, logical). The former is that which characterizes being or reality considered as actually existing or as proximately capable of existing: the unity of an individual nature or essence: the unity whereby a being is not merely undivided in itself but incapable of repetition or multiplication of itself. It is only the individual as such that can actually exist: the abstract and universal is incapable of actually existing as such. We shall examine presently what it is that individuates reality, and what it is that renders it capable of existing actually in the form of “things” or of “persons”—the forms in which it actually presents itself in our experience.
Abstract or universal unity is the unity which characterizes a reality conceived as an abstract, universal object by the human intellect. The object of a specific or generic concept, “man” or “animal,” for example, is one in this sense, undivided in itself, but capable of indefinite multiplication or repetition in the only mode in which it can actually exist—the individual mode. The universal is unum aptum inesse pluribus.
Finally, we can conceive any nature or essence without considering it in either of its alternative states—either as individual or as universal. Thus conceived it is characterized by a unity which has been commonly designated as abstract, or (by Scotists) as formal unity.
28. Multitude and Number.—The one has for its correlative [pg 119] the manifold. Units, one of which is not the other, constitute multitude or plurality. If unity is the negation of actual division in being, multitude results from a second negation, that, namely, by which the undivided being or unit is marked off or divided from other units.[139] We have defined unity by the negation of actual intrinsic dividedness; and we have seen it to be compatible with extrinsic dividedness, or otherness. Thus the vague notion of dividedness is anterior to that of unity. Now multitude involves dividedness; but it also involves and presupposes the intrinsic undividedness or unity of each constituent of the manifold. In the real order of things the one is prior to all dividedness; but on account of the sensuous origin of our concepts we can define the former only by exclusion of the latter. The order in which we obtain these ideas seems, therefore, to be as follows: “first being, then dividedness, next unity which excludes dividedness, and finally multitude which consists of units”.[140]
The relation of the one to the manifold is that of undivided being to divided being. The same reality cannot be one and manifold under the same aspect; though obviously a being may be actually one and potentially manifold or vice versa, or one under a certain aspect and manifold under another aspect.
From the transcendental plurality or multitude which we have just described we can distinguish predicamental or quantitative plurality: a distinction which is to be understood in the same way as when applied to unity. Quantitative multitude is the actually separated or divided condition of quantified being. Number is a multitude measured or counted by unity: it is a counted, and, therefore, necessarily a definite and finite multitude. Now it is mathematical unity that is, properly, the principle of number and the standard or measure of all counting; and therefore it is only to realities which fall within the category of quantity—in other words, to material being—that the concept of number is properly applicable. No doubt we can and do [pg 120] conceive transcendental unity after the analogy of the quantitative unity which is the principle of counting and measuring; and no doubt we can use the transcendental concept of “actually undivided being” as a principle of enumeration, and so “count” or “enumerate” spiritual beings; but this counting is only analogical; and many philosophers, following Aristotle and St. Thomas, hold that the concepts of numerical multiplicity and numerical distinction are not properly applicable to immaterial beings, that these latter differ individually from one another not numerically, but each by its whole nature or essence, that is, formally.[141]