28. MULTITUDE AND NUMBER.—The _one_ has for its correlative 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 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)