Metaphysics

​But those thinkers say that number is the existents; at any rate, they apply their theorems to bodies as though those bodies were composed of those numbers. —If, then, it is necessary, if indeed number is something self-existent among the existents, that it should be in one of these mentioned ways, and yet none of these is possible, it is clear that there is no such nature of number as those who make it separable construct. —Moreover, is each unit from the Great and the Small made equal, or is one from the Small and another from the Great? If, indeed, it is in the latter way, neither is each unit composed of all the elements, nor are the units without difference (for in one the Great is present, and in another the Small, which is contrary in nature). Moreover, how is it with the units in the Triad itself? For one is odd; but perhaps because of this they make the One itself the middle in the odd. But if each of the units is from both made equal, how will the Dyad exist, being some single nature, composed of the Great and the Small? Or how will it differ from the unit? Moreover, the unit is prior to the Dyad (for when it is abolished, the Dyad is abolished); therefore, being prior to an idea, it must itself be an idea of an idea, and must have been generated prior to it. From what, then, was it generated? For the indefinite Dyad was the maker of two. —Moreover, it is necessary that number be either infinite or finite; for they make number separable, so that it is not possible that one of these should not belong to it. That it is not possible, then, for it to be infinite is clear (for the infinite is neither odd nor even, but the generation of numbers is always either of an odd number or of an even number: in one way, when the One falls into the even, it is odd; in another way, when the Dyad falls in, it is that which is doubled from the One; and in another way, when the odd numbers fall in, it is the other even; moreover, if every idea is of something, and numbers are ideas, the infinite also will be an idea of something, either of sensible things or of something else; and yet this is possible neither according to their thesis nor according to reason, at least they arrange the ideas in this way). But if it is finite, up to what limit? For this must be stated not only as a fact, but also with its reason. But indeed, if number goes up to the Decad, as some say, in the first place the forms will quickly run short—for example, if the Triad is Man-itself, what number will be Horse-itself? For each number up to the Decad is some ‘itself’; it is necessary, then, that it should be one of the numbers within these (for these are substances and ideas); but nevertheless they will run short (for the forms of animal will exceed them). And at the same time it is clear that if in this way the Triad is Man-itself, so also are the other triads (for those in the same numbers are similar), so that there will be infinite men, if indeed each triad is an idea, each being Man-itself, and if not, at least they will be men. And if the smaller number is a part of the greater, being composed of the associable units in the same number, if indeed the Tetrad itself is the idea of something, for example of a horse or of white, man will be a part of a horse, if man is a Dyad. And it is also absurd that there should be an idea of the Decad, but not of the Hendecad, nor of the subsequent numbers. Moreover, some things both exist and come to be of which there are no forms; why then are there not forms of those things as well? Therefore, the forms are not causes.