Metaphysics

​First, then, we must consider whether the units are associable or inassociable, and if inassociable, in which of the two ways we distinguished. For, on the one hand, it is possible that any unit is inassociable with any other unit; on the other hand, that those in the Dyad-itself are inassociable with those in the Triad-itself, and similarly that those in each primary number are inassociable with one another. If, then, all the units are associable and non-different, the mathematical number arises, and this alone, and it is not possible for the Ideas to be numbers (for what sort of number will Man-itself or Animal-itself be, or any other of the Forms? For the Idea of each is one, e.g. of Man-itself one, and of Animal-itself another one; but the similar and non-different numbers are infinite, so that this particular Triad is no more Man-itself than any other Triad); and if the Ideas are not numbers, it is not possible for them to exist at all (for from what principles will the Ideas be? For number is from the One and the indefinite Dyad, and these are said to be the principles and elements of number, and it is possible to order them neither prior to numbers nor posterior); but if the units are inassociable, and inassociable in such a way that any one is inassociable with any other, neither is it possible for this number to be the mathematical one (for the mathematical is from non-different units, and the demonstrations concerning it apply to it as being of this character) nor that of the Forms. For the Dyad will not be the first from the One and the indefinite Dyad, and then the successive numbers, as they say ‘Dyad, Triad, Tetrad’—for the units in the first Dyad are generated together, whether as the first who said it held, from unequal things (for they were generated when these were equalized), or otherwise—, since if one unit is prior to the other, it will also be prior to the Dyad composed of them; for whenever there is something prior and something posterior, that which is composed of them will be prior to the one and posterior to the other. Further, since there is first the One-itself, then of the other things there is a certain first ‘one’, and a second after that, and again a third, which is second after the second and third after the first ‘one’—so that the units would be prior to the numbers from which they are said to be, for example in the Dyad there will be a third unit before the Three exists, and in the Triad a fourth and fifth unit before these numbers exist. Now no one indeed has said that the units are inassociable in this way; but according to their principles it is reasonable even so, though in truth impossible. For it is reasonable that the units should be prior and posterior, if indeed there is some first unit and a first One, and likewise also dyads, if indeed there is also a first Dyad; for after the first it is reasonable and necessary that there be a second, and if a second, a third, and so on with the others successively (but to say both at once, that there is a first and second unit after the One, and a first Dyad, is impossible). But they make a unit and a first One, but no longer a second and third, and a first Dyad, but no longer a second and third.