Book 13
1
First of all it would be well to define the differentia of a number; and of a unit, if it has a differentia. Now units must differ either in quantity or in quality; and clearly neither of these alternatives can be true. But units may differ, as number does, in quantity. But if units also differed in quantity, number would differ from number, although equal in number of units.
2
Again, are the first units greater or smaller, and do the later units increase in size, or the opposite? All these suggestions are absurd. Nor can units differ in quality; for no modification can ever be applicable to them, because these thinkers hold that even in numbers quality is a later attribute than quantity.Numbers have quality as being prime or composite, plane or solid (i.e., products of two or three factors); but these qualities are clearly incidental to quantity. Cf. Aristot. Met. 5.14.2.
3
Further, the units cannot derive quality either from unity or from the dyad; because unity has no quality, and the dyad produces quantity, because its nature causes things to be many. If, then, the units differ in some other way, they should most certainly state this at the outset, and explain, if possible, with regard to the differentia of the unit, why it must exist; or failing this, what differentia they mean.
4
Clearly, then, if the Ideas are numbers, the units cannot all be addible, nor can they all be inaddible in either sense. Nor again is the theory sound which certain other thinkersCf. Aristot. Met. 13.1.4. hold concerning numbers.
