Kitap 13
13
But according to them 4 was generated from the first 2 and the indeterminate dyad, thus consisting of two 2’s apart from the Ideal 2.Cf. sect. 18. Otherwise 4 will consist of the Ideal 2 and another 2 added to it, and the Ideal 2 will consist of the Ideal 1 and another 1; and if this is so the other element cannot be the indeterminate dyad, because it produces one unit and not a definite 2.The general argument is: Numbers are produced by addition; but this is incompatible with the belief in the Indeterminate Dyad as a generative principle, because, being duplicative, it cannot produce single units.
14
Again, how can there be other 3’s and 2’s besides the Ideal numbers 3 and 2, and in what way can they be composed of prior and posterior units? All these theories are absurd and fictitious, and there can be no primary 2 and Ideal 3. Yet there must be, if we are to regard Unity and the indeterminate dyad as elements.i.e., if numbers are not generated by addition, there must be Ideal (or natural) numbers.
15
But if the consequences are impossible, the principles cannot be of this nature.
15
If, then, any one unit differs in kind from any other, these and other similar consequences necessarily follow. If, on the other hand, while the units in different numbers are different, those which are in the same number are alone indistinguishable from one another, even so the consequences which follow are no less difficult.
16
For example, in the Ideal number 10 there are ten units, and 10 is composed both of these and of two 5’s. Now since the Ideal 10 is not a chance number,I think Ross’s interpretation of this passage must be right. The Ideal 10 is a unique number, and the numbers contained in it must be ideal and unique; therefore the two 5’s must be specifically different, and so must their units—which contradicts the view under discussion. and is not composed of chance 5’s, any more than of chance units, the units in this number 10 must be different;
