Book 13
9
For assuming that there is a first unit or first 1,i.e., the Ideal One. it is reasonable that the units should be prior and posterior; and similarly in the case of 2’s, if there is a first 2. For it is reasonable and indeed necessary that after the first there should be a second; and if a second, a third; and so on with the rest in sequence.
10
But the two statements, that there is after 1 a first and a second unit, and that there is a first 2, are incompatible. These thinkers, however, recognize a first unit and first 1, but not a second and third; and they recognize a first 2, but not a second and third.
10
It is also evident that if all units are inaddible, there cannot be an Ideal 2 and 3, and similarly with the other numbers;
11
for whether the units are indistinguishable or each is different in kind from every other, numbers must be produced by addition; e.g. 2 by adding 1 to another 1, and 3 by adding another 1 to the 2, and 4 similarly.This is of course not true of the natural numbers.
12
This being so, numbers cannot be generated as these thinkers try to generate them, from Unity and the dyad; because 2 becomes a part of 3,i.e., 3 is produced by adding 1 to 2. and 3 of 4, and the same applies to the following numbers.
