Book 13
26
Again, if every unit plus another unit makes 2, a unit from the Ideal 2 plus one from the Ideal 3 will make 2—a 2 composed of different unitsWhich conflicts with the view under discussion.; will this be prior or posterior to 3? It rather seems that it must be prior, because one of the units is contemporaneous with 3, and the other with 2.The implication seems to be, as Ross says, that the Platonists will refuse to admit that there is a number between 2 and 3.
27
We assume that in general 1 and 1, whether the things are equal or unequal, make 2; e.g. good and bad, or man and horse; but the supporters of this theory say that not even two units make 2.
27
If the number of the Ideal 3 is not greater than that of the Ideal 2, it is strange; and if it is greater, then clearly there is a number in it equal to the 2, so that this number is not different from the Ideal 2.
28
But this is impossible, if there is a first and second number.i.e., if numbers are specifically different. Cf. Aristot. Met. 13.6.1. Nor will the Ideas be numbers. For on this particular point they are right who claim that the units must be different if there are to be Ideas, as has been already stated.sect. 2-4 above. For the form is unique; but if the units are undifferentiated, the 2’s and 3’s will be undifferentiated.
