Book 13
17
Now if number only goes up to 10, as some hold,Cf. Aristot. Met. 12.8.2. The Platonists derived this view from the Pythagoreans; see Introduction. in the first place the Forms will soon run short. For example, if 3 is the Idea of Man, what number will be the Idea of Horse? Each number up to 10 is an Idea; the Idea of Horse, then, must be one of the numbers in this series, for they are substances or Ideas.
18
But the fact remains that they will run short, because the different types of animals will outnumber them. At the same time it is clear that if in this way the Ideal 3 is the Idea of Man, so will the other 3’s be also (for the 3’s in the same numbersRobin is probably right in taking this to mean that the 3 which is in the ideal 4 is like the 3 which is in the 4 which is in a higher ideal number, and so on (La Theorie platonicienne des Idees et des Nombres d’apres Aristote, p. 352). are similar), so that there will be an infinite number of men; and if each 3 is an Idea, each man will be an Idea of Man; or if not, they will still be men.
19
And if the smaller number is part of the greater, when it is composed of the addible units contained in the same number, then if the Ideal 4 is the Idea of something, e.g. horse or white, then man will be part of horse, if man is 2. It is absurd also that there should be an Idea of 10 and not of 11, nor of the following numbers.
20
Again, some things exist and come into being of which there are no FormsCf. Aristot. Met. 13.4.7, 8; Aristot. Met. 1.9.2, 3.; why, then, are there not Forms of these too? It follows that the Forms are not the causes of things.
20
Again, it is absurd that number up to 10 should be more really existent, and a Form, than 10 itself; although the former is not generated as a unity, whereas the latter is. However, they try to make out that the series up to 10 is a complete number;
