place the objects of mathematics between Ideas and sensible things. His divergence from the Pythagoreans in making the One and the Numbers separate from things, and his introduction of the Forms, were due to his inquiries in the region of definitory formulae (for the earlier thinkers had no tincture of dialectic), and his making the other entity besides the One a dyad was due to the belief that the numbers, except those which were prime, could be neatly produced out of the dyad as out of a plastic material.
Yet what happens is the contrary; the theory is not a reasonable one. For they make many things out of the matter, and the form generates only once, but what we observe is that one table is made from one matter, while the man who applies the form, though he is one, makes many tables. And the relation of the male to the female is similar; for the latter is impregnated by one copulation, but the male impregnates many females; yet these are analogues of those first principles.
Plato, then, declared himself thus on the points in question; it is evident from what has been said that he has used only two causes, that of the essence and the material cause (for the Forms are the cause of the essence of all other things, and the One is the cause of the essence of the Forms); and it is evident what the underlying matter is, of which the Forms are predicated in the case of sensible things, and the One in the case of Forms, viz. that this is a dyad, the great and the small. Further, he has assigned the cause of good and that of evil to the elements, one to each of the two, as we say some of his predecessors sought to do, e. g. Empedocles and Anaxagoras.
Our account of those who have spoken about first principles and reality and of the way in which they have spoken, has been
- This is not quite accurate. Really it is only powers of 2 that could be neatly produced out of this 1 and the indefinite dyad; cf. n. 1091a9. In Parmenides 143c-144a 3 is derived from 1 and 2 (the number 2, not, as Aristotle says, the indefinite 2) by addition, and the numbers higher than 3 are derived from 2 and 3 by multiplication. Primes are not there excepted; Plato speaks as if all the higher numbers could be got by multiplication. Nothing in the works of Plato corresponds exactly to what Aristotle says here.
- Cf. 984b18, 985a4.