They Footnote 1The Platonists. say that there is no generation of odd numbers, Footnote 2This statement was probably symbolical. They described the odd numbers as ungenerated because they likened them to the One, the principle of pure form
(Ross ad loc.). which clearly implies that there is generation of even ones; and some hold that the even is constructed first out of unequals—the Great and Small—when they are equalized. Footnote 3Cf. Aristot. Met. 13.7.5. Therefore the inequality must apply to them before they are equalized. If they had always been equalized they would not have been unequal before; for there is nothing prior to that which has always been.
Hence evidently it is not for the sake of a logical theory that they introduce the generation of numbers
A difficulty, and a discredit to those who make light of the difficulty, arises out of the question how the elements and first principles are related to the the Good and the Beautiful. The difficulty is this: whether any of the elements is such as we mean when we Footnote 4Aristotle speaks as a Platonist. See Introduction. speak of the Good or the Supreme Good, or whether on the contrary these are later in generation than the elements.
It would seem that there is an agreement between the mythologists and some present-day thinkers, Footnote 5The Pythagoreans and Speusippus; cf. Aristot. Met. 12.7.10. who deny that there is such an element, and say that it was only after some evolution in the natural order of things that both the Good and the Beautiful appeared. They do this to avoid a real difficulty which confronts those who hold, as some do, that unity is a first principle.
This difficulty arises not from ascribing goodness to the first principle as an attribute, but from treating unity as a principle, and a principle in the sense of an element, and then deriving number from unity. The early poets agree with this view in so far as they assert that it was not the original forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and ruler.
It was, however, on the ground of the changing of the rulers of the world that the poets were led to state these theories; because those of them who compromise by not describing everything in mythological language—e.g. Pherecydes Footnote 6Of Syros (circa -525 B.C.). He made Zeus one of the three primary beings (Diels,Vorsokratiker201, 202). and certain others—make the primary generator the Supreme Good; and so do the Magi, Footnote 7The Zoroastrian priestly caste. and some of the later philosophers such as Empedocles and Anaxagoras: the one making Love an element, Footnote 8Cf. Aristot. Met. 3.1.13. and the other making Mind a first principle. Footnote 9Cf. Aristot. Met. 1.3.16.
And of those who hold that unchangeable substances exist, some Footnote 10Plato; cf. Aristot. Met. 1.6.10. identify absolute unity with absolute goodness; but they considered that the essence of goodness was primarily unity.
This, then, is the problem: which of these two views we should hold.
Now it is remarkable if that which is primary and eternal and supremely self-sufficient does not possess this very quality, viz. self-sufficiency and immunity, in a primary degree and as something good. Moreover, it is imperishable and self-sufficient for no other reason than because it is good. Hence it is probably true to say that the first principle is of this nature.
But to say that this principle is unity, or if not that, that it is an element, and an element of numbers, is impossible; for this involves a serious difficulty, to avoid which some thinkers Footnote 11Speusippus and his followers; cf. sect. 3. have abandoned the theory (viz. those who agree that unity is a first principle and element, but of mathematical number). For on this view all units become identical with some good, and we get a great abundance of goods. Footnote 12If unity is goodness, and every unit is a kind of unity, every unit must be a kind of goodness—which is absurd.
Further, if the Forms are numbers, all Forms become identical with some good. Again, let us assume that there are Ideas of anything that we choose. If there are Ideas only of goods, the Ideas will not be substances Footnote 13Because they are Ideas not of substances but of qualities. ; and if there are Ideas of substances also, all animals and plants, and all things that participate in the Ideas, will be goods. Footnote 14Because the Ideas are goods.
Not only do these absurdities follow, but it also follows that the contrary element, whether it is plurality or the unequal, i.e. the Great and Small, is absolute badness. Hence one thinker Footnote 15Speusippus. avoided associating the Good with unity, on the ground that since generation proceeds from contraries, the nature of plurality would then necessarily be bad.
Others Footnote 16Plato and Xenocrates. hold that inequality is the nature of the bad. It follows, then, that all things partake of the Bad except one—absolute unity; and that numbers partake of it in a more unmitigated form than do spatial magnitudes Footnote 17As being more directly derived from the first principles. Cf. Aristot. Met. 1.9.23 n. ; and that the Bad is the province for the activity of the Good, and partakes of and tends towards that which is destructive of the Good; for a contrary is destructive of its contrary.
And if, as we said, Footnote 18Aristot. Met. 14.1.17. the matter of each thing is that which is it potentially—e.g., the matter of actual fire is that which is potentially fire—then the Bad will be simply the potentially Good.
Thus all these objections follow because (1.) they make every principle an element; (2.) they make contraries principles; (3.) they make unity a principle; and (4.) they make numbers the primary substances, and separable, and Forms.