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[1092a] [1] 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,1 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.

If, then, it is impossible both not to include the Good among the first principles, and to include it in this way, it is clear that the first principles are not being rightly represented, nor are the primary substances. Nor is a certain thinker2 right in his assumption when he likens the principles of the universe to that of animals and plants, on the ground that the more perfect forms are always produced from those which are indeterminate and imperfect, and is led by this to assert that this is true also of the ultimate principles; so that not even unity itself is a real thing.3 He is wrong; for even in the natural world the principles from which these things are derived are perfect and complete—for it is man that begets man; the seed does not come first.4 It is absurd also to generate space simultaneously with the mathematical solids (for space is peculiar to particular things, which is why they are separable in space, whereas the objects of mathematics have no position) [20] and to say that they must be somewhere, and yet not explain what their spatial position is.

Those who assert that reality is derived from elements, and that numbers are the primary realities, ought to have first distinguished the senses in which one thing is derived from another, and then explained in what way number is derived from the first principles. Is it by mixture? But (a) not everything admits of mixture5; (b) the result of mixture is something different; and unity will not be separable,6 nor will it be a distinct entity, as they intend it to be.Is it by composition, as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of unity and plurality we shall think of them separately. This, then, is what number will be—a unit plus plurality, or unity plus the Unequal.

And since a thing is derived from elements either as inherent or as not inherent in it, in which way is number so derived? Derivation from inherent elements is only possible for things which admit of generation.7 Is it derived as from seed?But nothing can be emitted from that which is indivisible.8 Is it derived from a contrary which does not persist? But all things which derive their being in this way derive it also from something else which does persist. Since, therefore, one thinker9 regards unity as contrary to plurality,

1 Aristot. Met. 14.1.17.

2 Evidently Speusippus; cf. Aristot. Met. 14.4.3.

3 Speusippus argued that since all things are originally imperfect, unity, which is the first principle, must be imperfect, and therefore distinct from the good. Aristotle objects that the imperfect does not really exist, and so Speusippus deprives his first principle of reality.

4 Cf. Aristot. Met. 9.8.5.

5 e.g. to admit of mixture a thing must first have a separate existence, and the Great-and-Small, which is an affection or quality of number (Aristot. Met. 14.1.14) cannot exist separately.

6 sc. when it has once been mixed. Cf. Aristot. De Gen. et Corr. 327b 21-26.

7 And numbers are supposed to be eternal. Cf. Aristot. Met. 14.2.1-3.

8 i.e., unity, being indivisible, cannot contribute the formal principle of generation in the way that the male parent contributes it.

9 Speusippus: Plato. Cf. Aristot. Met. 14.1.5.

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