Kitap 13
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ThoseSpeusippus and his followers. who recognize only the objects of mathematics as existing besides sensible things, abandoned Ideal number and posited mathematical number because they perceived the difficulty and artificiality of the Ideal theory. Others,Xenocrates and his followers. wishing to maintain both Forms and numbers, but not seeing how, if one posits theseUnity and the indeterminate dyad; for the difficulty see Aristot. Met. 13.7.3, 4. as first principles, mathematical number can exist besides Ideal number, identified Ideal with mathematical number,—but only in theory, since actually mathematical number is done away with, because the hypotheses which they state are peculiar to them and not mathematical.Cf. Aristot. Met. 13.6.10.
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And hePlato. who first assumed that there are Ideas, and that the Ideas are numbers, and that the objects of mathematics exist, naturally separated them. Thus it happens that all are right in some respect, but not altogether right; even they themselves admit as much by not agreeing but contradicting each other. The reason of this is that their assumptions and first principles are wrong;
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and it is difficult to propound a correct theory from faulty premisses: as Epicharmus says, no sooner is it said than it is seen to be wrong. Epicharmus, Fr. 14, Diels.
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We have now examined and analyzed the questions concerning numbers to a sufficient extent; for although one who is already convinced might be still more convinced by a fuller treatment, he who is not convinced would be brought no nearer to conviction.
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As for the first principles and causes and elements, the views expressed by those who discuss only sensible substance either have been described in the PhysicsAristot. Physics 1.4-6. or have no place in our present inquiry; but the views of those who assert that there are other substances besides sensible ones call for investigation next after those which we have just discussed.
