Speusippus in Iamblichus

Abstract

In ch. III of Isc Iamblichus had refused to identify the mathematicals with the soul. In ch. IX he insisted that the soul should be identified with all three branches of mathematics. While ch. IX is much more compatible with most of Isc and also with the Timaeus, ch. III is not completely inconsistent with some tendencies in Platonism as reported by Aristotle. While Plato, as Aristotle repeats time and again, supposed three ousiai only (sensibles, mathematicals, and ideas), some Platonists assumed more. One of the examples is Speusippus who, according to Aristotle (Met. Z 2, 1028b21-24; N 3,1090b13-19; fr. 33a; 50 Lang), not only made a difference between arithmeticals and geometricals, but also presumed the soul to be a separate ousia. It seems that the latter is precisely what the source of Isc ch. III did (“it is better to posit the soul in another genus of ousia, while assuming that mathematical principles and the mathematical ousia are nonmotive” p. 13, 12–15 F). Could it be that the inspiration of this chapter is ultimately Speusippean? Could it be that there are some other traces of Speusippus in Isc, in addition to what amounted to a quotation from Speusippus in Isc ch. IX (“... idea of the all-extended”)? To decide this question let us discuss Speusippus’ system as criticized by Aristotle.