The Religion and Philosophy of the Veda and Upanishads v2.c41.s8.6

v2.c41.s8.6

Frank,¹ as against Wilamowitz-Moellendorff, insists that in the fragment of Philolaos there is a reference to the twofold doctrine of the five regular bodies and their correspondence with the five elements, but he holds that this is merely one of many proofs that the ascription of the fragment to Philolaos is a mere error. He points out ² that the natural deduction to be made from Plato’s writings is that both the doctrine of the irrational and the discovery of the five figures were invented shortly before the time when he accepted them, apparently by Theaitetos. He denies to the real Pythagoras the mathematical achievements claimed for him, but ignored by Xenophanes, Herakleitos, Empedokles, and Herodotos,³ placing them in the Platonic age, while he traces the mathematical philosophy of the Pythagoreans to an effort to reconcile the doctrines of Anaxagoras and Demokritos, pointing out that their views are inconceivable before Anaxagoras (*c.* 460–430 B. C.) had clearly distinguished the ideas of quality and quantity, and first Protagoras and then Demokritos (*c.* 430 B. C.) had established the doctrine of the subjectivity of sense qualities. The Pythagorean view was thus one of points as monads, related to the dynamic conception of matter in Anaxagoras and the materialistic atomism of Demokritos as was the Monadologia physica of Kant’s youth to the dynamic conception of matter in Leibnitz and the atomism of Huyghens and Newton. Without necessarily accepting the whole of Frank’s contentions, and in particular the view that Speusippos is the real author of the Philolaos fragments, it is clear that we cannot safely accord to Pythagoras himself credit for his mathematical discoveries, and thus one important ground for the alleged derivation of his views from India disappears.