See Döring in _Arch._ v. pp. 505 sqq. There seems to be a reference to the theory of the “three lives” in Herakleitos, fr. 111. It was apparently taught in the Pythagorean Society of Phleious; for Herakleides made Pythagoras expound it in a conversation with the tyrant of Phleious (Cic. _Tusc._ v. 3; Diog. pr. 12, viii. 8), and it is developed by Plato in a dialogue which is, as it were, dedicated to Echekrates. If it should be thought that this is interpreting Pythagoras too much in the light of Schopenhauer, it may be answered that even the Orphics came very near such a theory. The soul must not drink of Lethe, but go past it and drink of the water of Memory, before it can claim to become one of the heroes. This has obvious points of contact with Plato’s ἀνάμνησις, and the only question is how much of the _Phaedo_ we are to ascribe to Pythagorean sources. A great deal, I suspect. See Prof. Stewart’s _Myths of Plato_, pp. 152 sqq. [Sidenote: Arithmetic.] 46. In his treatise on Arithmetic, Aristoxenos said that Pythagoras was the first to carry that study beyond the needs of commerce,[230] and his statement is confirmed by everything we otherwise know. By the end of the fifth century B.C., we find that there is a widespread interest in such subjects and that these are studied for their own sake. Now this new interest cannot have been wholly the work of a school; it must have originated with some great man, and there is no one but Pythagoras to whom we can refer it. As, however, he wrote nothing, we have no sure means of distinguishing his own teaching from that of his followers in the next generation or two. All we can safely say is that, the more primitive any Pythagorean doctrine appears, the more likely it is to be that of Pythagoras himself, and all the more so if it can be shown to have points of contact with views which we know to have been held in his own time or shortly before it. In particular, when we find the later Pythagoreans teaching things that were already something of an anachronism in their own day, we may be reasonably sure that we are dealing with survivals which only the authority of the master’s name could have preserved. Some of these must be mentioned at once, though the developed system belongs to a later part of our story. It is only by separating its earliest form from its later that the true place of Pythagoreanism in Greek thought can be made clear, though we must always remember that no one can now pretend to draw the line between its successive stages with any certainty. Footnote 230: Stob. i. p. 20, 1, ἐκ τῶν Ἀριστοξένου περὶ ἀριθμητικῆς, Τὴν δὲ περὶ τοὺς ἀριθμοὺς πραγματείαν μάλιστα πάντων τιμῆσαι δοκεῖ Πυθαγόρας καὶ προαγαγεῖν ἐπὶ τὸ πρόσθεν ἀπαγαγὼν ἀπὸ τῆς τῶν ἐμπόρων χρείας. [Sidenote: The figures.]