 In 1962, Guthrie, in his History of Greek Philosophy, regarded the issue of the authenticity of the fragments handed down in Philolaus’ name as undecided, although he commented that opponents of authenticity did “not seem to be at their best on the subject” (331). In that same year Burkert provided decisive arguments, which have led to a consensus that a core of the fragments of Philolaus are authentic. Earlier discussions of the authenticity of the fragments were often based on the faulty assumption that the fragments were either all genuine or all spurious. Opponents of authenticity typically showed that a few of the fragments were spurious and then assumed that all the rest were as well (e.g., Bywater 1868). Given the amount of forgery in the Pythagorean tradition, however, even if fragments from a genuine book of Philolaus survive, it is likely that fragments from spurious works survive as well. Burkert made a crucial distinction between two traditions concerning Pythagoreanism. One begins already in Plato’s Academy and treats Pythagoreanism as largely identical with later Platonic thought, including the postulation of the one and the indefinite dyad as first principles (1972a, 53–83). This is the tradition which came to dominate among later Neoplatonists and which served as the basis for the production of the pseudo-Pythagorean writings. The second tradition is represented by Aristotle, who presents fifth-century Pythagoreanism as having had some influence on Plato but as radically different from Plato in making no distinction between the intelligible and sensible world (1972a, 28–52). Burkert then showed that, while some of the fragments of Philolaus did employ Platonic and Aristotelian ideas and hence were spurious, other fragments were in very close agreement with Aristotle’s account of fifth-century Pythagoreanism and hence likely to be authentic.