 The catalogue includes several problematic names, such as Alcmaeon, Empedocles, Parmenides and Melissus. Alcmaeon was active in Croton when the Pythagoreans flourished there, but Aristotle explicitly distinguishes Alcmaeon from the Pythagoreans and scholarly consensus is that he is not a Pythagorean (see the entry on  Alcmaeon).  Most scholars would agree that Empedocles was heavily influenced by Pythagoreanism; in the later tradition fragments of Empedocles are routinely cited to support the Pythagorean doctrines of metempsychosis and vegetarianism (e.g., Sextus Empiricus, Adversus Mathematicos IX 126–30). On the other hand, both in the ancient and in the modern world, Empedocles is not usually labeled a Pythagorean, because, whatever the initial Pythagorean influences, he developed a philosophical system that was his own original contribution. Parmenides is again not usually identified as a Pythagorean in either the ancient or modern tradition and, although scholars have speculated on Pythagorean influences on Parmenides, there is little that can be identified as overtly Pythagorean in his philosophy. The reason for Parmenides’ inclusion in the catalogue is pretty clearly the tradition that his alleged teacher Ameinias was a Pythagorean (Diogenes Laertius IX 21). There is no reason to doubt this story, but it gives us no more reason to call Parmenides a Pythagorean than to call Plato a Socratic or Aristotle a Platonist. It would appear that Melissus was included on the list because he was regarded in turn as the pupil of Parmenides. Inclusion in the catalogue thus need not indicate that a figure lived a Pythagorean way of life or that he adopted metaphysical principles that were distinctively Pythagorean; he need only have had contact with a Pythagorean teacher. It is possible that Aristoxenus included Parmenides and Melissus on the list for these reasons or that he had better reasons for including them (e.g., evidence that they lived a Pythagorean life), but it is precisely famous names such as these that would be likely to have been added to the list in later times, and they may well not have appeared in Aristoxenus’ catalogue at all.