 Zhmud (2012a, 109–134) has argued that it begs the question to use a doctrinal criterion to identify Pythagoreans. We need to first identify Pythagoreans and then see what their doctrines are. Aristoxenus’ catalogue of Pythagoreans as preserved in Iamblichus is the crucial source. Zhmud takes the Pythagoreans on this list whom we can identify (the overwhelming majority are just names for us) and studies their interests and activities in order to arrive at a picture of early Pythagoreanism. Of the 235 names Zhmud finds only 15 about whom we know anything significant. Some of these are non-controversial (Hippasus, Philolaus, Eurytus and Archytas). However, Zhmud puts particular emphasis on a series of figures not typically regarded as Pythagoreans, e.g., Democedes, Alcmaeon, Iccus, Menestor,and Hippon. The range of interests of these figures leads him to conclude that there is no one characteristic that is shared by all Pythagoreans and that Wittgestein’s concept of a family resemblance should be employed to describe Pythagoreanism. Moreover, his reliance on figures like Alcmaeon and Menestor leads him to the surprising conclusion that natural science and medicine were more important than mathematics for the philosophical views of early Pythagoreans (2012a, 23). The foundation for this view of early Pythagoreanism is problematic since the scholarly consensus is that Alcmaeon was not a Pythagorean and it is also far from certain that Menestor was a Pythagorean (see below). As argued above, Iamblichus’ catalogue cannot be used mechanically as a guarantee that a given figure was a Pythagorean, because we cannot be sure that it always reflects Aristoxenus. What criteria should then be used?