 Interestingly, Protagoras’ critical attitude towards technai is also confirmed by other Platonic and, even more important, non-Platonic testimonies. In Protagoras 318e–319a Protagoras attacks Prodicus and Hippias because by only teaching technai such as “arithmetic, astronomy, geometry, and music” they do not teach the pupils what is really important for the polis (that is, political art). Protagoras’ argument seems to be that these specialised kinds of expertise are not really useful to the life of the polis, contrary to what is claimed by its supporters. Analogously, Aristotle (Metaphysics 998a2-4 = 80B7 DK) and Philodemus (On Poems, fr. 11 = 80B7a DK; but the reconstruction of this text is controversial, see Romeo 1992) inform us that Protagoras attacked geometry and perhaps astronomy and geodesics by arguing that their abstract investigations are hardly compatible with the results of empirical observation (“a hoop does not touch a straight edge at a point”, Protagoras argued according to Aristotle, Metaphysics 998a2-4 = 80B7 DK); therefore they amount to an insignificant verbal game of no utility. These are probably the arguments to which Plato himself was alluding to in the Sophist (232d–e = 80B8 DK) when he reports that Protagoras was teaching how “to contradict each of the artisans” in On Wrestling and the Other Arts. In Protagoras we therefore find two lines of attack against the technai. The first goes against the widespread view that the technai played a decisive role in achieving civilised society by arguing that they are necessary but not sufficient. Secondly, he attacked some specific technai such as geometry or astronomy as useless. These are admittedly different arguments and criticisms. But combined together, they seem to confirm the importance of politics and the political art, which are the objects of Protagoras’ teaching.