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Published online by Cambridge University Press: 16 July 2020
As we have repeatedly verified, competition with other ‘intellectuals’ was crucial for the sophists: while poets and philosophers were their primary targets, they engaged in an equally staunch polemic against the representatives of other forms of knowledge (the so-called technai), such as medicine, music, agriculture, and mathematics. The sophists affirmed the superiority of their teaching against such people as well. As far as we can tell, this claim was advanced in two different ways. In the case of Hippias (a famous polymath), and probably of Prodicus and Antiphon too, the sophists claimed to be as competent as specialists in a wide range of subjects: this explains the interest of sophists such as Hippias and Antiphon in geometrical problems (86B21 = 36D36L.-M.; 87B13 D.-K. = 37D 36a–b and R14–16 L.-M.), and Prodicus’ focus on agriculture.
1 See Soverini 1998: 90–114; and Chapter 6, n. 34.
2 Let us also consider Philodemus’ testimony: ‘the <things> are not knowable, <the> words are not acceptable, <as> Protagoras indeed [sc. said] about ma<thematics>’ (PHerc. 1676 = 80B7a D.-K. = 31D34 L.-M.). As regards the meaning of the polemic against geometry, we might posit (with Barnes 1979: ii.546) that in this case too Protagoras exploited his method of two contrasting logoi: geometry hinges on physical objects; now, if it does not deal with physical objects, all it amounts to is an insignificant verbal game; on the other hand, if it does deal with physical objects, it is subject to empirical evaluation; but any empirical evaluation is bound to offer different results from those provided by a priori analyses; thus even in relation to the apparent certainties of mathematics we find that for the same object there are two opposite logoi. Arguments of this sort were probably also used in the treatise On Mathematics (or On the Sciences) mentioned by Diogenes Laertius (80A1 D.-K. = 31D1 L.-M.). Besides, even in the Protagoras the sophist does not show himself to be very keen on the mathematical sciences (318d–e, 80A5 D.-K. = 31D37 L.-M.).
3 See Jori 1996: 333–57.
4 Fait 2007: xli.
5 In Protagoras’ case, it seems as though a more open position was adopted in relation to music (or at any rate the musical theories of Damon, who was a representative of the ‘new culture’): see Brancacci 2008.
6 Evidently, the term ‘philosophy’ here refers to the kind of activity in which rhetors and sophists engaged.