After locating Resp. 5.453b–454c in the wider context of the ‘triple wave’ (τρικυμία) literary motif, Section 1 concentrates on the terminological and argumentative peculiarities of the passage, and raises the central question addressed in this paper : why does Socrates refer to antilogy and eristic in the very context of the first wave concerned with the issue of the equal disposition of men and women to be guards of the ideal city ? Section 2 considers a possible answer to this question by examining the evidence available on the relation between the Republic and Protagoras, and the possible Protagorean background of Resp. 5.453b–454c. This examination turns out to be inconclusive. Section 3 then attempts to restore the original polemical context of the passage by considering some textual evidence on the Socratic discussion of the virtue of men and women.