  A difficulty for Protagoras’ position here is that, if all beliefs are true, then all beliefs about which beliefs are beneficial must be true. But surely, some beliefs about which beliefs are beneficial contradict other beliefs about which beliefs are beneficial; especially if some people are better than others at bringing about beneficial beliefs. (For example, no doubt Plato’s and Protagoras’ beliefs conflict at this point.) This means that Protagoras’ view entails a contradiction of the same sort as the next objection–the famous peritropê—seems to be meant to bring out.