It is not mere coincidence that several of Plato’s dialogues are set in gymnasia and palaistrai (wrestling schools), employ the gymnastic language of stripping, wrestling, tripping, even helping opponents to their feet, and imitate in argumentative form the athletic contests (agōnes) commonly associated with that place. The main explanation for this is, of course, historical. Sophists, orators, and intellectuals of all stripes, including the historical Socrates, really did frequent Athens’ gymnasia and palaistrai in search of ready audiences and potential students. Perhaps they were following the example of Pythagoras, who may have been a boxing coach (gymnastēs) and was, in any case, associated with the extraordinary Olympic success of at...