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6 TURNING TABLES Roots andVarieties of the Peritrope That the thesis of skepticism or relativism refutes itself to the extent that it claims to be true is an irrefutable argument. But what does it achieve?The reflective argument that proves successful here falls back on the arguer, in that it renders the truthfulness of all reflection suspect. It is not the reality of skepticism or of truth dissolving relativism, but the claim to truth of all formal argument that is affected.Thus the formalism of this kind of reflective argument is of specious philosophical legitimacy. In fact it tells us nothing.We are familiar with this kind of thing from the Greek sophists, whose inner hollowness Plato demonstrated. H.-G. Gadamer, Truth and Method Some of the strongest eikos arguments of the previous chapter are in fact the reverse-eikos arguments that we see in Aristotle and Antiphon (Gagarin 2002:113–14).These are the arguments, such as the strong/weak man example , where a particular likelihood is challenged as actually unlikely and effectively directed back at its proponent.The explicit argument is that X, which has been claimed as likely, is in fact unlikely. So the effect is more to reverse the form of argument, from eikos to non-eikos, rather than to turn someone’s actual argument back upon them. That strategy, variously understood, has gained the title peritrope. WHAT TROPE IS THE PERITROPE? Tropes are usually understood as styles of discourse, rather than figures of speech, as uses of a word, phrase, or image outside of their normally intended meaning, but the term has its origin in the Greek verb trepein, which means to turn.The peritrope, the‘turnabout’ or recoil (Blackburn 2005), might be seen, then, as an emphatic kind of trope. It was Sextus Empiricus (writing around 200 c.e.) who baptized the argument, specifically identifying it with the argument that Plato brings against Protagoras in the Theaetetus, the argument that supposedly refutes the Protagorean measure maxim.Thus it gains the sense of being or involving a ‘self-refutation’ since the measure maxim is deemed to 84 Sophistic Strategies of Argumentation assume its own contradictory and thus undermine itself. Here using another’s position or argument against them seems crucial. Certainly it would seem to have the sense of turning about on someone; hence Cornford’s (1935, 79) suggestion of “table-turning” may be the most appropriate translation to use. A peritrope turns the tables on one’s opponent—a very effective move to make in argumentation, if it is successful. Sextus Empiricus introduces the argument thus: “One cannot say that every appearance is true, because of its self-refutation [peritrope], as Democritus and Plato urged against Protagoras; for if every appearance is true, it will be true also, being in accordance with an appearance, that not every appearance is true, and thus will become a falsehood that every appearance is true” (Against the SchoolmastersVII 389 [DK 80A: 15]).1 There is some disagreement among the commentators as to whether Sextus is referring in the first instance to an argument form or type or just the specific argument used by Plato.Thus Cornford says “an argument of this form” (1935, 79n1), creating sufficient ambiguity for some scholars to draw the conclusion that only this specific argument was called the peritrope (Kirwin 1971, 104). But as Burnyeat (1976a, 48) shows, this reading is implausible in light of how Sextus goes on in the next sentence to attribute falsity to Protagorean relativism, “quite apart from the kind of peritrope that it is.” That he has in mind a type of argument follows also from his general discussion, for while Sextus’s introduction of the term peritrope arises rather late in the tradition that interests us, the strategy seems already to have been employed much earlier. Gorgias, for example, proclaimed that we should heed neither sense nor intellect, thus, according to Sextus, reversing the thesis that things should be judged by all the senses and all men’s intellects.2 But the question still remains as to what exactly should qualify as a peritrope .We have already seen several kinds of reversal that seem to involve the turning of the tables on another’s position or argument. Plato, for example (who is, of course, the one employing the peritrope in the Theaetetus), effectively turns the tables onThrasymachus in Republic I. As will be recalled from the discussion in chapter 3,Thrasymachus...

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