² See Diels, and Kranz, , Fragmente der Vorsokratiker (12th. edition, Zurich, 1966Google Scholar; hereafter ‘DK’), 80 Al, B5–6.

³ In fact, at least one writer has raised the possibility that Protagoras did take this first alternative (among other entertaining manoeuvres): Barnes, J., The Presocratic Philosophers (London, 1982), pp. 541–53Google Scholar.

⁴ Notice an argument, equal and opposite to what I call Protagoras' second alternative, which is suggested by Theaetetus 170e7ff.: that Protagorean relativism fails on its own terms, because, in fact, Protagorean relativism is not true even for Protagoras himself. So it does not seem even to Protagoras that how things seem to him is how things are. Presumably Protagoras can retort to this that it does not seem to Protagoras that it does not seem even to Protagoras that how things seem to him is how things are.

⁵ For the debate over whether this is what is meant, or whether Protagoras rather meant that the human race (as a whole) was the measure of all things, cp. McDowell, J., Plato: Theaetetus (Clarendon: Oxford, 1973), p. 118Google Scholar (for the former view); Versenyi, J., ‘Protagoras' Man-Measure Fragment’, Am. J. Philology 83 (1962), 178–84CrossRefGoogle Scholar (for the latter).

⁶ Barnes, , op. cit. n. 3, p. 543Google Scholar.

⁷ Or at any rate, all subject/predicate propositions.

⁸ Beside the loss of the laws of contradiction and excluded middle, it would make nonsense of modern formal logic, which would then have only one truth-table, and that a rather odd one. It would also make Aristotelian logic very difficult, since Aristotle defines a syllogism as ‘a set of propositions given which some other proposition must be true’ (Aristotle, , Prior Analytics 24b20Google Scholar). If all propositions are true, it is going to be difficult to tell which sets of propositions necessitate the truth of any further proposition; for that further proposition would equally have been true if conjoined with any set of other propositions.

⁹ Burnyeat, M. F., ‘Protagoras and self-refutation in Plato's Theaetetus’, Philosophical Review 85 (1976), 172–195CrossRefGoogle Scholar.

¹⁰ Burnyeat, M. F., The Theaetetus of Plato (Indianapolis, 1990), p. 30Google Scholar.

¹¹ Cp. Passmore, J., Philosophical Reasoning (London, 1961), p. 67Google Scholar: ‘Protagoras is still asserting that “p is true for x” and “p is not true for y”; these propositions he is taking to be true’. True simpliciter? Or true for their utterer?

¹² Denyer, Nicholas, in his brilliant Language, Thought & Falsehood in Ancient Greek Philosophy (London, 1991), pp. 90ffGoogle Scholar., argues the opposite view—that Protagoras' qualifiers (‘true for x’, etc.) are not in Protagoras' view ‘repeatable’. On the basis of Theaetetus 160b8–c2 Denyer, argues thus: ‘If the qualifiers were repeatable, then to demand that we insert them on every occasion would be to demand that we enter on an infinite regress’ (p. 93)Google Scholar. Not so if Protagoras would say merely: (i) that we can insert an appropriate qualifier before any sentence, if we like; and (ii) that we must insert the qualifiers whenever it is necessary to do so to block anti-Protagorean arguments. But this, I suggest, is that Protagoras would say. (Consider the analogy between the objectivist's ‘it is true that…’ and Protagoras; ‘it is true for x that…’.) So he can hold what Denyer, (op. cit. p. 94)Google Scholar says he ought to hold, that the qualifiers are repeatable.

¹³ Bostock, D. J., Plato's Theaetetus (Oxford, 1988), pp. 89–95Google Scholar.

¹⁴ Denyer, , op. cit. n. 12, pp. 94–100Google Scholar.

¹⁵ McDowell, , op. cit. n. 12, p. 171Google Scholar.

¹⁶ As an anonymous referee for CQ has rightly insisted to me.

¹⁷ Cp. Theaetetus 201a: ‘Orators and lawyers…persuade somehow—without teaching, but making the jurors believe whatever they like’. This contrast between (rational) teaching and (non-rational) persuading is (I suggest) exactly the contrast between the ways of making people believe things that are open respectively to a Protagorean relativist, and to an objectivist.

¹⁸ Perhaps this explains why Protagoras kept his homomensura doctrine secret (The. 152c). Perhaps his exoteric and esoteric pupils alike were taught crafty ways of logical argument and persuasion: but only the esoteric pupils were taught the doctrine discussed here. For that doctrine, by undermining the notion of the community of truth, undermines the very idea of strictly logical persuasion.

¹⁹ Bostock, , op. cit. n. 13, p. 95Google Scholar.

²⁰ Bostock, loc. cit. n. 19.