Abstract

Two readings of the much-discussed περιτροπή argument of "Theaetetus" 170c-171c have dominated the literature. One I call "the relativity reading". On this reading, the argument fails by ignoratio elenchi because it "carelessly" omits "the qualifications 'true for so-and-so' which [Protagoras'] theory insists on" (Bostock 1988: 90). The other reading I call "the many-worlds interpretation". On this view, Plato's argument succeeds in showing that "Protagoras' position becomes utterly self-contradictory" because "he claims that everyone lives in his own relativistic world, yet at the same time he is forced by that very claim to admit that no one does" (Burnyeat 1976b: 48). I discuss and criticise both readings, and present a third, according to which the point of the argument is, very roughly, that Protagoras is committed to equating truth and truth-for, and so, further, to their intersubstitutability. This further commitment proves fatal to his argument