Peritrope

The Peritrope is Socrates' argument against Protagoras' view of relative truth, as presented in Plato's book known as Theatetus (169–171e). The name comes from the ancient Greek for "turning around". Sextus Empiricus is attributed with coining the appellation in a commentary on the passage. The name has been in continuous use ever since, as Socrates' argument provides the foundation for classical propositional logic and hence much of traditional western philosophy (or analytic philosophy). Well-known attestations of Peritrope include Avicenna and Thomas Aquinas, and in modern times Myles Burnyeat and many others. The word is occasionally used to describe argument forms similar in nature to that of Socrates' overturning of Protagoras.

For many centuries the Peritrope was used primarily as a tool for refuting skepticism. Skepticism proposes that There is no truth, which can be challenged by responding with the Peritrope — the rhetorical question, Well, then, isn't that true? Skepticism and similar views are considered to be "self-refuting." In other words, a philosopher has retained what he has disavowed in and by the disavowal itself. In general, versions of the Peritrope can be used to challenge many kinds of assertion that universality is impossibile.

In What Plato Said, Paul Shorey notes: "The first argument advanced by Socrates is the so-called peritrope, to use the later technical term, that the opinion of Protagoras destroys itself, for, if truth is what each man troweth, and the majority of mankind in fact repudiates Protagoras' definition of truth, it is on Protagoras' own pragmatic showing more often false than true".