While Protagoras starts from relativism and on it bases his method of contradictory arguments, Gorgias, somewhat inferior to him in reputation and ability, begins instead from a position of nihilism.

In a work of his—which must certainly have been the systematic over turning of the philosophy of physis and especially of Eleaticism in the very way it had been presented by Melissus, and which is entitled On the Nature of Not-Being (which is the precise opposite title of the writing of Melissus) — Gorgias maintained the interconnection and mutual dependency of these three theses: a) being does not exist, that is, nothing exists; b) if being exists, it is inconceivable; c) even if it were conceivable, it would be incommunicable or inexplicable to others. The demonstration of the three propositions (which is accomplished through a series of dilemmas and using categories and techniques which are clearly Eleatic in origin), far from being an exhibition of rhetorical ability, as some have proposed, has the clear purpose of radically excluding the possibility of the existence, or the achievement, or generally of the expression of an objective truth. Sextus Empiricus himself, who has recorded one of the two paraphrases extant of the work, thus concludes:

Such, then, being the difficulties raised by Gorgias, if we go by them the criterion of truth is swept away; for there can be no criterion of that which neither exists nor can be known nor is naturally capable of being explained to another person.

Therefore, if there existed a relative truth for Protagoras (in the sense that everything is true which seems to be so to man), on the contrary for Gorgias, no truths exists and everything is false.

P. 165

¶ 7:20 AM