The Sophist Philosopher Gorgias came from Leontini in Syracuse wrote and argued from 485 to 375 B.C.E. I double-checked and made no mistake about it; most scholars believe he lived over a 100 years. For his legendary work, Gorgias is even considered the "Father of Sophistry."
Gorgias came to Athens in the last quarter of the fifth century B.C.E. as a political ambassador from Syracuse. Like Protagoras, he too accepted students to teach the art of rhetoric for political and legal purposes. Most consider Protagoras and Gorgias to be the first of the Sophist Philosophers.
In ancient resources, we find evidence that Gorgias studied under Empedocles. Gorgias wrote four works of which we are aware:Encomium on Helen, Epitaphios, On Non-Existence, and the Defense of Palamedes. The former pair exist in their entirety, but however, the last work On Non-Existence only exists in a summary and particular fragments.
In his Greek world, he was rather unique because he staunchly exonerated skepticism in unlikely places, most notably of which are metaphysics and epistemology. In fact, some now even considered him to be one of the first nihilists.
Using his Sophist rhetoric, Gorgias wishes to demonstrate that it was just as easy to prove "nothing exists" as it is to prove Parmenides' argument "something exists." To review this argument, which is found in On Non-Existence, I will merely summarize his argument.
We can all assume that something exists. To accept this proposition's opposite, "nothing exists," is absurd, but for the sake of argument we may suppose for a second "non-existence exists." This statement issues a quite obvious contradiction, so we "should" be same to assume that something exists.
So, if something exists, or has existence, then existence must either be eternal or something else must cause existence. Existence though cannot be eternal because it would be "timeless" and, thus, "limitless." That which is "limitless" cannot exist in space or in this world, because it would exist nowhere.
Thus, existence is not eternal, but something could cause existence. If a thing causes existence, we run into the following problems: a circular argument as existence causes existence, a contradiction as something other than existence, or non-existence, causes existence, or an infinite regressions as existence causes existence, which causes existence, ad infinitum.
As it stands, existence fails to justify existence, and non-existence cannot either because it either doesn't exist or because something cannot come from nothing. Therefore, we conclude that something cannot exist and, by process of elimination, we must accept nothing exists.
Gorgias continues after this to suggest that even if something exists, we can certainly know nothing about it because the mind cannot "hold" existing things. A unicorn, for instance, may exist in the mind but not in the world. This presupposes a dualism but Gorgias merely uses this distinction to illustrate that "thought" things don't come into existence, and the mind, our knowledge, and our thoughts have no capacity for holding "existing" things.
However, even if existence we could comprehend existence, we would be unable to speak about it because we speak "words" not "existing things." For example, Gorgias explains, "How can anyone communicate the idea of color by means of words since the ear does not hear colors but only sounds?"
Gorgias goes to the extremes to "prove" that nothing exists. We cannot be certain whether he actually believed that or not; but, we may more safely assume that we was merely using his sophist rhetoric to demonstrate the problems with absolute truth. In other words, he may have been flaunting his rhetorical ability.
To further support this claim, his three other works employ similar methods. He always promotes an absurd position by disproving or discrediting a popular belief, and challenging popular beliefs was a common Sophist strategy.
Naturally, later philosophers disapproved on this Sophists' methods, particularly Plato, who deemed their words as "rhetoric" and not "argument," or logos. Postmodern Philosophers have revisited Sophistry for its implications for truth and language.
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