Gorgias the Sophist produced a hilarious piece of bad reasoning that seems to be a parody of Parmenides. It's possible that he was simply trying to demonstrate how easy it is to put together a seemingly-convincing argument for a crazy thesis, to show that his skills as a rhetor as simply that good. He did hire his services out as a speech-writer. (In those days, you couldn't hire a lawyer to represent you in court. You had to do all the speaking yourself if someone had a complaint against you. But you could memorize a speech written by someone else, and the Sophists received pay both for teaching rhetorical skills and for simply writing speeches for people.) On the other hand, he may simply have thought Parmenides' style of argument and crazy thesis were worth making fun of.
The general structure of his argument is as follows:
1. If anything is, it is (a) what is or (b) what is not or (c) both what is and what is not.
2. It's not (a) what is.
3. It's not (b) what is not.
4. It's not (c) what is and what is not.
5. So nothing is.
His support for 3:
If what is is also what is not, then:
Problem 1: If what is not also is, then it is not, and it can't both be and not be.
Problem 2: If what is is not, then what is not is, and that's equally absurd, because
they're opposites. They can't both have the same properties of being and not being, or what would distinguish them from each other?
So (b) is false, and (3) is true.
His support for 2:
If what is is, then it's (d) everlasting or (e) generated or (f) everlasting and generated.
If (d), then it has no beginning. If it has no beginning, it's limitless. If it's limitless, then it is nowhere, because if it's anywhere then the place it's in is different from it, which would mean it's not limitless. So if it's everlasting, then it's nowhere. If it's nowhere, then it's not. So (d) is not an option.
If (e), then it either came into being (g) from something that is or (h) from something that's not. It couldn't be (g), because if it came from something that is then it hasn't come into being but already existed. It couldn't be (h), because something that doesn't exist can't make something exist. So it can't be generated, and (e) is not an option.
It can't be (f). For one thing, those are contradictory. Also, both were ruled out already, so how can both be true if they're both false? So (f) is not an option.
Therefore, it's not everlasting, generated, or both. By our premise, if it is, then it's one of these three. Therefore, it's not.
His support for 4:
Pretty much the same reasoning for why it can't be (f) above.
Your mission, should you choose to accept it: where does this argument go wrong and why? I can think of at last two problems.