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How did Plato and other Philosophers rebut the arguments of Gorgias about non-existence?

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How did Plato and other Philosophers rebut the arguments of Gorgias about non-existence?

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Georgias argued, “if the nonexistent exists, it will both exist and not exist at the same time”. You could, perhaps, excuse his contradiction except that contradictions cannot be excused when they are so blatant. If you have to dig through tons of thinking to prove that a contradictions exists, then perhaps the writer himself didn’t see it. Georgias could not have missed it, and seems to have used rhetoric and sophistry on purpose to prove that contradictions will be believed by some, if the arguments are only “logical enough” to persuade them. Most are not and never were persuaded. This contradiction of course was only the first part of his 3-part argument, but “In the dialogue “Gorgias”, Plato (through his mentor Socrates) expresses his contempt for sophistical rhetoric; all rhetoric is “a phantom of a branch of statesmanship (463d) …a kind of flattery …that is contemptible,” because its aim is simply pleasure rather than the welfare of the public.” All of his argument, including the

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