In Plato's Gorgias, what is the evidence of how Plato proves his position against Callicles or why does he not prove his position?

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Callicles in this text argued for a complete lack of morality and for self-serving interest, a world in which the powerful could do what they want because justice was just a sham to be seen through by the wise. For example, Callicles argued that the superior man must:

...allow his own appetites to get as large as possible and not restrain them. And when they are as large as possible, he ought to be competent to devote himself to them by virtue of his courage and intelligence, and to fill him with whatever he may have an appetite for at the time.

In Plato's argument against such position, in the guise of Socrates, he forces Callicles to accept that such a position means he is adopting an extreme form of hedonism in that he argues Callicles is stating pleasure is the ultimate aim of his philosophical outlook. Plato argues against such a position by debating the nature of pleasure, which he takes to mean a "filling up" where there is some lack or absence. Although the debate that they have over the precise nature of pleasure and what it constitutes may be viewed as being somewhat abstruse, at the same time Plato successfully manages to argue that true pleasure is not just based on ephemeral, passing pleasures, but is based on applying the mind to reason and wisdom, as these are pleasures that are eternal. He thus successfully debunks the claim of Callicles that hedonism is the goal of life.

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