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Regarding this, what was the goal of the Sophists?
The purpose of these works is primarily to display skill in intellectual argument, as well as to give pleasure. Persuasion may be a goal of some sophistic works, but it is not their primary goal; and teaching the art of persuasion was not a major concern of the Sophists.
In this way, what did the Sophists teach?
Many sophists specialized in using the tools of philosophy and rhetoric, though other sophists taught subjects such as music, athletics, and mathematics. In general, they claimed to teach arete ("excellence" or "virtue", applied to various subject areas), predominantly to young statesmen and nobility.
P's Soc claims that Sophists are interested only in belifs and opinions about justice and not justice itself . . . Plato's main concern about the sophists (56): They claim to teach about justice while having no real knowledge of justice itself. One who truly knows justice will be incapable of injustice.