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Justice Unanswered By Socrates

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In book I, we find Socrates in a discussion to find what is Justice. Every definition offered by Socrates’ friends is shot down as being inadequate. Finally, Thrasymachus accuses Socrates of only stating what is wrong with everyone’s ideas, and offers no definition of his own. However, I think that Plato purposefully left the question of ‘what is Justice’ unanswered by Socrates, because Plato believes in Thrasymachus’s notion of Justice.
Thrasymachus is enraged by Socrates because the latter does not provide his own definitions of justice, he merely refutes everyone else. Socrates, on his part, claims that he does not know what justice is and instead convinces Thrasymachus to give his own definition. Thrasymachus sees life as a competition

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