How does Plato in Gorgias argue against Callicles' position that 'justice is the right of the stronger'/ 'might makes right'?

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In response to the argument of Callicles that any notion of justice is man-made and therefore false as it is an artificial law and not a natural one, Socrates, the voice of Plato in this text, argues that nature clearly states that committing acts of injustice is more terrible than to suffer in justice based on the principle that equality is synonymous with justice. Note how he argues his point with Callicles:

Then is it the opinion of the many that—as you also said a moment ago—justice means having an equal share, and it is fouler to wrong than be wronged? Is that so, or not? And mind you are not caught this time in a bashful fit. Is it, or is it not, the opinion of the many that to have one's equal share, and not more than others, is just, and that it is fouler to wrong than be wronged?

Through such rhetoric Plato points out the flaws in Callicles' argument: it is impossible to argue that "might is right" and that natural law supports this if at the same time justice is defined by equality. By pointing out the inconsistencies in Callicles' argument, Plato argues that those who argue such a position are deeply happy, and then he returns to his argument that to be undisciplined is to be unhappy, and those who are undisciplined should be under the helpful yoke of justice.

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