There is no “being hot” or “being cold” as such...

There is no “being hot” or “being cold” as such; there is simply “seeming hot to this man” or “seeming cold to that man.” So it makes no sense to ask of a wind which feels warm to one man but chilly to another, Is it really hot or cold? The wind is nothing really; it is to each whatever it appears to each. Is it the same with moral values? Protagoras is in difficulty here over his own standing as a teacher.

For if Protagoras concedes that everything is as it seems to be to the individual subject, then he seems to allow that no one can ever judge falsely, and Plato does in fact put this admission into the mouth of Protagoras. But if no one judges falsely, then all are equal in respect of the truth, and nobody can be in the superior position of a teacher or in the inferior position of a pupil. So it seems to follow that if Protagoras’ doctrine is true, then he has no right to teach it.

For nobody’s doctrine is or can be truer than anyone else’s. Protagoras attempts to avoid this difficulty by arguing that although nobody’s judgment can be false, some men by their judgments produce better effects than others do. This of course only involves him in the same paradox in a different way; for the assertion that Protagoras’ judgments produce better effects than those of others is now treated as a truth such that, if a man denied it, he would judge falsely.

But on the original premises nobody ever judges falsely. So the paradox would be unresolved. Protagoras however is allowed by Plato to ignore this and consequently to argue that “the wise and good orators make good things seem just to their cities instead of pernicious ones. Whatever in any city is regarded as just and admirable is just and admirable in that city for so long as it is thought to be so.”10 Thus the criteria of justice are held to differ from state to state.

It does not of course follow that the criteria either must or can be entirely different in different states, and in another dialogue, the Protagoras, Plato appears to credit Protagoras with the view that there are some qualities necessary for the continuing social life of any city. But this is quite consistent with maintaining that there are no sufficient criteria for determining what is just or unjust, independent of the particular conventions of each particular city.

So what the sophist has to teach is what is held to be just in each different state. You cannot ask or answer the question, What is justice?