In my Discrete Mathematics class we discussed a few famous paradoxes, such as Russell’s paradox/barber paradox/librarian paradox, the liar’s paradox, and the naming numbers paradox.

Afterward, a student of mine shared with me this old legal paradox featuring Euathlus and Protagoras.

Euathlus wanted to become a lawyer but could not pay Protagoras. Protagoras agreed to teach him under the condition that if Euathlus won his first case, he would pay Protagoras, otherwise not. Euathlus finished his course of study and did nothing. Protagoras sued for his fee. He argued:

If Euathlus loses this case, then he must pay (by the judgment of the court).

If Euathlus wins this case, then he must pay (by the terms of the contract).

He must either win or lose this case.

Therefore Euathlus must pay me.

But Euathlus had learned well the art of rhetoric. He responded:

If I win this case, I do not have to pay (by the judgment of the court).

If I lose this case, I do not have to pay (by the contract).

I must either win or lose the case.

Therefore, I do not have to pay Protagoras.

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