A Lawyer named Protagoras teaches law for a hefty fee. He advertises his skills as a teacher by offering his students a contract, which states that they do not have to pay him until they have won their first case. If the student loses their first case, then they don't have to pay Protagoras at all.

One student of Protagoras sees a loophole, takes the course and fininshes it. After that, the student avoids arguing any cases. Since the student has not yet won his first case, he avoids paying Protagoras.

Protagoras feels cheated, and sues the student for his fee. When the case comes to trial, the student represents himself. If the student loses the case, then by the terms of their original agreement, there is no fee for the course. If the student wins the case however, then, since its the student's first case, there will be a fee. (But, of course, winning the case means that the student doesn't have to pay the fee, while losing it means that the fee must be paid.)

Will the student be obliged to pay Protagoras' fee or not?

(In reply to re: Solution by levik)

It's interesting that both comments aknowledge that this isn't a simple paradox, as it seems because it involves law as well as logic, because my take on does it also.

A case in a court of law must focus on just the situation presented, so the judge's decision whatever it is applies only as long as the student has neither won nor lost his first case. However, the moment the decision is announced, the situation is different from that which was ruled on. The new situation is that either the student has lost and so need not pay (under the original agreement) or he has won and must pay. It is in the student's best interest to lose the case.

Except that since the situation changes as soon as the judge announces his decision, that is before the judge dismisses the case. The case becomes moot, and since the trial "does not count" Protagoras and the student are back where they started. But then, the situation has not changed, and the judge's decision stands, which moots it again.

Herein lies the real paradox: whatever the judge decides is moot only if it is real and enforcible, and vice-versa

Posted by TomM on 2002-10-20 02:29:21