Long ago in ancient Greece, lawyers (to speak slightly anachronistically) learned their trade by paying an established lawyer to apprentice. Protagoras was one such lawyer who got very wealthy plying his trade. As such, he was also very much in demand as a teacher. Euathlus contracted with Protagoras to become his pupil. They agreed that Protagoras, however, would only be paid once Euathlus won his first case — as then clearly the training had proved of use.
Some time later, Protagoras noticed that Euathlus had not yet taken a case. He was determined to collect his teaching fee, and sued Euathlus to collect. He presented his case as follows. If Euathlus loses, he will hence have to pay Protagoras, because Protagoras will have won the case to collect. If, on the other hand, Euathlus wins, he will have won his first case and hence will have to pay Protagoras by the terms of the original contract.
Euathlus , for his part, argued as follows. If he wins, he will not have to pay, because Protagoras will have lost his suit to be paid. If, however, Eualthus loses, he will not have to pay, because the original contract was that he would only pay his fee once he won a case, and he will still have yet to win one.
Your mission, should you choose to accept it, is to resolve Protagoras’ lawsuit. Fields that might be interesting to explore concerning this conundrum: multivalued logics, contract law.

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