Philosophy
A student agreed to pay his teacher only if he won his first case — then never took one
The sophist Protagoras trained Euathlus in rhetoric on the deal that he'd be paid once Euathlus won his first court case. Euathlus took no cases at all, so Protagoras sued him for the fee, arguing that either he'd win the suit and be paid, or Euathlus would win his 'first case' and owe the fee anyway. Euathlus countered with the identical logic in reverse, and ancient sources say the jury simply refused to rule.