The logical paradox that you can take to court

One of the oldest logical paradoxes stems from a controversial figure in Greek history. Like most controversial figures, he was involved in a few lawsuits, and one in particular became known as The Paradox of the Court.

Protagoras was a divisive figure in his day. He was one of the first sophists, teachers who based their lessons on teaching the principle of "arete" or excellence. Unlike many teachers, he didn't just hang around in the public square sharing his teachings with the world. If you wanted excellence, you had to pay. This insistence on payment earned him the ire of Plato, and also reportedly landed him in court, in the middle of a logical paradox.

Euathlus was a young man studying law under the tutelage of Protagoras. Short on funds but rich in the potential for excellence, Euathlus agreed that he would pay Protagoras for his services the moment he won his first case. Protagoras agreed and taught the young man, and then sat back and watched Euathlus parade his ill-gotten knowledge around the city without taking on any cases. Protagoras decided to bring the man's first case to him. He sued Euathlus for payment. He then argued that if Euathlus lost in court, Euathlus would be forced to pay. However if Euathlus won, and the court declared that he didn't owe any money, Euathlus would officially have won his first case, and thus still have to pay up. Euathlus argued that the court's decision was what mattered, and that if the court decided he didn't owe any money, that was final. He wouldn't have to pay. And since he hadn't won any cases, the court could not fail to decide in his favor.

The paradox is a myth, not (as far as we know) a historical legal case. If it were an actual legal case, it's doubtful that either side would have come away happy. Courts are equipped to deal with the efficient disposal of assets and not deep philosophical problems. So Protagoras instead paid two non-philosophical thugs to rob and beat Euathlus as he left a bar one evening. I may be making that last part up, but that would be my solution to the problem.

Image: Sam Howzit

[Via Peter Suber]