Paradox of the pink slip

I was just thinking about the ancient Greek logic problem, “Paradox of the Court.” It is as follows (in the version told by Aulus Gellius in his Attic Nights). The sophist Protagoras has taken on a student Euathlus. He asks Euathlus to pay him half of the money up front and the other half after he wins his first court case. But Euathlus, after a long period of study in which he shows progress and prowess, does not take on any court cases at all. Protagoras then sues him for the amount owed.

When they appear before the judges, Protagoras offers the following argument: If I win the case, then I will be paid for the instruction. If I lose the case, then I will still be paid, as you will win your first court case and will therefore owe me the money.

Euathlus counters: Not so. If I win the case, then the court will relieve me of obligation toward you. If I lose the case, then I will have no obligation, as I will not have won a case.

The court finds itself unable to make a decision and postpones its decision to a distant date. (In a note to the story in the 1795 edition of Attic Nights, the translator Reverend W. Beloe commented, “This notion of deferring a decision to a distant period of a perplexing and difficult question, is ridiculously followed by our houses of parliament. It is common to defer the discussion of a question in the house of commons to a period when it is well known the parliament will not meet.”)

To resolve this paradox, we have to assume that we have all the necessary information. That is, we have to exclude the possibility that the agreement might have been invalid in the first place or that some other circumstance might have rendered it null and void. (Otherwise the argument becomes trivial.)

Assuming, then, that the agreement between Protagoras and Euathlus is valid, and that Euathlus has not won a court case so far, then Protagoras’s first scenario, in which he wins the case, is implausible if not impossible. The only condition under which he might win the case would be a misjudgment of the court or the emergence of new information.

Protagoras neglected to include in the agreement a provision that Euathlus would actually take on court cases. Had that provision been included, Protagoras might have stood a chance. But Euathlus is not under any obligation to plead a case, and it appears that he’s enjoying his ongoing studies. It’s possible (though it seems far-fetched here) that the judges could decide that the “essence” of the agreement included an implicit understanding that Euathlus would take on cases after a certain period of study. But once one gets into essences, all sorts of things are possible.

So, the overwhelming odds are that Protagoras will lose the case. It is true that, once the court has made its ruling, Euathlus will have won his first case. But until the court makes this ruling, Euathlus still has not won. Thus, Protagoras cannot claim that he is owed money for something that had not taken place yet at the time of his claim. In fact, he may owe money to Euathlus for causing such a stir in the first place.

Protagoras might decide, after the ruling, to sue for the money, and in that case he’d be entitled to it. But the costs of the previous lawsuit (assuming there were any) could diminish his final returns.

Protagoras’s tactical approach is to sue preemptively, as it seems it can only benefit him. But his logic is flawed, because one option really doesn’t exist, and the other won’t be as profitable as he thinks.

In addition, he commits a moral error, which does not come up in the logic problem. It is an error of indifference to his rightness or wrongness. His attitude is: “It doesn’t matter if my case has basis or not, so long as I get the money.”

It seems that a similar tactic (though different logic) is involved in firing at least 50 percent of the school staff (one of the school turnaround options under Race to the Top). Someone might reason, “If this helps the school improve, we win, because the school improves. If it doesn’t help the school improve, we still win (funds, anyway), because we have shown that we are taking the required steps toward improvement.”

But, just as Protagoras neglected to consider the sequence of events, so those who recommend the firing of a school’s staff neglect the discrepancy between taking “required steps” toward improvement and doing something that might actually help. Although the reasoning in the two situations is different, the moral error is similar: it consists in taking action regardless of whether it is right or wrong, with the assumption that it will pay off in one way or another.