Paradox of the Court

The Paradox of the Court, also known as the counterdilemma of Euathlus, is a very old problem in logic stemming from ancient Greece. It is said that the famous sophist Protagoras took on a pupil, Euathlus, on the understanding that the student pay Protagoras for his instruction after he wins his first court case. Protagoras decided to sue Euathlus for the amount owed.

Protagoras argued that if he won the case he would be paid his money. If Euathlus won the case, Protagoras would still be paid according to the original contract, because Euathlus would have won his first case.

Euathlus, however, claimed that if he won then by the court's decision he would not have to pay Protagoras. If on the other hand Protagoras won then Euathlus would still not have won a case and therefore not be obliged to pay.

The question is: which of the two men is in the right?

The story is related by the Latin author Aulus Gellius in Attic Nights.^[1]

Analysis

From a moral standpoint it may be that either party was right, or that both weren't, due to the ambiguous nature of the scenario. However, as a matter of law, if the Court were to rule in favor of Protagoras, the conditions of the original contract between him and his pupil would be invalid and Euathlus would have to pay Protagoras. If, on the other hand, Euathlus were to win, the Court could also void Euathlus's obligation of payment.

How, from an objective standpoint, the way the Court could make its ruling is not necessarily a paradox either. The Court would either rule that Euathlus (as the defendant) had violated the terms of the contract, or had not. The subsequent conundrum would have no legal bearing on the court's decision.

In some civil cases the respondent, if he receives the favor of the court, is also shielded from payments associated with the act of going to court. The Court could indeed rule that Protagoras, as the unsuccessful plaintiff, pay Euathlus the amount which it cost to win. In this case, Euathlus would pay Protagoras only to have the money returned by order of the court. The original contract would have been fulfilled, and Euathlus would bear no further obligation to pay Protagoras for his instruction. The net outcome for Protagoras would be to lose his case, receive payment per the original contract, and then have to pay for the defendant's losses due to his failed suit (Which would be equal to, or exceeding, the cost of Euathlus's education.)

Additionally, Euathlus could hire a lawyer to take on the case, thus invalidating this case as a standard for payment.

Another theory

Another means of viewing this case is as follows:

Euathlus would win his case because Protagoras sued him BEFORE Euathlus won his first case. Protagoras would lose that particular case because Euathlus has not yet won a case, and therefore Protagoras's cause of action had not yet manifested itself.

The new victory of Euathlus would qualify as new evidence for Protagoras, thus constituting grounds for a new trial.

It has been criticized that though this represents a practical solution, it does not solve the logical paradox^[2]. This however can be challenged by identifying a key assumption in the logic, that of eternal states.

This solution works because it targets the assumption of eternal states, that a description applies during all time. If such assumption were false, that the court makes the decision without knowledge of the outcome of the court (or excludes evidence any time after the case start but before the case end), then it is resolvable because the student has not won the case at that time. Court can rule he has not won, therefore does not have to pay without contradiction. Protagoras suing again is neither contradictory. At the second suing the state of the student has changed: he now has won a case. The second suing will now include the outcome of the first trial because it happened prior to the second trial, and the court can freely rule in favor of Protagoras. If assumption of eternal states is in play, the court is required to have all knowledge of all cases student has fought in his lifetime, both past and future. Then there will be a contradiction from the assumption, albeit an unrealistic one. In this solution the student can have both won his first case and not won the first case, because they occur at different times of evaluation.

Other versions of the paradox

In some versions Protagoras would demand the money if and only if Euathlus wins his first court case.^[3] Some accounts claim that Protagoras demanded his money as soon as Euathlus completed his education, others say that Protagoras waited until it was obvious that Euathlus was making no effort to take on clients^[4] and still others ^[5] assert that Euathlus made a genuine attempt but that no clients ever came.

See also

• List of paradoxes

References

1. ^ Aulus Gellius, Attic Nights, book 5, chapter 10.
2. ^ W. Hughes, J. Lavery. "Critical Thinking An Introduction to the Basic Skills Fifth Edition", pp. 327-328, Broadview Press, 2008.
3. ^ L. Alqvist, "Deontic Logic", in Handbook of Philosophical logic, vol. II, pp. 605-714, 1984.
4. ^ Peter Suber, Protagoras v. Euathlus, a section within The Paradox of Self-Amendment, Peter Lang Publishing, 1990.
5. ^ Eugene P. Northrop, "Riddles in Mathematics", Penguin Books