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. After instruction, Euathlus decided to not enter the profession of law, and 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 would therefore not be obliged to pay.
The question is: which of the two men is in the right?
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From a moral standpoint it may be that either party was right, or that both were not right, 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.
However, 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, but contrary to the law of Ancient Athens where defendants were obligated to represent themselves in court, Euathlus could hire a lawyer to take on the case, thus invalidating this case as a standard for payment. Legal counsel in the form of a logographos was only permitted outside the courtroom for both defendants and accusers.
The Two Case Solution
This solution asserts that there are in fact two legal arguments to be resolved
i) Protagoras argues that an unwritten clause of the original contract is that the student must enter into the profession of law.
If Protagoras wins this case then Euathlus must pay. If Protagoras loses then Euathlus must pay under the original contract. However, in this event Euathlus may argue...
ii) An unwritten assumption of the contract is that cases between the two individuals are exempt from the contract. Citing logical rules preventing the application of a condition to itself.
Euathlus can only avoid payment if he wins both case i) and case ii).
Other versions of the paradox
In some versions Protagoras would demand the money if and only if Euathlus wins his first court case. 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 and still others assert that Euathlus made a genuine attempt but that no clients ever came.
- Aulus Gellius, Attic Nights, book 5, chapter 10.
- L. Alqvist, "Deontic Logic", in Handbook of Philosophical logic, vol. II, pp. 605-714, 1984.
- Peter Suber, Protagoras v. Euathlus, a section within The Paradox of Self-Amendment, Peter Lang Publishing, 1990.
- Eugene P. Northrop, "Riddles in Mathematics", Penguin Books