Paradox of Self-Amendment by Peter Suber Section 20: Other Selected Paradoxes and Reflexivities in Law This section is a brief introduction to the abundance of reflexivities and paradoxes in law. The lessons learned under the paradox of self- amendment do not necessarily apply to these, which is one reason to include them now. But all raise the question whether a strictly logical legal system could tolerate them and, if not, whether our legal system ought to continue to tolerate them. And oughts aside, as long as our legal system does tolerate them, empirically-minded legal theorists must take this toleration into account when describing legal reasoning and the respective roles of policy and formal logic in legal decision-making. Reflexivities and paradoxes that present "insoluble" problems to logicians reveal much about legal reasoning when they are "solved" without more ado by courts or legislatures, or imperturbably left unsolved. I do not have as precise a definition of "reflexivity" as I gave of "paradox" in Section 1. "Reflexivity" is the generic term for all types of logical circularity: the self-reference of signs, the self-application of principles, the self-justification and self-refutation of propositions and inferences, the self-creation and self-destruction of legal and logical entities, the self-limitation and self-augmentation of powers, circular reasoning, circular causation, vicious and benign circles, and feedback systems.[Note 1] The common practice of using "self-reference" to cover all this territory is inaccurate and unfortunate. Some legal terms use the language of reflexivity to denote what are plainly irreflexive phenomena. For example, "self-authenticating documents" in the law of evidence, and "self-proving wills" in probate, are not documents that, by their own lights, supply all the premises needed to conclude that they are what they purport to be. They are documents that, if they meet some externally stipulated requirements, are presumed to be what they purport to be. "Self-defense" and "self-incrimination" in criminal law emphasize the personal self more than the circularity of the process, while "self-dealing" comes much closer to a reflexive application. Reflexivities are not necessarily paradoxical. "This very sentence is false" is a classical reflexive paradox (see Section 1); it is true if false, and false if true. But "This very sentence is true" is equally reflexive but not at all paradoxical. The following is simply a list of some reflexivities that arise in other domains of law. The heads under which they are collected are crude; many of the examples could fit under more than one of them. With a few exceptions, too important to omit, I have tried to avoid examples that have been noted in the literature before. I omit redundant examples that would not present new logical features. For the most part I have also omitted hypothetical statutes, contracts, etc., invented solely to create reflexivity problems. In order to present a wide range of examples, I have had to limit my commentary and analysis. I am confident, however, that each of these examples, no matter how innocuous it may seem, could sustain the kind of in-depth study that the larger work has given to self-amendment. A. Protagoras v. Euathlus This case deserves separate, special treatment as a classical illustration of the reflexive use of the "counter-dilemma" to respond to a "dilemma". Protagoras taught rhetoric and argumentation, which in ancient Greece comprised the education of a lawyer. Euathlus wished to learn these arts and asked Protagoras to teach him. He said he could not pay right away but promised to pay in full after he won his first case. Protagoras agreed, and taught Euathlus rhetoric and argumentation. Some accounts say Protagoras sued Euathlus for payment immediately upon the completion of the lessons; other accounts say he waited until it was evident that Euathlus was not taking on any cases. The case was heard in the court of Areopagus in Athens. The judge asked Protagoras why he thought he had a claim against Euathlus. Protagoras argued, "I will either win this case or lose it. If I win it, then Euathlus must pay me, by the judgment of the court. If I lose it, then he must pay me, under our contract. So he must pay me either way." The judge was impressed, and asked Euathlus to reply. Euathlus had learned his lessons well, and replied, "I too will either win this case or lose it. If I win it, then I need not pay Protagoras, by the judgment of the court. If I lose it, then I need not pay him, under our contract. So I need not pay him either way."[Note 2] It is said that the court was so puzzled that it adjourned for 100 years. Aulus Gellius reports that Protagoras had a "wily scheme" in bringing the suit in the first place (probably to win in a second suit if he lost the first), and that Euathlus knew he'd escape paradox if he hired another advocate to argue his case but that he wanted to show off his cleverness. Euathlus would be better off hiring a lawyer because, if he won with a lawyer, his victory would be non-paradoxical, and if he lost with a lawyer, he would not yet have won his first case. By adjourning, the court in effect waits for Euathlus to take another case, which is equivalent to a judgment for Euathlus. There is a small literature on the case, all of it suggesting that Euathlus should have won.[Note 3] Most commentators then observe that Protagoras could have sued a second time and won. A few observe that Euathlus might then sue for malicious prosecution, but they divide on who should win that suit.[Note 4] None deals deeply with Protagoras' "wily scheme", assuming it was to win in either the first or second suit.[Note 5] By bringing the first suit, even if he is certain to lose it, Protagoras guarantees his victory in the second suit. If equity wants to thwart Protagoras' scheme, then holding for Euathlus in the first case does not suffice; it plays into Protagoras' hands. Many solutions are available to law that are unavailable to logic. For example, the judge could thwart Protagoras' wily scheme by ordering Euathlus to hire a lawyer in the first case. The contract could be reinterpreted, reading its terms in light of the situation or "trade usage". For example, the 132