Paradox of Self-Amendment by Peter Suber grateful for the indefinite time and unhurried pace allowed to their predecessors, and the relative freedom from risk if they are wrong. Lawyers under a deadline are normally unaware of the centuries of prior thought on the paradoxes, and in any case might find it irrelevant to the "condensation" of the paradox in their particular case and to the inherited rules under which they must devise a solution. Logicians would never be satisfied with a provisional solution to a paradox, or with a solution that admittedly took no heed of the consequences for the ultimate principles of the logical system under scrutiny. For logicians are scientists who are studying the very integrity of their systems. If that integrity is in doubt, then a "solution" that preserved the doubt or hid it behind a practical indifference to theory would be the very opposite of a scientific solution. Scientists are fortunate, then, that their calling requires only honest study and progress, not solution. Even negative results and the discovery of new difficulties are praiseworthy in science. Logicians feel urgency to solve the paradoxes because their systems will be less certain than they might be until a solution can free them from suspicion; but no judge will order them to prepare for final arguments within a month. Logicians would wait one thousand years for an adequate solution to the Liar paradox, and would reconstruct their systems from the ground up if necessary. In fact, they have already waited twice as long and have reconstructed their systems radically more than once. Lawyers cannot wait, must employ provisional solutions, and lack the same freedom to reconstruct their systems. Lawyers work within legal systems, and strive to preserve them, in a way very different from the way in which logicians work with and strive to preserve logical systems. I will argue that a legal system is distinct from a logical system (inter alia) in its capacity to tolerate contradiction.[Note 14] The difference between the two systems, and the results of conceiving a system of legal rules naively to be a logical-type system of logical-type rules, are central topics of this essay. Lawyers and logicians also have different concepts of solving a problem. If a paradox is compared to a maze, lawyers would be content to "solve" it by knocking down the walls, if the relevant rules did not forbid it. To a logician that would be the height of intellectual dishonesty and self- deception. But we should not think the lawyer's "solution" a cheat, for it is a solution to a different problem; or, from another perspective, it is an optimum defined by different constraints. To the logician the problem is abstract and epistemic: how to understand the paradoxical statement and the system of rules pertaining to meaning and truth in order to bring the two into harmony at the least cost to the bodies of logical and mathematical science. To the lawyer the problem is concrete and practical: how best to adjudicate the interests of these two parties, or how best to achieve a certain state of affairs, in accordance with an inherited system of rules that contains material content, vagueness, ambiguity, and inconsistency. In what follows I will consider legal solutions to logical paradoxes in part under criteria suited to legal decisions and actions. Legal solutions are not, to me, dishonest or unscientific merely for emphasizing the practical. They may well be illogical in the technical sense. But if they are, then they may merely reveal and symptomize differences between logical and legal systems, not necessarily defects in the latter. I will resist the temptation to view formal logic as the rightful legislator for all spheres of intellectual labor.[Note 15] Modern formal logic is more like a game, whose rules should not be allowed to govern non-playing behavior, than a sovereign that can establish its own efficacy by punishing dissenters. That legal rules may be bad logic and good jurisprudence at the same time is yet to be established, of course, but I will at least allow myself to proceed as if that conclusion were not foreclosed a priori. C. Self-amendment I have chosen one veridical paradox on which to concentrate. A more complete study of logical paradoxes as they arise in law must wait (but see Section 20). The paradox on which I will focus arises from the question whether the clause of a constitution that authorizes amendments may authorize its own amendment or repeal. May a rule that permits the change of other rules also permit its own change, especially its irrevocable change into a form inconsistent with its original form?[Note 16] This paradox does not have a strict counterpart in logic, for it pertains to changing the rules of the system by means of a rule within the system. In logic rules are traditionally thought to be either immutable and eternal, or arbitrary postulates changeable by logicians but not by the postulates' own authority.[Note 17] This paradox is a form of another paradox, however, which has been studied more frequently —the paradox of omnipotence. In law the paradox is of parliamentary, legislative, or sovereign omnipotence: the power to make any law at any time.[Note 18] In philosophy generally the paradox is of divine or admittedly hypothetical omnipotence: the power to do any act at any time.[Note 19] If an entity has the power to make any law or do any act at any time, then can it limit its own power to act or make law? If it can, then it can't, and if it can't, then it can. If it can do any act at any time, then it can limit or destroy itself, because that is an act; but it cannot do so, because doing it means it cannot and could not do any act at any time. In the legal version we can say that either there is a law that the sovereign cannot make or a law that it cannot repeal.[Note 20] Like the Barber, if we allow the postulate of the deity or sovereign's existence to stand unchallenged, then it leads to genuine paradox. But also like the Barber, the postulate of its existence implies the affirmation and the negation of a paradoxical predicate (here "can limit its power irrevocably"). Because the postulate implies a contradiction, it is false, and because its falsehood does not also imply its truth, it is not paradoxical like the Liar and we may call it false with finality. Advocates of (non-hypothetical) omnipotent sovereigns or deities may propose distinctions, particularly as to the duration and self-applicability of power, that may save recognizable versions of their entities from paradox, and these will be examined (see Sections 10 and 11). But at first the legally omnipotent sovereign and metaphysically omnipotent deity appear to suffer the fate of the Barber: they cannot exist as defined. 5