Paradox of Self-Amendment by Peter Suber To "solve" a paradox is to restate our rules about truth-values or about meaning or about some other feature of the proposition or its interpretation so that the statement no longer violates them, and so that the body of truths determined by the rules is saved, as far as possible, from loss of meaning or truth. These attempts break into two broad classes: those that attack the statement as ill-formed, and those that attack the system of rules as inconsistent or incomplete. The former allows the rules of the system to defend themselves by "overruling" the attempt by the paradox to fit comfortably into the system. The latter allows the statement to stand as a meaningful utterance, and uses it as leverage against the system of rules that cannot, so far, accommodate it.[Note 9] The former attempt often seems to beg the question by presupposing the adequacy of the logical system under suspicion. The latter attempt often risks the destruction, or the relegation to logical limbo, of too much meaningful language, useful rules, and good logic and mathematics. Laws may be paradoxical within the system of legal rules just as propositions may be paradoxical within the system of logical rules. (What is more interesting is that laws as propositions may be paradoxical within the system of logical rules and yet not be paradoxical within the system of legal rules, as we shall see.) The methods of coping with legal paradoxes fall into the same two broad categories. On the one hand, a paradoxical law may be attacked as void or, on the other, the legal rules about validity, authority, and permissibility may be attacked as inconsistent, incomplete, or inadequate in some other way. In logic we may reformulate and tighten the statement of rules to eliminate vagueness and inconsistency, and we may add others that seem to solve the problem. But in law only certain officials have these powers. In logic we may decide that the paradoxical statement is to blame, and brand it meaningless or non-cognitive, but in law the power to nullify the paradoxical law is vested only in some, although all have the power to disregard the paradox. A logical solution to a logical paradox in law, therefore, will only rarely be a legal solution too. For the same reason, a logical solution that would brand a paradoxical law as a nullity lacks the requisite legal authority to nullify, and therefore we must admit that a law can persist in legal validity despite paradox or contradiction. This conclusion cannot be winked away by the a priori application of logic to law, nor can its importance to legal reasoning be overestimated. Many jurists, especially those inclined to respect formal logic, deny that any actual contradictions exist in law. Apparent contradictions, they hold, may always in principle be ironed out by the canons of interpretation and priority; that is, in any apparent conflict of legal rules, all but one rule is either inapplicable to the given circumstances or invalid.[Note 10] One canon of interpretation requires that inconsistent rules be read in a way that reconciles them, and if they are irreconcilable, to favor the recent law at the expense of the older one (see Section 16). David Daube complains that we know very little about impossible and contradictory laws because they are typically "construed away" by judges armed with the canons of interpretation and a fear of contradiction.[Note 11] I will regard the question of the existence of actual (as opposed to apparent) contradictions in law as an empirical question, if only for methodological purposes, to allow me to look for them. To assume a priori that they cannot exist would close many doors of my inquiry and, I believe, distort our understanding of law. Exploration of the possible roots of a paradox may well disclose deeply hidden flaws in our rules of meaning, which make the paradoxical statement seem meaningful, in our rules about truth-values, which seem to support both the truth and the falsehood of the paradoxical statement, or in our legal rules of validity, which give the paradoxical law apparent or actual validity. Or else it may simply stir endless controversy. As Quine put it,[Note 12] The argument that sustains a paradox may expose the absurdity of a buried premise or of some preconception previously reckoned as central to physical theory, to mathematics or to the thinking process. Catastrophe may lurk, therefore, in the most innocent-seeming paradox. More than once in history the discovery of paradox has been the occasion for major reconstruction at the foundation of thought. Russell's paradox, for example, showed catastrophe in the form of contradiction lurking in the basic assumptions of set theory, namely, that a set could comprise any collection of any elements or that the same rules applied to all sets of any elements. Doing without either of these broad propositions is difficult and inelegant, but preferable to living with paradox or doing without a consistent set theory. By far the majority of attempts to solve the logical paradoxes have been undertaken by logicians and mathematicians. One cause and one effect of this concentration is that paradoxes have been studied in comparative isolation as statements that must be contended with, simply qua strings of words which our formal and linguistic rules apparently permit, or qua postulates which common sense finds unobjectionable. The appearance of paradoxes has only rarely been studied in particular domains of human thought where purposes other than clarity and consistency are foremost. This essay is a contribution to the study of logical paradoxes in law. Statements that are logically similar to the paradoxes studied by logicians, and arguments that are logically similar to those that support paradoxes in mathematics, appear in law. Sometimes they appear to judges, sometimes to legislators, and sometimes to advocates (see Section 20). The tangled complexes of rules, the lack of clarity on the ultimate presuppositions of the system, self-reference and circular inferences, and other conditions that give rise to the various paradoxes frequently occur in legal cases, contracts, statutes, constitutions, and legal systems. The phenomenon of logical paradoxes in law is especially intriguing because lawyers do not share the logical scruples of logicians,[Note 13] do not share the luxury or freedom to let controversies run on endlessly, and yet are constrained by their professionalism and by their roles (judge, legislator, advocate, counselor, administrator) to be principled in all their decisions. Logicians need not ever decide the correct approach to the paradoxes, whereas lawyers must not only resolve them when they arise, but must frequently do so under a deadline. Logicians who have decided, to their own satisfaction, the correct approach to a paradox may nevertheless be 5