Paradox of Self-Amendment by Peter Suber immutability altogether; on the contrary, it would prevent the enactment of any rules of change, which would make every rule in the system immutable. Nor could the immutable set in the 100s be shrunk after the system got started; all its members are immune to amendment from one another and from subsequently enacted rules. An infinite regress of rules of change need not develop and could not: rules would be added to the top end of the series as needed by society. Because they would be added seriatim in real time, they could not surpass a finite number. A real legal system which evolved without regard to such a theory of types or levels might nevertheless be explained by it. If the system had a core of apparently immutable secondary rules, of which some might be tacit, then they could be identified as the initial set, which designates logical not temporal priority. Subsequent enactments could be placed on the scale in their logical positions, assuming the theory is sufficiently faithful to the phenomenon to have made positions for all. Mutability is authorized only by logically prior (lower numbered) rules of logically posterior (higher numbered) rules. If in a real system logically prior rules are enacted later in time than logically posterior rules, then we may say that the logically posterior (temporally prior) rules were either enacted unlawfully or enacted on the basis of logically and temporally prior, but unwritten, rules. Enacting the logically prior, temporally posterior rules might be considered (i) the enactment of explicit forms of previously tacit or unwritten rules that once authorized existing logically posterior rules, or (ii) the enactment of explicit rules that simultaneously made explicit and amended previously tacit rules. If a logically posterior rule seemed to authorize the amendment of a logically prior rule, or (which is the same thing) if two rules seemed to authorize one another's amendment, then we could say that the system is violating its own rules, perhaps in ignorance or with a winked eye, or that the system actually uses circular applications. In the latter case the system could not be explained by the theory of types. To insist on the former case without more evidence, then, just to make the theory of types applicable, would prematurely deny the possibility of circular applicability and direct self-application, which might be made intelligible by another theory, explanatory of actual legal phenomena, and free of illegality if not of paradox (see Sections 5, 10, 11, and 21). 2. The initial set of secondary rules of change, or the entire set at a given time, could be taken as the explanandum, not the explanans. How could it have come into existence by legal means? If self-applicability is to be avoided, then the present set could only have been enacted by means of a logically (and temporally) prior set —tertiary rules— which was not itself self-applicable and so requires an even prior set —quaternary rules— to explain itself, and so on. But once such antecedents are postulated, the same mechanism by which they produced the present set could be used to produce a successor to the present set and all future successors. This fourth theory really does require an infinite regress. Rules are not added by legislators seriatim in real time as needed; they are added by logicians en masse at the speed of inference in order to explain or justify the present set. The infinity required here is not the infinity of Dworkin or Birmingham,[Note 4] but a temporal and logical series of antecedent authorities that, by its nature, cannot end or, more properly, has no beginning. Hence, it requires that every rule of change in the present that is deemed to be lawful have an infinite genealogy. Even if legal systems contain an infinity of rules, none has an infinite genealogy, if only because the world itself has no infinite genealogy. Hence, either this theory is false or no legal system with rules of change has an adequate explanation for its own lawful existence (see Appendix 1.D). Either way, this theory shows us that any theory that we accept as explaining how the present rules of change may be amended must also explain how they came into being. B. Weaknesses of these four methods All four of these theories are weak, although only Hart's unsupplemented view fails to provide any answer at all. The others are all empirically implausible as explanations of how actual legal systems accomplish the legal change of their rules of change. The fourth theory saves itself only by denying the adequacy of the legal justification of all actual secondary rules of change, and hence of all legal systems built on them. Such a recourse is implausible but, more important, by denying that any application of any rules (including rules of change) is lawful, it begs the question of how the lawful change of secondary rules of change is actually brought about. The see-saw method employs a mechanism which no one would seriously propose has been used by actual sovereigns in most of the attested cases of amendment to rules of change (see e.g. Appendix 2). Whether it depends for its success upon a particular plurality of rules of change which few, if any, actual ACs already possess, or whether it may be made to work for most, if not all, ACs, will be explored in Section 13. But even if it may be made to work for all ACs, it can explain the historical acts of self- amendment of comparatively few ACs. The theory of types method requires immutable rules which, if nothing else, begs the question of the mutability of the rules of change (see Section 3.B). Hart does not offer reasons for skirting the question of self-applicability of the rules of change, not even the fear of paradox. He does not even explicitly say he denies self- applicability, but displays his rejection of it in his language.[Note 5] 22