Paradox of Self-Amendment by Peter Suber Op = p is obligatory O ~ p = refrainment from p is obligatory Pp = p is permissible P ~ p = refrainment from p is permissible Let us take these equations as fundamental axioms: Op = ~ P ~ p O ~ p = ~ Pp Pp = ~ O ~ p P ~ p = ~ Op This is to suppose that obligation translates into the impermissibility of refrainment, and permissibility translates into the absence of an obligation to refrain. Georg Henrik von Wright believes that the negation of Op is P ~ p.[Note 11] Alf Ross, who is probably better known for his contribution to deontic logic than to jurisprudence, disagrees, believing that the negation of Op is O ~ p.[Note 12] In full prose, the negation of p is obligatory is either refrainment from p is permissible (von Wright) or refrainment from p is obligatory (Ross). Both von Wright and Ross would agree, however, that the two formulas are "inconsistent" with Op. In addition to the intramural disputes of deontic logic,[Note 13] there is the problem of applying the doctrines of formal logic straightaway to law. As Lon Fuller described the task of discerning inconsistencies in law,[Note 14] It is generally assumed that the problem is a simple one of logic. A contradiction is something that violates the law of identity by which A cannot be not-A. This formal principle, however, if it has any value at all, has none whatsoever in dealing with contradictory laws. The legal tests of inconsistency are the only legally relevant tests, and whether they incorporate any particular logical test is contingent. Like Ross on self-amendment, many logicians who have turned to jurisprudence are unreflective and hasty in assuming the unqualified applicability of formal logic to law, or more precisely, the unqualified adherence of law to formal logic.[Note 15] Of the more sophisticated legal treatments of this problem, special mention should be made of Lon Fuller, Howard Zelling, Ilmar Tammelo, Allan Murray-Jones, Gary R. Rumble, Dennis Lloyd, and A.G. Guest.[Note 16] Summarizing and paraphrasing Murray-Jones,[Note 17] the chief legal tests of inconsistency appear to be four: Whether a superior law purports to preempt the field of its subject matter, or to claim exclusivity, when an inferior law enters that field in any way (I will call this the "preemption" test); Whether simultaneous compliance with two laws is impossible (the "compliance" test); Whether one law forbids what another permits, or permits what another forbids (the "deontic" test);[Note 18] and Whether an inferior law impairs or obstructs the operation of a superior law (the "obstruction" test). The compliance test seems at first sight the closest to a bare logical test, but Fuller asks whether there is "any violation of logic in asking a man to do something and then punishing him for it?"[Note 19] He argues that such a dilemma only violates policy, not logic, which seems perfectly true. Fuller's ultimate point seems to be that inconsistency in law is a matter of policy, not logic, and is found to exist or not to exist only for certain alogical policies.[Note 20] The obstruction test is always a policy question insofar as it differs from the preemption test. The preemption test involves policy questions when an intent to preempt the field must be inferred or presumed,[Note 21] or when "the field" preempted must be defined.[Note 22] Depending upon which test we select, the inference that models amendment may or may not be invalid (the conclusion and premises may or may not be inconsistent). I prefer the deontic test because it is the weakest or minimal test of inconsistency. Whatever we mean by inconsistency in law, at least we mean the deontic test. Therefore it imports the fewest assumptions and hidden premises. The other three tests or types of inconsistency are special and limited cases of the deontic test. A preempting or exclusive superior rule only conflicts with an inferior rule if the latter attempts to permit or forbid what the superior rule forbids or permits. Simultaneous obedience to two rules is impossible only if one forbids what the other requires (and therefore permits). And an inferior rule can only obstruct the operation of a superior rule by permitting delay or circuity or by forbidding efficiencies not contemplated by the superior rule. Of course a narrow concept of inconsistency will allow self-amendment under the inference model when the deontic test would forbid it. If the old AC provides two methods of amendment between which the legislature may choose with unfettered discretion, and if the new AC eliminates one 91