Paradox of Self-Amendment by Peter Suber which might seem the least troublesome examples; but in fact they create difficulties. If the original AC has been interpreted as the exclusive set of methods of amendment, then is amendment to provide another method a change to a form inconsistent with the original form? The answer must be yes, if we consider the meaning of constitutional language, even for purposes of deciding such "logical" questions as consistency, to be a function of the interpretation of the courts, especially the highest courts. The AC by its exclusivity "preempted the field", making all additions "inconsistent" with the original AC. However, this is a case in which specific authorization will prevent inconsistency (see Section 11.A and below in this sub-section). A specific authorization to add new methods of amendment will rebut the original presumption or refute the original interpretation of exclusivity. A federal statute that was intended to preempt the field, say, by specifically authorizing state additions or modifications, is not inconsistent with such state modifications, except by other tests of inconsistency. This shows that when an AC really is exclusive, then even self-amendment by addition will create an AC inconsistent with the original AC. And even when the theory of exclusivity has been abandoned, self-amendment by addition might create an AC inconsistent with the original AC by some other test of inconsistency, for example, by permitting what was once forbidden. This also shows that ascertaining the "inconsistency" of laws is not a simple problem, and that various tests might come into play. Amendments by addition that merely fill voids left by silence, as opposed to providing new methods of amendment to an exclusive AC, may create the same problems. One is not contradicting the exclusivity of the original AC by expansion, but one is in effect doing the opposite, contradicting the openness of the original AC by limitation. But again, one may do it by specific authorization. If an AC is amended to limit the number of proposals that may be submitted to the people at once, when no such limit existed before, then presumably 25 proposals could have been submitted for ratification at once under the original AC. The amendment, then, has the effect of prohibiting what was once permitted, which is one way to define legal inconsistency. If we look to amendments that modify existing sections or clauses, rather than merely add new ones or fill voids, then the problems are even greater. Obviously most such amendments will have the effect of prohibiting what was once permitted, or of permitting what was once prohibited. That will usually be the point of the amendment, of course. Indeed, the only exceptions appear to be amendments designed to make no difference. Still, there have been amendments designed to make no substantive difference. The AC may be used to reorder and renumber the sections of the constitution, including the AC, or to reorder and renumber just the sections within the AC. These clearly count as cases of self-amendment, though they do not change the substance of the constitution or AC in any way. As examples one may cite amendments in Pennsylvania in 1967, Minnesota in 1974, Hawaii in 1978, and North Dakota in 1979.[Note 8] Aside from these restructuring and renumbering amendments, might we find another species of self-amendment without inconsistency in amendments that, for example, lengthen or shorten the minimum period between legislative proposal and popular ratification? These amendments raise the fascinating question whether more of a quantity is "inconsistent" with less of it, or merely cumulative.[Note 9] The question has never been answered in constitutional law for any quantity associated with amendments.[Note 10] The reason may be that nothing turns on the answer, since self-amendment is permissible whether or not the new AC is inconsistent with the old AC. But the question has been answered in other branches of law. In probate, settled doctrine asserts that a later will "inconsistent" with an earlier will automatically revokes the earlier will. If a later will gives a particular heir $2,000, and an earlier will identical in every other respect gave only $1,000, then are the two wills inconsistent? Is more money inconsistent with less money, or cumulative? The legal answer mostly ignores the logic of consistency and addresses the presumed intent of the decedent. The two amounts are rebuttably presumed to be cumulative or additive, not inconsistent or "substitutional". See Gould v. Chamberlain, 68 N.E. 39 (1903). By analogy, the question in the law of constitutional amendments would most likely address the ultimate policy issues rather than the mere logic of consistency. In any event, it should be noted, to lengthen or shorten the minimum period between proposal and ratification would certainly permit what had been prohibited or prohibit what had been permitted. If the latter is taken as the operational definition of change to a form inconsistent with the original form, then we are left with the perhaps surprising result that there seem to be no cases of self-amendment without inconsistency except cases of mere restructuring and renumbering. Before we go on it is worth noting explicitly that these rare and apparently trivial cases of self-amendment without inconsistency are nevertheless important to theory. They show that if one does not object to self-reference per se (as Ross does), then one has no logical objection to all self- amendment. One must limit the logical objection to those cases of self-amendment that create inconsistencies between the old and new ACs. Now what is the proper legal test of inconsistency? The simplest logical test applies only to declarative statements: that they are inconsistent if and only if their conjunction is a contradiction. It does not carry over into the realm of prescriptive statements, if only because prescriptive statements are either non-cognitive (neither true nor false) or the object of a dispute as to their cognitivity. Some propositions of law are prescriptive; few are declarative or descriptive; but the logic of declarative statements will not apply without modification to the propositions of law. The logic of prescriptive statements, commands, and terms such as "obligatory", "permissible", and "impermissible", is called deontic logic, from "deon", the Greek for "duty". The test of inconsistency in deontic logic is itself unsettled. Let us adopt the following standard symbols, when "p" stands for some action: 90