Paradox of Self-Amendment by Peter Suber or allows one only for certain types of amendment, then the deontic test shows inconsistency (the new AC forbids what the old AC permitted), but the compliance test shows consistency (simultaneous obedience is possible by refraining from using the restricted or abolished method). Choosing between these tests is not completely amenable to logical methods. There is some logical support for using that test that makes everything inconsistent that any test makes inconsistent, because inconsistency is so absolutely unacceptable in formal logic and because the minimal sense carries the fewest presuppositions. These criteria favor the deontic test, but not conclusively. For legal purposes, which vary from one context to another, other tests may be desirable. The compliance test is best suited to identifying inconsistency among criminal statutes, where clear notice is a strong policy and attainable compliance is an important goal (see Section 21.B). The preemption and obstruction tests are most suitable for preserving the supremacy of federal law in the face of state encroachments, which is desirable primarily for policy reasons such as uniformity and predictability, or for preserving the supremacy of constitutional rules over inferior rules, which is desirable for the policy reasons of federalism and the shielding of fundamental rules from easy and hasty change. The deontic test has been applied to conflicts between constitutional rules and amendments in In re Interrogatories Propounded by Senate Committee Concerning House Bill 1078, 189 Colo. 11, 536 P.2d 308 (1975). The policy questions behind the tests of inconsistency prevent the objective tests of formal logic from finding useful application in law and from being decisive grounds for findings of consistency and inconsistency. For the same reason, inconsistency in law is a different type of relationship than in formal logic. As Fuller put it,[Note 23] [W]hat we call contradictory laws are laws that fight each other, though without necessarily killing one another off as contradictory statements are assumed to do in logic. In logic one of the most unquestioned certainties is that both poles of a contradiction cannot be true at once; they "kill one another off". To assert one is demonstrably and unavoidably to deny the other. This is the work of the principle of non-contradiction ("not both p and not-p") conjoined with the principle of excluded middle ("not neither p nor not-p"). The principle of excluded middle was regarded as the natural partner of the principle of non-contradiction for centuries until some paradoxes of logic and difficulties in the mathematics of the infinite seemed best soluble by its separate denial. In law neither the principle of non-contradiction nor the principle of excluded middle holds without qualification. If two rules that are contradictory by one test are interpreted under another test, for policy reasons peculiar to law and inadmissible in logic, then they might be found consistent.[Note 24] Both the "inconsistent" rules of law might remain valid. Their coexistence in validity, or failure to kill one another off, is a sign that in law policy triumphs over logic whenever policy requires it. As noted in Section 11.A, it is tempting, but incorrect, to believe that if rule P specifically authorizes rule Q, then P and Q cannot be inconsistent (authorization fallacy). If rule P is an AC, then it may authorize an additional method of amendment or the repeal of an existing method, in both cases creating a successor-AC that is inconsistent with the P by the deontic test. If P repeals and replaces itself with completely different methods of amendment, then P and Q could be inconsistent by the compliance test. Among ACs and their successors, the preemption and obstruction tests do not apply, for an AC and its successors are on the same hierarchical level.[Note 25] However, if rule P authorizes a change Q in a lower level rule, then most likely the preemption and obstruction tests could find no inconsistency, for Q would prove that P did not preempt the field or forbid the type of obstruction represented by Q. Because authorization does not remove inconsistency, for the deontic and compliance tests, the paradox of self-amendment cannot be resolved be rewording the AC to insure specific authorization of the important varieties of self-amendment. Such rewording would only insure that the legal problems were surmounted, i.e., that self-amendment would be recognized as valid by legal criteria. (But even without such rewording self- amendment has never been legally problematic.) Inconsistencies would remain by logical and legal tests; indeed, the point of specific authorization is to legitimate such inconsistencies and establish new law despite their presence. However, rewording the AC to provide specific authorization for self-amendment will make even more tempting what I have called the authorization fallacy.[Note 26] One might be tempted to add a proviso to one of the standard tests of inconsistency, saying essentially, "...provided that any rule specifically authorized by a (prior, higher) rule is not inconsistent with the latter." This proviso would make authorization part of a test of inconsistency, in fact, an infallible cure or rectification of inconsistency. It is a fallacy (logically) because it reverses the logical order of investigation, or (legally) because it confuses legal and logical authority. Logically, if a premise and conclusion are inconsistent (when the premises are consistent with one another), then the alleged authorization is denied; the inference is invalid. The validity of the inference depends upon the consistency of its premises and conclusion, not vice versa. A good example is the concept of self-embracing omnipotence, which is defined so as to authorize any self-amendment. Immutable self-limitation contradicts the authority, which prevents it from occurring under the inference model or formal logic generally. Authorization provides a legally sufficient reason to accept an outcome as valid; if the authority and outcome are inconsistent, then authorization provides a legally valid excuse to ignore the inconsistency. This is significantly different from eliminating or curing inconsistency. Authorization provides no logically sufficient reason to ignore inconsistency. If an AC limits itself even revocably, then the new AC is inconsistent with the old AC by the deontic test. Until the revocable limitation is repealed, something is impermissible that was once permissible. Specific authorization by an AC for a certain change may rebut a presumption of exclusivity or preemption, but it cannot negate any inconsistency under the deontic or compliance tests. Here we must admit that law is superior to logic because its rules can authorize inconsistencies. Alf Ross's basic principle held that from a valid norm no inconsistent norm may validly be derived; it 92