Paradox of Self-Amendment by Peter Suber Section 21: Conclusions and Explorations A. Summary Restating my theses with their supporting arguments would, I hope, nearly double the size of this book. But a restatement of my chief theses with their chief supporting propositions may be done far more briefly, and with the effect of bringing all the various strands of the problem together. This summary covers Part One only. Sections 21.B-E, below, go beyond summary to explore some of the consequences of my position. Summary of analysis and argument Because the paradox of self-amendment is a special case of the paradox of omnipotence, our central question is whether a deity or AC can irrevocably limit its own power. Logicians using strictly logical criteria offer the answer that such self-limitation is self-contradictory; the same answer is given by lawyers and theologians who adopt the criteria of formal logic for their disciplines. No one using strictly legal criteria has ever said that self-limitation is self-contradictory, let alone impermissible. The logical or formalist view of law as it affects this problem I am calling the inference model of legal change and validity. Under the inference model, legal change is modeled by deductive inference. The authorizing rule of change (for example, the old AC) is one premise, the fact of enactment under the authorizing rule or procedure is another, and the validity of the new rule (new AC) is the conclusion. Rule: If act A is done, then rule B is valid. Fact: Act A is done. ------------------------------------------- Conclusion: Therefore, rule B is valid. The theory is that the amendment is lawful if and only if this deduction is valid and its premises are true. Self-amendment occurs when the rule affirmed in the conclusion is meant to replace the rule in the premises, that is, when the rule in the premises refers to itself. Irrevocable self-limitation is self-contradictory on this model because it requires an inconsistency between a premise and the conclusion of the inference, when the premises themselves are (or may as well be) internally consistent. The rule of change that sits in the premise is inconsistent with its own invalidation, or with the exclusive validity of its successor asserted in the conclusion. Alf Ross, the Danish logician and jurist, has argued in detail[Note 1] that by formal criteria such an inference must be invalid. The esteem of Alf Ross in both logic and law forces us to take his arguments and his model of legal change seriously. Apart from this, we are led to take the inference model seriously by virtue of the widespread, usually unreflective belief that law is logical. Under the inference model what is logically impossible is therefore legally impermissible, and any legal practice or tradition to the contrary is itself a violation of both law and logic. There may well be a way to dissolve the paradox for the inference model or for formal logic generally. (We will see that satisfying the inference model is more difficult than satisfying formal logic alone.) Such dissolution would take the form of removing the inconsistency between premise and conclusion in the inference that models the act of amendment. A dissolution of this kind would satisfy logicians even if it had absurd consequences for law; but I have not been able to find even one dissolution of this kind that stands up to analysis.[Note 2] We may distinguish two ways to "solve" a paradox. Paradoxes are not mere contradictions; they are not nearly as tame. But their bite lies in their way of making contradiction appear inescapable. One kind of solution is to escape contradiction by a path not seen by others. I am calling this a dissolution of the paradox. Another way is to explain why contradiction is harmless, whether it is escapable or not. This will only work when contradiction is harmless, of course, and most of the argument in support of solutions of this kind will be spent in that cause. This will not dissolve the paradox, but will excuse and domesticate it, removing its sting and threat. It is much like what lawyers call an "affirmative defense": admit that you did it, but claim some excuse like insanity. The second kind of solution is more radical than it seems and requires, in effect, an insanity defense for law itself. In short, my thesis is that no dissolution satisfies the terms of the inference model, but that when we reject that model we find a number of plausible domesticating strategies. First I will consider various attempts to dissolve the paradox. Attempted dissolutions In standard logic all propositions follow validly from a contradiction. Therefore, one solution might be deliberately to make the premises of the inference that models the change internally inconsistent. This would certainly work to make the new AC a logically valid consequence of the old one. But it would work only at the cost of assuring that every AC is internally inconsistent. This result is inadmissible for the inference model, which cannot allow inconsistent rules simultaneous validity. However, if one likes, one may consider the total invalidation of the AC a solution satisfactory to logic that is repugnant only to law. My aim, however, is to explain how actual change of ACs has been possible, or how far it is logical. The actuality of self-amendment is a fact that is part of the explanandum (see Appendix 2). Even a logical dissolution must deal with it, much as approaches to the Liar cannot pretend that the lying words do not exist or cannot form the paradoxical statement. Most philosophers who have approached the problem (primarily through the theological paradox of omnipotence) evidently hope that a solution can be found that does not violate or require the inapplicability of formal logic. I have not argued for any conclusion that should dampen that hope. 149