But the essential Godelian contradiction that underlies incompleteness is to find that one can generate statements from within a system that both say the statement in question is true and that it is false. This is a contradiction, but does not establish that it is definitely false, quite clearly.
I think that you are right about the nature of the US constitution and law codes in general, although I am not a lawyer or student of law. They are not axiomatic systems and by their very nature involve contradictory impulses that are in conflct, if not outright logically contradictory statements. We know that they embody in various ways the contradictions and the class conflicts that exist within a society in various ways as has been argued for the US constitution by Beard and others. The working out of these conflicts and contradictions reflects the ongoing power struggles in society and the evolution of related legal and political interpretations and outcomes.
Of course James Madison recognized this in nascent form, but saw the process as one of seeking some kind of equilibrium through the famous checks and balances. One could call this a neoclassical theory of the constitution. Of course there is the reactionary "law and economics" movement that seeks to impose neoclassical optimality and free market concepts as presumed underpinnings of the constitution, or at least of law more generally.
I have heard both on the list and off further accounts of Godel's naturalization hearing and of his dispute with the judge. I am curious to learn more of the details. In particular, I am curious as to whether he found logical contradictions (perfectly possible even in a non- axiomatic system) or merely observed the existence of conflicting tendencies of the sort that have been mentioned by many on this list reflecting underlying conflicts in society. The statement that the constitution does not preclude the growth of fascism is certainly true and does not seem to reflect any kind of contradiction or logical inconsistency, unless he perceived it as inconsistent with the presumed impulse to democracy. But as has been noted, the authors of the US constitution were quite concerned to limit democracy in various ways.
Apologies for my outbreak of pomposity in my earlier response to Paul. For a fairly recent discussion of Godelian ideas in economics and game theory see a paper on my website, "Everything I Might Say Will Have Already Passed Through Your Mind" (with Roger Koppl), at http://cob.jmu.edu/rosserjb. I note that this paper draws on some insights of Oskar Morgenstern who cofounded game theory with John (Janos) von Neumann and who was also probably Godel's closest friend in his later life. Barkley Rosser -----Original Message----- From: Paul Henry Rosenberg <rad at gte.net> To: lbo-talk at lists.panix.com <lbo-talk at lists.panix.com> Date: Monday, May 24, 1999 10:51 PM Subject: Re: incompleteness theorem (was: gun control)
>J. Barkley Rosser, Jr. wrote:
>
>> Paul,
>> A statement is "unprovable within a system" if
>> any effort to prove it within that system inevitably leads
>> to a contradiction. You are lecturing the wrong person
>> on the work of Kurt Godel. (See "Godel Theorems for
>> Nonconstructive Logics," J. Barkley Rosser, Journal of
>> Symbolic Logic, 1937, vol. 2, pp. 129-137).
>
>(1) I'm not going to argue qualifications here. The subject as we're
>discussing no longer rises to the highest levels of mathematical
>understanding, tho it remains rather mystifying to non-mathematicians.
>I attended seminars on Godel as an undergrad, and had a friend who did
>his baccalaureate thesis on the subject. I admit to be rather rusty on
>the details, but not on the major points, which were hammered at over
>and over again in many discussions, formal and informal.
>
>(2) If even ONE effort to prove a statement within a system leads to a
>contradiction, then that statement is FALSE, not unprovable.
>
>
>--
>Paul Rosenberg
>Reason and Democracy
>rad at gte.net
>
>"Let's put the information BACK into the information age!"
>