There was a popular book _Goedel, Escher and Bach_ a number of years ago, which demonstrates the ubiquitousness of paradox, including in the transformations in octaves in music and in Escher's famous paradoxical paintings.
It also seems that paradoxes occur routinely in the history of mathematics. This would not seem odd to someone approaching philosophical mathematics based on Hegelian dialectics. Dialecticians expect and focus on paradoxical contradictions. Engels describes this as the basis for the movement of thought in mathematics. (See _Dialectical Contradictions: Contemporary Marxist Discussions_ (Marxist Educational Press, 1982)
Hegel mentions jurisprudence as like mathematics in that both privilege the priniciple of identity (A is A). They are formal logics. But, for Hegel, formal logics must be comprehended dialectically, sublated. For dialectics the first principle is contradiction, the basis for change; but formal logic is a necessary moment in dialectical logic without which there is no definiteness or certainty
Anyway, it is not "surprising" that Goedel would find a "surprising" inconsistency in the U.S. Constitution, with law and all of its tightass logical consistency. Any contradiction in the Constitution would no doubt be a potential point of development of the Constit., an instability. I have discussed a contradiction between the First and Fourthteenth Amendments on this list.
One fundamental contradiction in the Constititution is the problem of democratic centralism, though not called that. This is the contradiction between "republicanism" (representationalism) and " democracy" or direct democracy. It is the contradiction between popular sovereignty ("We the People", self-governance) and the practicalities of large populations. This contradiction existed for Lenin as well as Madison.
The Constitution also has a general recognition of dialecticality in its Amendment Provision. Theoretically, anything in the Constitution can be changed. Without disputing that the Constitution retains backward aspects, this provision is "surprisingly" fresh for an old , sacred parchment. Of course, Hegel was something of a contemporary of the original Constitution.
Charles Brown
>>> Rakesh Bhandari <bhandari at phoenix.Princeton.EDU> 05/26/99 03:10PM >>>
There is a five page intro to Goedel's Theorem by George Boolos reprinted
as an appendix to Reuben Hersch's What is Mathematics Really (Oxford,
1997)? It seems like a good place to start. Perhaps someone could scan
it...And then I and others who are still confused could pose questions to
Chuck, Paul, Barkley and others who have mastered the theorem.
Yours, rnb