> Paul,
> 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.
However, this does NOT refer to contradictions within the system (of arithmetic in original case) itself, but the proposed (Godel numbering) axiomatization.
This is a crucial difference which I'm sure you understand implicitly, but which was not at all evident to the lay reader. What you wrote, literally, made no such distinction, which is why I said that it was false.
I'm sorry to be so nit-pciky, but when you see how wildly people extrapolate from misunderstandings or misapprehensions of Godel's Theorem, it can really get to you. Heck, there are webpages out there trying to use it to refute evolution, for cryin' out loud!
I, too, would like to know the details regarding Godel's encounter with the judge & the Constitution. As opposed to the uncountably infinite urban legends thereof.
-- Paul Rosenberg Reason and Democracy rad at gte.net
"Let's put the information BACK into the information age!"