> 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!"