From: Jeff Bone (jbone@jump.net)
Date: Thu Aug 17 2000 - 21:06:17 PDT
> nothing's really provable
> anyway :-) ;-) :-)".
>
By the way, lest I just sit back let Gordo's accusation stick, I *do not* hold that opinion. There's lots
of stuff that can be proven. It's easy (at this point, standing on the shoulders of giants) to prove that
any self-consistent, finite, formal deductive system can express statements unprovable under that system.
It's possible to prove that the Entscheidungsproblem is unsolvable, or similarly that given a machine M
with a program P, there is no formal way to predict whether P will complete. Less easily, it's possible to
prove that the transfinite numbers are not closed under the operations of addition, multiplication,
exponentiation, and so on. It's even possible --- though very, very difficult to do ab initio --- to
demonstrate that x^n + y^n = z^n has no whole number solution when n is greater than 2.
OTOH, it's generally pointless except as an exercise in entertainment or as a tool for achieving personal
enlightenment to try to prove anything at all about things like "happiness," "beauty," "moral right and
wrong," and so on. As Bonevac, my logic instructor, put it years ago: "the [logical] analysis of moral
and practical reasoning still abounds with controversy." The best we can hope for in such discussions,
IETF style, is "rough consensus of opinion" and perhaps some social equivalent of "working code."
And that *really* is my story, and I'm sticking to it.
jb
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