>OK, let me explain this. First, Goedel's theorem says that within any logical
>system, there are statements that you can KNOW to be true but you can't prove
>to be true. There are technical limitations on the type of logical system.
>Goedel's theorem does not apply to arithmetic with only +/- operations, (See
>Tipler, Physics of Immortality p 193 (I think, my book is at home and this is
>from memory)).
Well, maybe we need to find a mathematician on the list to referee (since
Glenn didn't like the opinion of the one I consulted). But I'm pretty sure
the statement of Godel's theorem above is just plain wrong. Let me repeat
my friend's version:
>Suppose you have
>any collection of axioms that include the axioms that postulate the
>existence of the natural numbers. Then there are statements about the
>natural numbers that can be neither proved false nor true with these
>axioms.
There would not seem to be any way to get from this the existence of things
you "know" to be true but can't prove. In fact, in the context of
mathematics and logic, the concept of "knowing" something to be true without
rigorously proving it seems entirely meaningless.
Maybe a red flag should be the reference to Tipler's book. While I haven't
read it, the reviews from scientists pretty uniformly say that he has gone
off into crackpot-land and makes almost as little sense as Velikovsky.
Again, I should say that all this discussion, while not unimportant (since
we do not serve a God of confusion) does not take away from the original
point, which is that there is little if anything that science can prove with
absolute rigor, because of its inherently inductive nature. I'm just
pointing out (or at least claiming) that the point has nothing to do with
Godel's theorem.
---------------------------------------------------------------------------
| Dr. Allan H. Harvey | aharvey@boulder.nist.gov |
| Thermophysics Division | Phone: (303)497-3555 |
| National Institute of Standards & Technology | Fax: (303)497-5224 |
| 325 Broadway, Boulder, CO 80303 | |
|-------------------------------------------------------------------------|
| "Don't blame the government for what I say, or vice versa." |
---------------------------------------------------------------------------