Re: Godel [was Re: qmail Re: freebsd - Re: recommended Virus Scanner?]
On Sun, Nov 30, 2003 at 10:19:28AM -0800, Deryk Barker wrote:
> Thus spake Tom (tb.31123.nospam@comcast.net):
> ...
> > I thought it was neither complete (the doesn't capture all truths thing)
> > nor consistent (may contain both a statement and its complement)[1].
> > But I can look that up.
> >
> > The Stanford prof told me the Lambda calculus (Lisp-ish stuff) almost
> > proved one of the two.
Yeah, I know I *said* disprove Godel, but that's not what I meant :-)
I've read a lot overnight...
At least now I know why everyone is so willing to play games. It's all
formalism.
>
> "Almost"? Hardly counts. I also don't understand what he was telling
> you. Church's lambda-calculus and Turing's turing machine are
> equivalent (as I believe Turing showed as part of his PhD thesis,
> which Church supervised) and AFIK neither was trying to disprove
> Go"del which, as someone has already pointed out, is well proved and,
> the nature of mathematical proof being what it is, it is highly
> unlikely that anyone is going to find a logical error almost 75 years
> later - Go"del's proof has, after all, been pored over by countless
> mathematicins and many of them must have desparately wanted to be able
> to refute it.
>
> AIR Go"del says that in any axiomatic system which is at least complex
> enough to contain the axioms of arithmetic, then there are statements
> which can be made but not proved within that system. It is possible to
> add further axioms to prove the statements, but then this richer
> axiomatic base will lead to new statements which cannot be proved with
> the richer set of axioms.
> --
> |Deryk Barker, Computer Science Dept. | Music does not have to be understood|
> |Camosun College, Victoria, BC, Canada| It has to be listened to. |
> |email: dbarker@camosun.bc.ca | |
> |phone: +1 250 370 4452 | Hermann Scherchen. |
>
>
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