On Sun, Nov 30, 2003 at 10:19:28AM -0800, Deryk Barker wrote: > Thus spake Tom ([EMAIL PROTECTED]): > ... > > 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: [EMAIL PROTECTED] | | > |phone: +1 250 370 4452 | Hermann Scherchen. | > > > -- > To UNSUBSCRIBE, email to [EMAIL PROTECTED] > with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED] > -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]