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.
"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]