Re: Godel [was Re: qmail Re: freebsd - Re: recommended Virus Scanner?]

From: Deryk Barker (dbarker_at_turing.cs.camosun.bc.ca)
Date: 11/30/03

  • Next message: Hugo Vanwoerkom: "Re: Modem detection and installation problems" 
    Date: Sun, 30 Nov 2003 10:19:28 -0800
To: Debian Users <debian-user@lists.debian.org>

    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.

    "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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