From: Eschatoon Magic (eschatoon@gmail.com)
Date: Tue Feb 24 2009 - 00:18:29 MST
Godel demonstrated that there must be arithmetic statements which
cannot be proven algorithmically, but just "happen to be" true for all
natural numbers. I have used the Goldbach conjecture (which may be
unprovable in the Godel sense) as an example.
If something is true but cannot be proven true, the only thing we can
say is that it is "experimentally true".
I am very intrigued by he suggestion that maths is really the physics
of bottlecaps, which seems to me a very pragmatic and sane way to look
at it.
On Tue, Feb 17, 2009 at 3:57 PM, Stuart Armstrong
<dragondreaming@googlemail.com> wrote:
>> That's an interesting point. Thank you for the description of Godel's
>> incompleteness as "Mathematics is an experimental science.", it is an
>> intriguing way of looking at it.
>
> Maybe, but it's also false. You can see mathematics as an experimental
> science in some ways, but Godel has nothing to do with it. He
> demonstrates simply that there exists statements in arithmetic that
> cannot be proved or disproved algorithmically; Turign then extends the
> result to show that not only does there exists statements of the above
> type - but that you cannot be sure to identify one if you meet one.
-- Eschatoon Magic http://cosmeng.org/index.php/Eschatoon aka Giulio Prisco http://cosmeng.org/index.php/Giulio_Prisco
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