On Wed, Jan 18, 2012 at 2:30 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

"And are non computable real numbers fundamental?"
>

If they can not be derived from anything else, and they can not be, then
they must be fundamental.

" None occur in any theory."
>

Well they occurred in Turing's 1936 paper and many after it, or at least
the concept of them did, no specific non-computable number was mentioned
because none can be specified.  As Ludwig Wittgenstein said "what
cannot bespoken about must be passed over in silence".

" In physics and math all real constant seems to be gentle and computable
> (albeit often transcendent) like PI, e, gamma, etc."
>

I admit I'm just speculating here and might be dead wrong but maybe the
fact that physics can not exactly specify the position and velocity of
every particle and the fact that mathematics can not specify every real
number are related.

" With comp, analysis and physics belongs to the natural numbers
> epistemology."
>

Yes but if a theory of everything is really about everything then that is
insufficient.

" Jacques Arsac is a french catholic who wrote a book against mechanism. He
> is not solipsist, and he doubts mechanism. One example is enough."
>

That is not a example that is a name. I have never doubted that
individuals, especially religious individuals, can be illogical and
simultaneously hold diametrically opposite views.

"Frankly why would a non mechanist be solipsist?"


Although it can not be proven to be false no sane person can be a
solipsist, except perhaps in a philosophy classroom when they are trying to
sound provocative. A better question would be why would anyone think it
controversial to say "things happen for a reason or they do not"?

 John K Clark

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