Hi Bruno,

Thank you for the information. I understand these parts for the others it
seems I need to search in archives of the
list for some keywords that I do not understand. I'm not an old member.
I just wanted to say, most of links in
your page lead to nowhere!(Error), It would be nice if you fix them.

Mohsen Ravanbakhsh

On 5/23/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>
>
> Hi Mohsen,
>
> Le 22-mai-07, à 12:20, Mohsen Ravanbakhsh a écrit :
>
>
> > Hi Bruno,
> >
> > My sixth sens says you're talking about something important :) but I
> > don't get it.
>
>
> Note that it could help me if you could be a little more specific. OK I
> see another post of you.
>
>
>
>
> > It could have been of much more interest, if you could elaborate, or
> > provide us with some references for each part of your
>
>
> So you are able to make sense of the fact that
> [LOGIC+ADDITION+MULTIPLICATION] gives already a Universal Turing
> Machine. This is no more astosnishing than the fact that the K and S
> combinators provides already turing-universality, or that the Conway
> Game of Life is already turing universal.
> The advantage of [LOGIC+ADDITION+MULTIPLICATION]  is that (universal)
> computability is seen as a particular case of provability.
>
> What is more long to explain in details is that
> [LOGIC+ADDITION+MULTIPLICATION + INDUCTION] is already lobian.  But I
> will first look to your other post which title refer to incompleteness.
>
>
>
> > argument.(Beginning from the 'OBVIOUS IMPORTANT QUESTION' it
> > becomesvague for me)
>
>
> The key point consists in understanding the difference between
> computability/simulability and provability. I will come back on this,
> but the idea is that, assuming comp, I can simulate Einstein's brain
> exactly, and still not share his beliefs. Similarly the very non
> powerful Little-Robinson-arithmetic can simulate rich theories like
> PEANO or ZF, but cannot prove the theorem of PA or ZF.
>
> For example PA can prove that ZF can prove the consistency of PA, yet,
> PA cannot prove the consistency of PA.
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
> >
>


-- 

Mohsen Ravanbakhsh,
Sharif University of Technology,
Tehran.

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