Re: Smullyan Shmullyan, give me a real example

From: Russell Standish <r.standish.domain.name.hidden>
Date: Wed, 24 May 2006 13:05:34 +1000

On Tue, May 23, 2006 at 12:25:35PM +0200, Bruno Marchal wrote:
>
>
> In a sense, you are obviously right. That is why I said "some"
> knowledge of comp science or even just in math will make the existence
> of the UD, and of the Universal Machine astonishing. Precisely it is
> the knowledge of diagonalization. Godel will miss the universal machine
> and Church thesis, and will describe those things as a sort of miracle.
> More later. I will comment again with much more detail the rest of
> your post much later. If I comment it here now I will introduce
> confusion. It is preferable people get much more familiarity with the
> effective and not effective daigonalisations procedures before, I
> think.
>

I guess by this you mean that whilst it is impossible enumerate all
descriptions (the books in the infinite version of the Library of
Babel such as I take as my starting point), nor all true mathematical
facts, or even all programs (not sure on this one, obviously one can
enumerate all halting programs), it is however possible to execute all
possible programs. Yes, put that way, I suppose it is astonishing.

Cheers

-- 
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Received on Wed May 24 2006 - 00:00:16 PDT