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From: geert@sparc.aie.nl (Geert-Jan van Opdorp)
Subject: Re: Is Penrose Right?
Sender: news@aie.nl (Usenet News)
Message-ID: <GEERT.95Sep25173614@sparc.aie.nl>
In-Reply-To: Chris Gordon-Smith's message of Sun, 24 Sep 1995 20:56:33 +0100
Date: Mon, 25 Sep 1995 16:36:13 GMT
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References: <201348657wnr@smithg.demon.co.uk>
Organization: AI Engineering BV, Amsterdam, Netherlands

In article <201348657wnr@smithg.demon.co.uk> Chris Gordon-Smith <Chris@smithg.demon.co.uk> writes:


> Hello All
> 
> I've been on my holidays and took the chance to read Roger Penrose's book "Shadows 
> of the Mind". It seems to me that the points he is making have considerable bearing on 
> the future of Alife and AI, and I wonder whether anyone can make a reasoned counter 
> argument.
> 
> I won't attempt to summarise all the arguments given in the book here. However, the key 
> assertions/speculations (as I understand them) are:-
> 
> 1	Consciousness and intelligence cannot be produced by any process (eg GA or 
> ANN) which is equivalent to a Turing Machine.
> 
> His main support for this is that Godel's Theorem demonstrates that there are 
> mathematical truths which are evident to human minds which cannot be determined 
> algorithmically.
> 

For me, the key is this 'evident'. Not only do you need
a platonistic view of logic and mathematics (or else
there is  nothing to 'See'), you also have to believe
we can have direct unquestionable knowledge about
such a platonistic logic. Furthermore it seems to me
(but I'm not quite sure of this) that even if we `Saw'
the truth of every possible  godel-sentence in general,
including the one for the logic of our own belief-system, 
this could still leave us a turing machine if our
belief system is inconsistent.

Wasn't it `evident' at one time that Euclid's fifth 
postulate was necessarily true given the other axioms,
even though this could not be proven?

It maybe so that the Buddha cannot be a Turing machine
since he `Sees' all Truth, and is entirely consistent
(clearly not the Zen variety :). 


Geert-Jan

-- 
Geert-Jan van Opdorp
AI-Engineering
Amsterdam, The Netherlands
geert@aie.nl
