Marchal wrote:
> Hi Juergen,
> I would like to nuance my last Post I send to you.
> First I see in other posts, written by you, that your
> computable real numbers are *limit* computable. It still
> seems to me possible to diagonalize against that,
> although it is probably less trivial.
> But I think it isn't really relevant in our present discussion, 
> because the
> continuum I am talking about appears in the first person discourse 
> of the machines, so it is better to 
> keep discussing the main point, which is the relevance
> of the first person point of view, with comp, when
> we are searching for a TOE.

It seems to me that the cardinality of UD*, or whether UD* is a
continuum or not is rather irrelevant. My understanding is that the UD
argument implies a first person indeterminancy, ie every first person
experience will have access to a random oracle.

I think the argument goes something like this:

1) UD algorithms will have high measure in the space of all
computations, much higher than a direct implementation of a conscious AI
(assuming such things exist).

2) Therefore, it is more likely that a conscious AI will find itself
imbedded in the output of a UD, with access to a random oracle

(Of course my viewpoint is that consciousness _requires_ access to a
random oracle, making conclusion 2 even stronger, but it is not
necessary for the argument).

> You makes me hesitating between pointing to modal logic
> and self-reference or keeping insisting on the
> thought experiments. Mmh... I dunno.
> Bruno

Modal logic needn't apply just to machines, but describes any form of
formal knowledge - knowledge based on consistency <> and proof [].

However, this just appears to be mathematical knowledge. It doesn't
describe how we know things in science, which might be better
described in the Popperian tradition as know(p) = <>p & <>!p
(consistency but falsifiability of p) ...

Of course, there is a whole realm of other knowledge domains to
tackle, such as common sense etc.


Dr. Russell Standish                     Director
High Performance Computing Support Unit, Phone 9385 6967                    
UNSW SYDNEY 2052                         Fax   9385 6965                    
Australia                                [EMAIL PROTECTED]             
Room 2075, Red Centre          

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