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.

                                                Cheers


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