# Re: Smullyan Shmullyan, give me a real example


Le 15-mai-06, à 13:59, Russell Standish a écrit :

>> OK, why not taking that difference [description/computation] into
>> account. I think it is a
>> crucial point.
>
> I do :). However, its makes no difference as far as I can tell to the
> Occam's razor issue.

You do? See below.

>
>>
>>
>>
>>> given a reference Turing machine U. This appears
>>> to be a 3rd person description, but it need not be so.
>>
>>
>> I am not sure I understand.
>>
>
> Do you mean you don't think it is a 3rd person description, or do you
> mean you don't think it can be anything else?

I  think it is a third person description.

<snip>

>> I really don't understand.
>>
>> Bruno
>>
>
> The details, of course are in my paper "Why Occams Razor". To
> summarise, an observer induces a map O(x) from the space of
> descriptions, which is equivalent AFAIK to the output of your UD,

?   The UD has neither inputs nor outputs. (like any "universe" or
"everything", note)

> to
> the space of meanings.

Which space is it?  What do you mean (here) by "meanings"?  If it is a
mathematical semantics then which one, if not, I don't understand. I

> For any given meaning y, let omega(y,l) be the
> number of equivalent descriptions of length l mapping to y (for
> infinite length description we need the length l prefixes). So
>
> omega(y,l) = |{x: O(x)=y & len(x)=l}|
>
> Now P(y) = lim_{l->\infty} omega(y,l)/2^l is a probability
> distribution, related to the Solomonoff-Levin universal
> distribution.
>
> C(y)=-log_2 P(y)
>
> is a complexity measure related to Kolmogorov Complexity.

Note that this approach is non constructive (and thus cannot be first
person, at least as I use it and modelize it). I have already argued
that it can be refined through the notion of depth (a la Bennett),
which takes a notion of "long" computation into account; but it is
still incomplete relatively to the first person indeterminacy problem
(pertaining on the set of *all* (relative) computations, and not at all
on the set of descriptions).
The non-constructibility is a problem here, given the goal of deducing
physical laws or principles "without physics".

>
> Basically this is an Occams Razor theorem - the probability of
> observing something decreases dramatically with its observed
> complexity. And this is a pure 1st person result.

?

> It doesn't get rid
> of all white rabbits, but the remaining ones are dealt with the
> Malcolm-Standish argument.

If you have succeed in eliminating all the "many person pov" - white
rabbits,  then publish!

Frankly it seems to me you don't really address the first person issue
(and thus the mind/body issue). For example, what is your theory of
mind? In particular, do you say yes to the comp doctor?
I think that eventually, we have to limit ourself to the discourses
that a self-referentially correct machine (or entity, or growing
entities of such lobian kind) can have about herself and her
possibilities.

I am not saying your argument is wrong, just that is incomplete (and
unclear, but this could be my incompetence).

Bruno

http://iridia.ulb.ac.be/~marchal/

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