As I remember it, my interpretation/expansion of the "Yes Doctor"
assumption is that 1) there is a (finite of course) level of (digital)
substitution (called the "correct level of substitution") that is
sufficient to represent "all that I am", and "all that I could be if I
hadn't undergone a substitution", and 2) we (including the doctor)
cannot know what the correct level of substitution is, therefore we
have to gamble that the doctor will get it right when we say "Yes
Doctor".
Suppose that the level of substitution actually *performed* by the
Doctor is S_p. Denote the *correct* level of substitution S_c. S_p
can be expressed by a finite number, since the substitution itself can
be expressed by a finite number (whatever is written on the tape/CD or
other storage/transmitting device). We know what S_p is and it is a
*fixed* finite number. But since S_c (*correct* level) is totally
unknowable, all we "know" about it is our assumption that it is finite.
The next *obvious* step in the logical process is that the probability
that S_p >= S_c is infinitesimal. I.e. the probability that the doctor
got it right is zilch. This is because most numbers are bigger than
any fixed finite number S_p.
So it seems that our step of faith in saying Yes Doctor in not well
founded. It's definitely a bad bet.
It seems that we need a stronger statement than S_c is finite.
Tom
Bruno Marchal wrote:
> Le 21-août-06, à 07:11, Stathis Papaioannou a écrit :
>
> >
> > It seems to me that there are two main sticking points in the
> > discussions on
> > several list threads in recent weeks. One is computationalism: is it
> > right or wrong?
> > This at least is straightforward in that it comes down to a question
> > of faith, in the
> > final analysis, as to whether you would accept a digital replacement
> > brain or not
> > (Bruno's "yes doctor" choice).
>
> Yes. Unfortunately this gives not a purely operational definition of
> comp.
> Someone could say yes to the doctor, just thinking that God exists, and
> that God is infinitely Good so that he will manage to resuscitate him
> through the reconstitution (he believes also God is infinitely
> powerful).
> So comp is really the belief that you can survive with an artificial
> brain *qua computatio", that is, through the respect of some digital
> relation only.
>
>
>
> > The other sticking point is, given computationalism
> > is right, what does it take to implement a computation? There have
> > been arguments
> > that a computation is implemented by any physical system (Putnam,
> > Searle, Moravec)
> > and by no physical system (Maudlin, Bruno Marchal).
>
>
>
> OK. To be sure Maudlin would only partially agree. Maudlin shows (like
> me) that we have:
>
> NOT COMP or NOT PHYSICAL SUPERVENIENCE
>
> But apparently Maudlin want to keep physical supervenience, and thus
> concludes there is a problem with comp. I keep comp, and thus I
> conclude there is a problem with physical supervenience.
> Actually I just abandon the thesis of the physical supervenience, to
> replace it by a thesis of number-theoretical supervenience.
>
>
> > The discussion about Platonism
> > and the ontological status of mathematical structures, in particular,
> > relates to this
> > second issue. Bruno alludes to it in several papers and posts, and
> > also alludes to his
> > "movie graph argument", but as far as I can tell that argument in its
> > entirety is only
> > available in French.
>
>
> That's true. I should do something about that. I don't feel it is so
> urgent in the list because there are more simple problem to tackle
> before, and also, most "MWI", or "Everything"-people can easily imagine
> the UD doesn't need to be run. But this is a subtle problem for those
> who have faith in their uniqueness or in the uniqueness of the world.
> Still you are right, I should write an english version of the movie
> graph.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
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Received on Mon Aug 21 2006 - 13:34:38 PDT