> 6) This shows that if we are in a massive computer running in 
> a universe,  then (supposing we know it or believe it) to 
> predict the future of any experiment we decide to carry one 
> (for example testing A or B) we need to take into account all 
> reconstitutions at any time of the computer (in the relevant 
> state) in that universe, and actually also in any other 
> universes (from our first person perspective we could not be 
> aware of the difference of universes from inside the computer).

Yes, but this is just a fancy version of the good old-fashioned Humean
problem of induction, isn't it?

Indeed, predicting the future on a sound "a priori" basis is not
possible.  One must make arbitrary assumptions in order to guide

This is a limitation, not of the "comp" hypothesis specifically, but of
the notion of prediction itself.

You cannot solve the problem of induction with or without "comp", so I
don't think you should use problem-of-induction related difficulties as
an argument against "comp."

In fact, "comp" comes with a kind of workaround to the problem of
induction, which is: To justify induction, make an arbitrary assumption
of a certain universal computer, use this to gauge simplicity, and then
judge predictions based on their simplicity (to use a verbal shorthand
for a lot of math a la Solomonoff, Levin, Hutter, etc.).  This is not a
solution to the problem of induction (which is that one must make
arbitrary assumptions to do induction), just an elegant way of
introducing the arbitrary assumptions.

So, in my view, we are faced with a couple different ways of introducing
the arbitrary assumptions needed to justify induction:

1) make an arbitrary assumption that the apparently real physical
universe is real

2) make an arbitrary assumption that simpler hypotheses are better,
where simplicity is judged by some fixed universal computing system

There is no scientific (i.e. inductive or deductive) way to choose
between these.  From a human perspective, the choice lies outside the
domain of science and math; it's a metaphysical or even ethical choice.

-- Ben Goertzel

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