Hi,

Le Vendredi 18 Août 2006 22:17, complexitystudies a écrit :
> > I think it has been said several times :
> >
> > The existence of a number/arithmetical proposition is the fact that its
> > existence/truth does not depend on the fact that you exist/that it exists
> > conscious beings capable of thinking of it.
> >
> > So the truth value of a proposition is independant of me.
>
> Well, let's see: in Alice in Wonderland, Humpty Dumpty fell off a
> wall. This is true, isn't it? It is certainly true independent
> of our minds. Indeed, it is true in such a way that even when
> all humans have died, this universe will have a contained a life-form
> which produced an author who wrote a book in which Humpty Dumpty
> fell off a wall. But neither Humpty Dumpty nor the fact that he
> fell off a wall were ever true in this universe - only that this
> story was written, and that many people read about it and could
> converse about it.
>
> So if you believe that numbers have an independent existence, then you
> would definitely also have to believe that Humpty Dumpty exists.
> Both are products of the mind. Either both exist, or both don't
> (other than as brain patterns).

Well, if computationalism is true, then there exists observer moment of an "I" 
(not talking about me here ;) who is Humpty Dumpty, so there is an universe 
where Humpty Dumpty exists in the same sense I exist. The fact that in our 
universe Humpty Dumpty only exist in a story does not tell anything about a 
real Humpty Dumpty living in (at least) one (but in fact an infinity) of the 
computed universe by for example the UD (Universal Dovetailer). You must at 
least accept multiple world, ie a multiverse. This multiverse should also be 
fairly large (the UD trace is very very large ;).

Now I think UD could be false if it is impossible to have a real turing 
machine (no memory bound, no time bound), because if it is possible then the 
majority of OM will be computed by the UD, so the probability of your current 
OM being computed on a "physical" computer is zero. UD could also be false if 
we are not turing emulable... ie consciousness is not a computation 
process... but physicalism doesn't tell what it is then.

Regards,
Quentin

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