Le 18-avr.-05, à 02:39, Jonathan Colvin a écrit :
> Well, I was elaborating on Bruno's statement that worlds ("maximal
> consistent set of propositions") of a FS are not computable; that even
> given
> infinite resources (ie. infinite time) it is not possible to generate a
> "complete" world. This suggests to me that it is *not* the case that
> given
> infinite time, eveything that can happen must happen. I must admit
> this is
> not my area of expertise; but it seems to me that the only other
> option of
> defining a world (identifying it with the FS itself) will, by Godel's
> incompleteness theorem, necessitate that there exist unprovable true
> propositions of world; the world will be incomplete, so again, not
> everything that can happen will happen.
But here I disagree, unless you put some "constructive" or "effective"
constraint on what is a "reality", but then you must abandon the comp
hyp. The reason is admittedly subtle, perhaps, and is based on the
distinction between first person point of view (pov) and third person
pov. The comp hyp is a bet that "I" am a machine, and this entails that
reality, whatever it is, cannot be described by an effective entity.
That is: if I am a machine then reality cannot be a machine (the idea
is that reality emerges from ALL computations relative to my state and
this is essentially due to the fact that a first person cannot be aware
of delays in some effective presentation of all computations (which
exist by Church's thesis)). Please see the links to the Universal
Dovetailer Argument (UDA) in the list and/or in my url. We can discuss
that later 'cause now I'm too buzy alas ... But read the UDA and don't
hesitate to send a catalog of objections, or questions. In english you
can read either
http://iridia.ulb.ac.be/~marchal/publications/
SANE2004MARCHALAbstract.html or
http://iridia.ulb.ac.be/~marchal/publications/CC&Q.pdf
From the (pure) computer science point of view the difficulty here is
related to the fact that a set can be effective although some of its
subset is not (see the diagonalization posts in my url). This is not so
astonishing the painting of the Joconde is more complex than the white
paper which "contains" it.
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Mon Apr 18 2005 - 06:36:49 PDT