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/
