>> Bruno:In general worlds are not effective (computable) objects: we cannot
>> mechanically (even allowing infinite resources) generate a world.<
>JC: Hmmm..but then if such worlds are not effective objects, how
>can they be
>said to be "instantiated"? If we extend this to Tegmark, this
>even given infinite time, a world can never be "complete"
>Which implies that even given infinite time, not everything that *can*
>happen *will* happen; which was my argument to begin with.
>I have seen it stated that, given infinite time, everything
>that CAN happen
>MUST happen, not only once but uncountable times. You argue
>that this is
>incorrect. Can you show why it is incorrect? Thanks,
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.