On Sat, Oct 01, 2011 at 05:15:34PM +0200, Bruno Marchal wrote: > > On 01 Oct 2011, at 09:31, Russell Standish wrote: > > >On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote: > >> > >>OK. But note that in this case you are using the notion of 3-OM (or > >>computational state), not Bostrom notion of 1-OM (or my notion of > >>first person state). > >>The 3-OM are countable, but the 1-OMs are not. > > > >Could you explain more why you think this? AFAICT, Bostrom makes no > >mention of the cardinality of his OMs. > > I don't think that Bostrom mentions the cardinality of his OMs, > indeed. I don't think that he clearly distinguish the 1-OMs and the > 3-OMs either. By "3-OM" I refer to the computational state per se, > as defined relatively to the UD deployment (UD*). Those are clearly > infinite and countable, even recursively countable. > > The 1-OMs, for any person, are not recursively countable, indeed by > an application of a theorem of Rice, they are not even > 3-recognizable. Or more simply because you cannot know your > substitution level. In front of some portion of UD*, you cannot > recognize your 1-OMs in general. You cannot say "I am here, and > there, etc." But they are (non constructively) well defined. "God" > can know that you are here, and there, ... And the measure on the > 1-OMs should be defined on those unrecognizable 1-OMs. >
I'm still struggling to understand what you mean by 1-OM here. Are you talking about the infinite histories making up UD*? There are an uncountable number of these, it is true. But then, I wouldn't call these OMs. An OM must surely be related to the set of all such histories passing through your current "here and now". Such things, I am convinced, must be countable, implying that each such sets histories is a continuum. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
