On 02 Oct 2011, at 01:55, Russell Standish wrote:

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.

Only those going through some computational state being mine, from my points of view. It looks like a relativistic cone, except that futures might be more numerous than past. Now the 1-OM is the subjective part of this: it is an indexical, whose logics will obey the modalities having a connection with truth (like Bp & p, and Bp & Dy & p).

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

Yes. And there are non countably many such histories.

Such things, I am convinced, must be countable, implying that
each such sets histories is a continuum.

The states are countable, but not the (3-)states + the neighborhhood of (infinite) computations that you are mentioning yourselves. Not sure if I see where is the problem. It seems that you have answered it. The 1-OMs *are* set of histories, but with a particular 3- state, single out in the indexical way, and which will play the role of the "Bp". The "& p" will force the logic of the computational extensions to be different.



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