Bruno Marchal writes:

If on the basis of a coin toss the world splits, and in one branch I am instantaneously killed while in the other I continue living, there are several possible ways this might be interpreted from the 1st person viewpoint:

(a) Pr(I live) = Pr(I die) = 0.5

I hope everyone sees that this (a) is not defensible once we *assume* comp.

Good, we agree here. I don't think everyone on this list would agree.

(b) Pr(I live) = 1, Pr(I die) = 0

And this one (b) is a consequence of comp.

(c) Pr(I live) = 0, Pr(I die) = 1

Option (c) may look a bit strange but is the one that I favour: all first person experiences are transient, all branches are dead ends, no world is accessible from any other world.

I think I figure out why you say that and why you take it probably as a consequence of comp.
Let us see.

However, the various independent, transient observer moments are ordered in such a way in what we experience as ordinary life that the illusion of (b) occurs.

Yes right. But that "illusion" is all what the first person notion is all about. Your "c" is too strong. What would you say if your comp doctor proposes you an artificial brain and adds that the Pr(I die), for you, is 1. I think you would say "no doctor". Then the doctor (not you!, I know you are doctor!) adds that in all case Pr(I die) = 1. Then you will tell him that he has not given any clue about the probability your first person "illusion" (I hate this word) lasts. The real question we ask to the doctor is what is the probability my "illusion" will lasts *as* it lasts for any other medical operation when it is said the operation has been successful. What I have called "Papaioannou's multiverse" are just your transient observer moments *together* with the order you are indeed adding on them for giving sense to ordinary experience. That order *is* an accessibility relation.

OK, you've put that quite well. Even if continuity of identity is an illusion, it is an important illusion. An analogy would be going to the cinema to see a movie: the "reality" might be that we are watching a series of still images, but the important thing for the audience is that the illusion of motion is maintained by having a certain minimum frame rate. So yes, this does give rise to an accessibility relationship, but it presupposes a theory of personal identity. Even on this list, there are people who might say (a) above is the case rather than (b) or (c).

This covers such (theoretical, at present) cases as the apparent continuity of identity between two observer moments that just happen to seem to be consecutive "frames" in a person's life even though there is no physical or informational connection between them.

But you cannot deny that with comp, there *is* some informational connection between them. The connection will appear to be exclusively mathematical and immaterial. And will appear to be the logical root of another "illusion": a physical world. We know this by UDA (the Universal Dovetailer Argument), but we need to isolate completely the structure of the multiverse extractible from comp if we want to derive the precise physics from comp (and then to compare with the empirical physics to evaluate empirically the plausibility of comp (or of its many variants).

What I meant by "informational connection" was actual information transfer from one frame to the next, by some physical process. This is what happens normally by virtue of the fact that consecutive frames are implemented by the same physical brain. It is also what would happen, in a different way, with teleportation. This is sufficient for the experience of continuity of consciousness, but it is not necessary: the appropriate frames or observer moments might occur completely randomly in different parts of the multiverse, and the first person experience would be the same. (Such is not the case for observation of third persons: the frames or observer moments must be explicitly ordered, or they will be lost in the noise). Is this what you mean by "the connection will appear to be exclusively mathematical and immaterial"?

Stathis Papaioannou

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