Le 24-nov.-05, à 08:52, Stathis Papaioannou a écrit :

Bruno Marchal writes:

The main idea of Kripke has consisted in saying that the modal formula Bp (also written []p) is true at world a, if p is true in all the worlds you can access from a. p is relatively necessary at a. For example, if the world are countries and if you have to pay taxes in all countries that you can access from where you are, then taxes are necessary (relatively to a).

That is, p is "necessary" at world a if p is true for all worlds b such that aRb. It is intuitively normal: a proposition is necessary for you if it is true in all world you can access.

[I have cut this short - Bruno continues at some length from this beginning]

What counts as an accessible world? It seems that in answering this you have to propose or imply a theory of personal identity.

Actually I would say it is the other way round. Kripke introduces its abstract "multiverses" in order to be able to make simple the reasoning for large class of modal logics, which are somehow traditional tools for handling complex philosophical notions, including notions of personal identity. That is the way I proceed to. By comp I inherit of the modal logic G and G* from the most standard theory of self-reference (the Godel one) and I use them to analyse two (at least) notions of personal identity (the third person one and the first person one).

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.

(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.

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).



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