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
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
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
(a) Pr(I live) = Pr(I die) = 0.5
I hope everyone sees that this (a) is not defensible once we *assume*
(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
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