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. 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

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

(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. 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. 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.

Stathis Papaiaonnou

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