Le 14-déc.-05, à 01:34, Stathis Papaioannou a écrit :

In the multiverse, only other people end up in dead ends. Although from a third person perspective every entity in the multiverse could be said to exist only transiently because at every point of an entity's history we can say that there sprouts a dead end branch of zero extent, from a first person perspective, these branches cannot by definition ever be experienced.

If the laws of physics are contingent on the continuation of consciousness, it is very well possible that a very large majority of branches are very short and dead ends. In other words every nanoseconds we suffer a thousand deaths through events which are perceived to be unlikely due to the apparent stability of the physical laws, events such as proton decay, beta capture, nuclear fusion due to nucleus tunneling, etc...

Bruno Marchal wrote:

I know you have solved the "only if" part of following exercise:

(W, R) is reflexive     iff      (W,R) respects Bp -> p.

I will come back on the "if" part later.

Have you done this: showing that

(W,R) is a "Papaioannou multiverse" iff (W,R) respects Dt -> D(Bf).

Note that this question is a little bit academical. I have already explain how I will choose the modal logics. Actually I will not choose them, I will extract them from a conversation with the machine (and its "guardian angel"). This will leave no choice. It will happen that the formula Dt -> D(Bf) will appear in the discourse machine; indeed perhaps some of you know already that this is just the second incompleteness of Godel, once you interpret Bp by "the machine proves p", coded in some language the machine can use.


George

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