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

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

All right.

`Could I take this as a defence of the "Papaioannou multiverse" for some`

`third person description: those where each world where you have a next`

`state leads to a dead end?`

`I call them "realist frames" in Conscience & Mechanism". Sometimes they`

`are called "terminal frames" in the literature.`

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.`

============================= Exercises for those who begins the study of modal logics: Does every one see that all the following formula are equivalent? : Dt -> ~B(Dt) Dt -> D(Bf) BDt -> Bf ~Bf -> ~B(~Bf)

`Those are equivalent (in all the modal logics we will meet), and the`

`only things people should know to prove those equivalences are that:`

1) ~Bp is equivalent with D~p (not necessary p = possible not p) ~Dp is equivalent with B~p (not possible p = necessary not p) Bp is equivalent with ~D~p Dp is equivalent with ~B~p

`From this you can deduce a nice memo: a not "~" can jump over boxes by`

`transforming them into diamonds, and reciprocally:`

For example: ~BBBBBBBBBBBBBBf is equivalent with DDDDDDDDDDDDDt and 2) the contraposition law: (A -> B) is equivalent with (~B -> ~A).

`I urge people who have difficulties NOT to hesitate to ask me question`

`OUT of line. Too bad to miss the marvel of all marvels (G and G*) for`

`reason of math-notation-anxiety!!!`

Bruno http://iridia.ulb.ac.be/~marchal/