Bruno,

`There's a lot to digest in this post. I should clarify that in my original`

`post I had in mind two different usages of the word "death". One is what`

`happens to you in destructive teleportation: you vanish at one set of`

`spacetime coordinates, then reappear in almost exactly the same material`

`configuration at a different set of spacetime coordinates. Ordinary moment`

`to moment life is a special case of this process where the difference`

`between the "before" and "after" coordinates is infinitesimal, and therefore`

`there is no subjective discontinuity between one moment and the next. I`

`would call what happens when you vanish "provisional death". Provisional`

`death becomes "real death" if (contra QTI) there is no successor OM (or no`

`next moment, or no reachable world): if the teleporter breaks down and loses`

`the information obtained in a destructive scan before it can be sent, or if`

`you are killed in an accident in ordinary life. It is interesting to note`

`that memory loss is effectively the same as real death, or real death with a`

`backup that is not up to date (eg. the original is killed a few minutes`

`after undergoing non-destructive teleportation) if the memory loss is`

`incomplete. Real death and memory loss cause a cul-de-sac in a stream of`

`consciousness, whereas provisional death does not.`

`If you can convince yourself that you undergo provisional death all the`

`time, and real death when you experience memory loss, then it may be`

`possible to convince yourself that death is no big deal. However, our`

`evolved minds would fight very hard against such a conclusion.`

In this post I will try to make clearer my argument with Lee by using aminimal amount of modal logic (and so it's good "revision" ;)Then I will explain how Stathis seems to have (re)discovered, in its"DEATH" thread, what I call sometime "The Smallest Theory of Life andDeath", or "Near Death Logic", or just C.I have never abandon C, but the interview of the Lobian machine will give Cagain, but through some of its most notable extensions which are G and G*.To prevent falling in the 1004-fallacy, I will use (at least temporarily)the words "state", "world", "situation", "observer-moment", "OM", etc. assynonymous. I will use "world" (if you don't mind), and I will designateindividual world by w, w1, w2, w3, w4, etc.Like Stathis (and Kripke!), I will accept that some world can have*successor* world (successor OMs in Stathis terminology). More generally wesuppose a relation of accessibility among worlds (that's Kripke's idea howto enrich Leibniz).

`These words - successor, accessibility, reachability - are figures of`

`speech, right? What is important is the relationship between the worlds, not`

`that someone or something "reaches" physically from one world to the next.`

I will be interested in the discourse which are true at each world, and Iwill assume that classical logic holds at each world.p, q, r, ... denotes propositions. And a "semantics" is given when it issaid which one of p, q, r ... are true or false in each world.I suppose you know some classical logic: (p & q) is true if both p and q is true, else it is false (p v q) is true if at least one among p, q is true, else it is false (~p) is true if and only if p is false (p -> q) is true if p is false or q is true(to be sure this last one is tricky. "->" has nothing to do withcausality: the following is a tautology (((p & q) -> r) -> ((p -> r) v (q-> r))) although it is false with "->" interpreted as "causality", (wet &cold) -> ice would imply ((wet -> ice) or (cold -> ice)). Someday I willshow you that the material implication "->" (as Bertrand Russell called it)is arguably the "IF ... THEN ..." of the mathematician working in Platonia.

`That last one always got me: a false proposition can imply any proposition.`

`All the rest seem like a formalisation of what most people intuitively`

`understand by the term "logic", but not that one. Why the difference?`

(p <-> q) is true if (p->q) is true and (q->p) is true. I could have said(p <-> q) is true if p and q have the same truth value. The truth value aretrue and false, and I will write them t and f.You can see t as a fixed tautology like (p -> p), and f as a fixedcontradiction like (p & (~p)), or add t and f in the proposition symbolsand stipulate thatf is always false t is always trueThat classical logic holds in the worlds means the "usual things", forexample that- if p holds at w, and if q holds at w, then (p & q) holds at w, - if p holds at w, then p v q (read p or q) holds at w, - if p holds at w and p -> q holds at w, then q holds at w. - t holds in all world - f does not hold in any world - etc.Etc. All "tautologies" will be true in all world (p -> p), (p -> (q -> p)),((p & q) -> p), etc.(whatever the truth value of p, q, r, ... in the worlds).I hope most of you knows the "truth table method" to verify if aproposition is a tautology or not. But I can explain or give reference oryou could google.Remark.Note that if the excluded middle principle (p v (~p))is a classicaltautology, it is not an intuitionist logic, and (much later) we will metthis logic. We live the modern time where even the classical (Platonic)logician must aknowledge the importance of the many many many many possiblelogics.For example in Quantum Logic and in the Relevant Logics, the classicaltautology which is "guilty" is the "a fortiori principle": (p -> (q -> p))One of the main utility of modal logic, imo, is to give a tool to"modelize" non-classical logics in a classical setting. But this we don'tneed to know now.KRIPKE:Now, and this is the important line, with Kripke, some worlds can bereachable from others; and I will say that the modal proposition Bp, alsooften written []p or \Box p (in LATEX), is true at some world w if and onlyif p is true in each world which are successor of w.

`Is this the same B which is the modal logic operator for necesssity = true`

`in all possible worlds?`

I say it again:KRIPKE IMPORTANT LINE: Bp is true in w if for all world x such that wRxwe have that p is true in x.You can read wRx as the world w reaches the world x, or x is accessiblefrom w.For example, with a drawing, where the (broken) line represents theoriented accessibility relations (please add an arrow so you see that it isthe worlds on the top which are accessible from the world at the bottom:p p \ / \ / \/ BpLet us consider that "multiverse" M with only three worlds: w, w0, w1, andwith "successor" or "accessibility relation" R given by wRw0, and wRw1.Meaning obviously that w0 and w1 are accessible from w, and that's all.Now what I was trying to say to Lee was just that if p is true in w0, andif q is true in w1, then, B(p v q) is true in w0.p q \ / \ / \/ B(p v q)And if the world represents subjective observer moment a-la Bostrom, and ifthe accessibility relation represents scanning-annihilation followed byreconstitutions, the diagram with w, w0, w1 + wRw0 and wRw1 fits well thesituation.OBJECTION?Ah! but Lee could have build an objection by saying that in Stathis' theorywe die, or can die, at each "instant", or at each teleportation experiment.He told us this in its death thread.

I don't think Lee accepts my idea of death.

Stathis was doing Kripke semantics, perhaps like Jourdain was doing prose.He suggests to define a state (world, OM, ..) as being "alive" when it is"transient":The state/world/OM... x is "alive" when there is a y such that xRyand a state is "dead" when there is no such accessible world from x. x isterminal, or cul-de-sac, dead-end, etc.Now in Stathis' theory, we die at each instant and this means that alltransient states reach dead-end worlds!

What do you mean by "transient state"? Aren't all states transient?

Now suppose x is alive. This means there is y such that xRy. But theproposition true, t, is true in all world, and thus it is true in y. Thismeans Bf is false in x (by KRIPKE IMPORTANT LINE). It is just false that fis true in all accessible world from x, giving that in y t is true (andxRy). So in any world x which is alive, Bf is false. This means that ~Bfis true (worlds obeys classical logic). and giving that f equivalent with~t, this means that ~B~t is true in the alive state.What about ~B~t, or ~Bf, in a dead-end state? What about Bf in a dead-end state?

`If you specifically define B as above, you could say Bf is false because`

`there are no reachable worlds for it to be true in. However, the same could`

`be said for Bt, which doesn't seem right, since t is by definition true in`

`any possible world. Could I go for a third option, "undefined"?`

This is a little bit tricky and I let you think (I must go now). It isimportant also for getting a "theory" (set of propositions through in allworlds in some multiverse, where a multiverse is just a set of worlds (OMs)with some specified accessibility relation among worlds (OMs).The main exercise now consists in finding all formulas true in all worlds,whatever is the valuations of p, q, r in the worlds, when the worldsbelongs to Papaioannou multiverse, and I recall that a Papaioannoumultiverse is characterized by the fact that all transient (alive) statereaches dead-end.For this the first problem is the truth/false status of Bf in a cul-de-sacworld.Stathis, dont' hesitate to accuse me of betraying your idea if that is thecase,

`I think you got it basically right. I was not aware of Kripke's work, but`

`have encountered similar ideas in reading philosophers of personal identity.`

Sorry for those holiday exercises,Don't hesitate to ask questions, it is cumbersome to explain Kripkesemantics without easy drawing abilities (I already regret the combinators;-)I will come back on this asap (or just a little bit later), Bruno

--Stathis Papaioannou _________________________________________________________________

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