Le 17-juil.-05, à 11:07, Stathis Papaioannou wrote :

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Bruno, There's a lot to digest in this post.

Take your time. No problem.

I should clarify that in my original post I had in mind two differentusages of the word "death". One is what happens to you in destructiveteleportation: you vanish at one set of spacetime coordinates, thenreappear in almost exactly the same material configuration at adifferent set of spacetime coordinates.

OK.

Ordinary moment to moment life is a special case of this process wherethe difference between the "before" and "after" coordinates isinfinitesimal, and therefore there is no subjective discontinuitybetween one moment and the next.

`The first person point of view cannot be aware of "the time" between`

`annihilation and reconstitution. (Step 4 of the UD Argument (UDA)).`

I would call what happens when you vanish "provisional death".Provisional death becomes "real death" if (contra QTI) there is nosuccessor OM (or no next moment, or no reachable world): if theteleporter breaks down and loses the information obtained in adestructive scan before it can be sent, or if you are killed in anaccident in ordinary life. It is interesting to note that memory lossis effectively the same as real death, or real death with a backupthat is not up to date (eg. the original is killed a few minutes afterundergoing non-destructive teleportation) if the memory loss isincomplete. Real death and memory loss cause a cul-de-sac in a streamof consciousness, whereas provisional death does not.

`OK. Now we can never be sure that there will be a next observer moment,`

`and this makes the provisional death a possible absolute death. I`

`thought this was your justification that we die at each`

`instant/observer-moment. Each accessibility arrow bifurcates, and there`

`is always one leading to a dead-end, so that we (can) die at each`

`instant/observer-moment.`

If you can convince yourself that you undergo provisional death allthe time, and real death when you experience memory loss, then it maybe possible to convince yourself that death is no big deal. However,our evolved minds would fight very hard against such a conclusion.

It is counterintuitive indeed.

In this post I will try to make clearer my argument with Lee by usinga minimal 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 willgive C again, but through some of its most notable extensions whichare G and G*.To prevent falling in the 1004-fallacy, I will use (at leasttemporarily) the words "state", "world", "situation","observer-moment", "OM", etc. as synonymous. I will use "world" (ifyou don't mind), and I will designate individual 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). Moregenerally we suppose a relation of accessibility among worlds (that'sKripke's idea how to enrich Leibniz).These words - successor, accessibility, reachability - are figures ofspeech, right? What is important is the relationship between theworlds, not that someone or something "reaches" physically from oneworld to the next.

`I am not sure I understand what you mean by "figure of speech". All`

`theories build their concept from "figure of speech" (being the`

`punctual mass in Newton or the strings in String theory, or perhaps`

`just the real numbers, etc.).`

I will be interested in the discourse which are true at each world,and I will assume that classical logic holds at each world.p, q, r, ... denotes propositions. And a "semantics" is given when itis said 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 will show you that the material implication "->"(as Bertrand Russell called it) is arguably the "IF ... THEN ..." ofthe mathematician working in Platonia.That last one always got me: a false proposition can imply anyproposition. All the rest seem like a formalisation of what mostpeople intuitively understand by the term "logic", but not that one.Why the difference?

This is important. It was the object of the thread "just a question".

`Suppose that you are in a room with only men inside. The statement "all`

`women in the room are 42 km high" will be trivially correct. It really`

`means that if x is a woman in the room she is 42 km high. it is true`

`because the premiss "x is a woman in the room" is false. Nobody can`

`build a contradiction from it.`

`Of course, in the same condition you can say "all woman in the room are`

`not 42 km high". It is again true. From this you can conclude that "all`

`women in the room are both 42 km high and not 42 km high", from this`

`you can conclude that "if x is a woman in the room then false":`

(x is a woman in the room) -> f

`but (p -> f) is the same as (~p) as you can verify with a two-line`

`truth table, so you can conclude ~(x is a woman in the room), from`

`which you can conclude that there is no woman in the room (which we`

`knew of course).`

`The idea that false implies anything explain why in math an error in a`

`paper jeopardize in principle the whole paper.`

`The idea is natural in some common expression, which I know better in`

`french than in english. People says things like this "if you are good`

`at joke then I am Napoleon", meaning "you are not good at joke". Or if`

`"if bin Laden is a gentleman then you can put Paris is mach box".`

`In any case you can just remember that "p->q" is the same by definition`

`as ((~p) v q).`

`For example: "if 0 is bigger than 2 then 0 is bigger than 1", is the`

`same as`

`(~(0 is bigger than 1) or (0 is bigger than 1)) which gives (t v f)`

`which gives t.`

OK?

(p <-> q) is true if (p->q) is true and (q->p) is true. I could havesaid (p <-> q) is true if p and q have the same truth value. Thetruth value are true 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 propositionsymbols and stipulate thatf is always false t is always trueThat classical logic holds in the worlds means the "usual things",for example 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 givereference or you 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 willmet this logic. We live the modern time where even the classical(Platonic) logician must aknowledge the importance of the many manymany many possible logics.For example in Quantum Logic and in the Relevant Logics, theclassical tautology 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 wedon't need 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,also often written []p or \Box p (in LATEX), is true at some world wif and only if 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?

`Yes and no. B, out of context represents any box. In Aristotle/Leibniz`

`this has indeed the meaning of "true in all possible worlds". With`

`Kripke it means "true in all accessible possible world", and it is`

`supposed that worlds can be linked by some accessibility relation.`

`Kripke relativizes the notion of "necessity" and "possibility" to each`

`world.`

`I think that the passage from Leibniz to Kripke is a good modal mirror`

`of the passage from the ASSA to the RSSA.`

I say it again:KRIPKE IMPORTANT LINE: Bp is true in w if for all world x such thatwRx we have that p is true in x.You can read wRx as the world w reaches the world x, or x isaccessible from w.For example, with a drawing, where the (broken) line represents theoriented accessibility relations (please add an arrow so you see thatit is the worlds on the top which are accessible from the world atthe bottom:p p \ / \ / \/ BpLet us consider that "multiverse" M with only three worlds: w, w0,w1, and with "successor" or "accessibility relation" R given bywRw0, and wRw1. Meaning obviously that w0 and w1 are accessible fromw, and that's all.Now what I was trying to say to Lee was just that if p is true in w0,and if 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 if the accessibility relation represents scanning-annihilationfollowed by reconstitutions, the diagram with w, w0, w1 + wRw0 andwRw1 fits well the situation.OBJECTION?Ah! but Lee could have build an objection by saying that in Stathis'theory we die, or can die, at each "instant", or at eachteleportation experiment. He told us this in its death thread.I don't think Lee accepts my idea of death.

`I have seen that. But Science is supposed to avoid wishful thinking.`

`The question is "does Lee proposes some alternative? Lee sees clearly`

`the difference between first and third point of view, but it seems he`

`want to identify himself with some fuzzy notion of recent duplicates,`

`and this apparently forces him to abstract from the 1-3 person pov`

`difference.`

Stathis was doing Kripke semantics, perhaps like Jourdain was doingprose. 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 is terminal, or cul-de-sac, dead-end, etc.Now in Stathis' theory, we die at each instant and this means thatall transient states reach dead-end worlds!What do you mean by "transient state"? Aren't all states transient?

`Certainly not the dead-end states. I took the world "transient" from`

`some of your post.`

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.This means Bf is false in x (by KRIPKE IMPORTANT LINE). It is justfalse that f is true in all accessible world from x, giving that in yt is true (and xRy). So in any world x which is alive, Bf is false.This means that ~Bf is true (worlds obeys classical logic). andgiving that f equivalent with ~t, this means that ~B~t is true in thealive 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 falsebecause 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 bydefinition true in any possible world. Could I go for a third option,"undefined"?

`Nothing is left undefined in (arithmetical) Platonia, except from the`

`point of view of the creatures living *in* that Platonia. The option`

`"undefined" is premature at this stage. Bf and Bt are just "trivially"`

`true in the dead-end worlds. It is just elementary classical logic. I`

`mean it is not a crazy idea by me, it is a fact admitted and used by`

`all mathematicians, even before Boole (Boole did just make this`

`explicit).`

`It would help me to proceed if you tell me, you Stathis or any reader`

`of the list, if you have understand (or not) that the fact that [Bf,`

`Bt, actually any B<something> hold in the dead-end world] is as`

`"obvious" as the fact that [for ALL numbers x, if x is bigger than 2`

`then x is bigger than 1.]`

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