Re: Stathis, Lee and the NEAR DEATH LOGIC
Le 17-juil.-05, à 11:07, Stathis Papaioannou wrote : 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 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. OK. 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. 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 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. 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 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. It is counterintuitive indeed. In this post I will try to make clearer my argument with Lee by using a 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 and Death, or Near Death Logic, or just C. I have never abandon C, but the interview of the Lobian machine will give C again, 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. as synonymous. I will use world (if you 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). More generally we suppose a relation of accessibility among worlds (that's Kripke's idea how to 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 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 it is 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 with causality: 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 ... 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? 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
RE: Stathis, Lee and the NEAR DEATH LOGIC
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 a 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 and Death, or Near Death Logic, or just C. I have never abandon C, but the interview of the Lobian machine will give C again, 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. as synonymous. I will use world (if you 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). More generally we suppose a relation of accessibility among worlds (that's Kripke's idea how to 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 I will assume that classical logic holds at each world. p, q, r, ... denotes propositions. And a semantics is given when it is 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 with causality: 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 ... 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 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 fixed contradiction like (p (~p)), or add t and f in the proposition symbols and stipulate that f is always false t is always true That 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 a proposition is a tautology or not. But I can explain or give reference or you could google. Remark. Note
Re: Stathis, Lee and the NEAR DEATH LOGIC
I clarify and progress a little bit. Then I jump a little bit.
(Sorry for quoting myself)
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 each teleportation
experiment. He told us this in its death thread.
The objection is that the idea that Bp true in world w represents
Probability(p) = 1 in world w, although quite obvious in ideal
multiverses (multiiverse where all worlds or observer-moments are
transient), is not obvious at all in Stathis multiverse where we die
or can die at each observer-moment (that is, all transient world leads
to (at least) a cul-de-sac world).
This led us to the following problem Bf is true or false in a
dead-end. I will come back to it below.
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 xRy
Note that x could be equal to y, in which case the world x reaches
itself. Such a world/state/OM is of course transient, or alive.
and 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 that all
transient states reach dead-end worlds!
Let me give you examples of a Stathis's multiverse (near death
multiverses)
1) {w1, w2} with the accessibility relation w1Rw1, w1Rw2 (and nothing
else).
There is only one alive state (w1), and one dead state (w2). It follows
stathis rule that all alive states reach a dead-end. I suggest people
(interested) do the drawing. Drawing does not survive the archive
without coming up a little surreal!
2) {w, w1, w2, w3, w4, w5, w6, ...} with accessibility relation:
w1 R w2, w2 R w3, w3 R w4, etc., together with for all i wi R w.
Note that w is here a cul-de-sac world reached by all transient worlds
wi
exercise: Draw 5 examples of finite near death multiverse, and 5
examples of infinite one (drawing ... is permitted).
Now suppose x is alive. This means there is y such that xRy. But the
proposition 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 just
false that f is true in all accessible world from x, giving that in y
t 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). and
giving that f equivalent with ~t, this means that ~B~t is true in the
alive state.
Is that OK for everybody? (among those interested)
What about ~B~t, or ~Bf, in a dead-end state?
What about Bf in a dead-end state?
Is that question clear? Nobody wants to propose an answer? ( the
answer is below).
This is a little bit tricky and I let you think (I must go now). It is
important also for getting a theory (set of propositions through in
all worlds in some multiverse, where a multiverse is just a set of
worlds (OMs) with some specified accessibility relation among worlds
(OMs).
Ouh la la!!! Please read true instead of through !
The idea that a theory (set of propositions) should be true in all
worlds is natural among physicists. SWE is supposed to be true
everywhere in the quantum multiverse. If a law changes it is
arguably not a law. Many expected that my way to isolate physics would
lead to classical propositional calculus. The only laws would be the
(classical) laws of logic! Well, my answer was that if that was the
case (with comp) that would mean that physics is empty (no physical law
at all). Only history and geography. A little like Smullyan describes
the difference between math and physics in FU (Forever Undecided) page
47, when he says:
Given any possible world, the set of all propositions that are true
for that world, together with the set of all propositions which are
false for that world, constitute the state of affairs holding for that
world. A tautology, then is true, not only for this world, but for all
possible worlds. The physical sciences are interested in the state of
affairs that holds for the actual world, whereas pure mathematics and
logic study all possible states of affairs.
Comp makes this statements false, even staying in classical logic (in
Platonia). That's not obvious. Would Smullyan's statement be a
consequence of comp, then, as I said, physics would be a branch of
geography, and all physical laws would be contingent.
Bf ?
Let us come back to the question of the truth or the falsity of Bf in a
dead-end observer moment w. (f = false, and a dead-end world/state/OM
is an OM without reachable world, or without successor as Stathis
said). Here w stands for an arbitrary cul-de-sac state.
Bf true in w would mean that for all y such that wRy, f is true in y.
This means that for all y : if wRy then f is true in y.
But w is a cul-de-sac so wRy
