Le 01-déc.-05, à 07:17, Stathis Papaioannou a écrit :

Why does an OM need to contain so much information to link it to other OMs making up a person? [the complete message is below].


I am not sure I understand. Are you saying, like Saibal Mitra, that OMs (Observer-Moments) are not related? How, in this case, would you interpret your own talk about "next observer moment" (those which could be dead end)? Is there not a confusion between the idea of physicalist (causal) view of the relation between OMs (which, as Brent meeker said should be explained from a more primitive (mathematical, immaterial, not causal, ...) notion of OM, with those very (more primitive) OMs. Are you assuming some notion of multiverse richer than (or just different from) a notion of multi-OMs?

At least, when you "interview" a sound lobian machine on such questions (through the modal logic G), or better when you interview its "guardian angel" (through its modal logic G*), you can understand that the "ultimate" multiverse can reasonably be said not having structure, and that multiverse-structures *appear* for each notion of self-referential points of view (not necessarily first person pov). The first person pov makes the "multiverse" a temporal structure, the first person plural pov makes the multiverse a quantum probability structure.

***

Mmmmmhhhhhh.... I know this could look like jargon. Let me give "easy" exercises for anybody following this list.

Let me define a Multiverse (called also "frame" by Kripke) as any non-empty set W together with an accessibility relation R defined on the set. Elements of that set are called "world", by definition, and I follow the convention to denote worlds by greek letters (or their english transcription: alpha, beta, gamma, delta, eta, epsilon, iota, kappa, omega, nu, theta, etc.). R is called the accessibility relation. So the simplest example of multiverse is given by the set {alpha} + the empty relation (so just one dead end!). Another example is the set of natural numbers with the divisibility relation ( n R m iff n divide m iff there is a k such that n * k = m).


Let me define a notion of illuminated multiverse (called "model" by the modal logicians). It is just a Kripke multiverse where we associate to each world a value 1 or 0 to each sentence letter. The Kripke multiverse is "illuminated" when a truth value (1 or 0) is assigned to each proposition, in each world. Remember that in (propositional) logic we have sentence letter p, q, r, etc. We also say that p is true in alpha for p has value 1 in alpha (in some illuminated multiverse).


Now Kripke semantics can be given in a very simple way, by just asking that,

1) each world obeys to classical logic (that is: if 1 is assigned to p in the world alpha, and if 1 is assigned to q in alpha, then 1 is assigned to (p & q) in alpha, etc. The "etc" is just a pointer to the usual truth table of classical propositional logic. I have already explain this on this list but I can do it again if asked). In particular each classical tautologies are true in all worlds, whatver the illumination chosen (whatever the truth value of the sentence letter are in each world: like (p -> p) or (p v ~p), etc.

2) Kripke says that Bp (also written box p, []p, etc.) is true in the world alpha if p is true in all worlds beta accessible from alpha. From this it follows that Dp (defined as an abbreviation of ~B~p) will be true in some world alpha if there is some world beta, accessible from alpha, and with p true in the world beta.

Now I will say that a formula A of modal logic is valid in a illuminated multiverse (W, R, V) if A is true in all the worlds of that illuminated multiverse.

And I will say that a formula A of modal logic is respected by a multiverse (W,R) if A is valid in all illuminated multiverse (W, R, V). Or equivalently: A is respected in (W,R) if A is true in all worlds in W and this for all "illuminations" V, i.e. for all assignment of truth value of the sentence letters in all worlds.

Last definition: a multiverse (W,R) is said to be reflexive if the relation R is reflexive (that is: if for all world in W we have xRx, i.e. if each world is accessible to itself by the relation R.

The easy exercise is the following: show that if the multiverse is reflexive then the multiverse respects the formula Bp -> p.

Slightly less easy: show that the reverse is true: show that if a multiverse respects Bp -> p, then the multiverse is reflexive.

I would like to know if that exercise *seems* difficult. For those who cannot do it, it just means there is a need to refresh some "naive set theory" knowledge, and I will think about a book who can help.

Don't hesitate to answer out of line if you prefer.

Sorry to annoy you with that modal stuff, but we are at a point I could no more comment the posts without making nuances which will resemble jargon if you don't invest a little bit in modal logic. This, by the way, could provide us with a language capable of make clearer many other "everything-like philosophy clearer.


Bruno


The complete original message by Stathis Papaioannou:

Why does an OM need to contain so much information to link it to other OMs making up a person? I certainly don't spend every waking moment reminding myself of who I am, let alone going over my entire past history, and I still think all my thoughts are my thoughts. I don't think that the fact these thoughts are contained in my head makes the difference, because as you seemed to agree, continuity of consciousness can in theory extend over discontinuities in time and/or space, as in teleportation. On the other hand, I could suddenly become psychotic and as a result believe I am a completely different person, with a different past; or perhaps my mind could be taken over by an alien intelligence with a similar effect. As for one OM potentially representing a thought from thousands of different people, that is exactly what happens in the multiverse and is one of the key advantages of the concept. Suppose you and I happened to have *exactly* the same subjective experience at a particular time, say seeing a red shape on a white wall at the age of two. This would mean that, for that moment, your mind and my mind could have been interchanged, or one of our two minds could have been temporarily suspended, without making any subjective difference to either of us. An external observer monitoring my body might have noticed a momentary blankness if my mental processes were suspended at the moment of coincidence, but as far as I was concerned, it would have been exactly the same as if I were teleported away to have the red shape experience (which I would have had anyway) and teleported back.

Stathis Papaioannou

Stathis Papaioannou wrote:
Brent Meeker writes:

I agree with all you have written below as an explication of what we mean by a person in the multiverse. But it assumes an objective spacetime in order to define persons by causal continuity. I thought the point of OMs was to provide
a fundamental ontology from which spacetime would be constructed.


While it always seems in real life, as in my example, that there is a causal connection between related OMs, this need not necessarily be the case. For a2 to think, "I stepped into the teleporter a moment ago" and to consider himself the person a1a2, it is sufficient simply that a2 exist. That is, given that a2 exists, it makes no difference whether there is information transfer from a1 to a2, whether a1 precedes a2, or whether a1 exists at all. In general, if the only thing that exists is the set of all possible OMs, not ordered in any particular way and each OM completely independent and isolated, then the apparent multiverse with its complex physical laws results as an emergent phenomenon, or if you prefer, an illusion.

That's taking an OM to be like Barbour's time capsule. They are ordered according to their contents. a1a2's OM with the thought that he was in a teleporter and was a1, connects to a1's OM with the thought that now I am stepping into a teleporter. But that brings me back to my objection to OMs. Barbour's time capsules contain whole states of the world. OMs don't have enough information to provide the specificity required for connections. a1a2's OM thought could be the thought of thousands of other people. To be sure, if we take a sequence of a1a2's thoughts and lump them into one OM then that OM will have enough information to place in a unique sequence indentifying a person.
But then we've really assumed the thing to be explained.

Brent Meeker






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


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