Le 27-juin-05, à 17:12, Brian Holtz a écrit :

I reply to Prof. Pruss:

BH: I have the vague suspicion here that by using words like physical/matter/concrete/chunk, you're skirting the issue of how worlds are specified in the general case, by narrowing the scope to worlds whose only constituents are material -- literally, having mass and occupying space. What about worlds consisting of a single point of space, populated by (soul-like?) entities whose (of course non-spatial) internal specifications and external relationships change over time? I fear you're taking a short-cut that relies on our intuition that ordinary baryonic matter has a privileged and obvious and natural way to be specified.

AP: The question of whether two chunks of matter are the same surely has little to do with specifications.You just did it again. Would you still say "surely" if in your statement you replace "chunks of matter" with "souls" or "spirits" or "logically possible entities"?

AP: just as a world should be able to contain s-t-disconnected regions, there is nothing impossible about it containing causally disconnected regions, unless God necessarily exists (which Lewis doesn't think, but I do).If two spacetime-disconnected regions are causally disconnected (such that none of the events in each has any possibility of influence on any events in the other), then it seems pure artifice to say the regions are in the same world. You could as easily say that all possible events in all possible worlds are in fact in the same world.

AP: But what, then, ARE the worlds? Are they IDENTICAL with their specifications? Or are they concrete entities? If they are identical with their specifications, then I do not see how to meaningfully formulate Lewis's extreme modal realism: We would have to say something like that the specifications are all true or something like that, and we can't do that without contradiction since the specifications contradict one another.I'm not sure how Lewis's extreme modal realism is inconsistent with a world being identical with the class of specifications that do an equally good job of specifying it. If two specifications contradict each other, they surely specify different worlds, right?

What are the worlds? I would say they are of the same ontological category as numbers.

I am not sure we can already say that. I have never understand the meaning of "worlds" in Lewis modal realism, especially when he insists that they are concrete like our own. I have no evidence for the existence of "concrete" world. All (enough rich) immaterial worlds with self-aware local substructure will make those substructures developing notion of concreteness and actuality. But this does not make worlds belonging necessarily to the same category as numbers, because worlds could emerges from "coherence conditions" on number's dream (computation seen from inside, to simplify).

With comp if you are "right" on this point it is just wrong to say we "know" the identification between worlds and numbers, and that will depends from point of views.

I disagree with AP on world/specification. And Lewis evolved on that matter as I said before. Worlds can be identify with their "free algebra or Herbrand Models", that is, by maximal consistent sets of "specification" (= closed formula, atomic formula). Moreover, it can be shown that from an (immaterial) turing machine point of view, the machine is unable to distinguish a "world" from an "ersatz world like the set of sentences true in a possible world or in a (stantard or not) model of a theory.

If our universe can be fully specified by a (possibly infinite) bit string, then there is a sense in which it is irrelevant whether or not ours is a "concrete" world that "really" exists. Here's something I wrote a few years ago that gives a flavor of what I mean:

I agree with you. "Concreteness" could be (at least) an indexical.

Consider gliders in Conway's game of Life. Even if nobody ever wrote down the rules of Life, gliders would still be a logical consequent of certain possible configurations of the logically possible game of Life. It has been proven that Life is rich enough to instantiate a Turing machine, which are of course known to be able to compute anything computable. So if mind is computable, consider a configuration of Life that instantiates a Turing machine that instantiates some mind.

Consider the particular Life configuration in which that mind eventually comes to ask itself "why is there something instead of nothing?". Even if in our universe no such Life configuration is ever instantiated, that particular configuration would still be logically possible, and the asking of the Big Why would still be a virtual event in the logically possible universe of that Life configuration. The epiphenomenal quality of that event for that logically possible mind would surely be the same, regardless of whether our universe ever actually ran that Life configuration. So the answer to that mind's Big Why would be: because your existence is logically possible.

So pop up a level, and consider that you are that mind, and that your universe too is just a (highly complex) logically possible state machine. In that case, the answer to your Big Why would be the same.

Note that, while the Life thought experiment depends on mind being computable, the logically possible universe (LPU) thought experiment only assumes that our universe could be considered as a logically possible sequence of (not necessarily finitely describable) universe-states. The LPU hypothesis also depends on the thesis that physicalism is right and that qualia and consciousness are epiphenomena.So if EVERY universe "really is" something like the possible universe described above, then what you talk of as "concreta" isn't fundamentally very concrete after all, and talk of concreteness and tangibility and materiality isn't very helpful in deciding whether two similar universes are identical. Instead, identity becomes more a question of whether there is a certain sort of equivalence between the specifications of the two universes. There may be lots of ways to specify the number seven, but that doesn't mean there are multiple copies of it.

AP: Is a world which consists of a particle of type A one meter apart from a particle of type B, neither of which ever moves, distinct from a world which consists of a particle of type B one meter apart from a particle of type A, neither of which ever moves?No.

AP: What I am getting at is that if one thinks in terms of descriptions, it would make more sense to identify worlds with equivalence classes of descriptions than with individual descriptions.Precisely! What I've meant all along by a "specification" of a universe has to do with a certain sort of equivalence class among possible descriptions, abstracting over differences like the font size in which the description is written. I don't know enough about Kolmogorov-complexity to know whether what I would consider the same universe can have multiple minimal K-specifications.

AP: Lewis is wrong to suppose the numbers are equal. To get that, he needs to assume that there is an upper bound on the cardinality of things in a world, but his reasons for supposing such an upper bound are wrong. He neglects the possibility that there may be multiple things, even infinitely many, at one point in s-t.I agree it would be wrong to assume that there can only be one thing at one point in spacetime.

I clearly need to learn more about infinite measures, but my intuition is still that apparently regular worlds should predominate over apparently irregular worlds, even if apparently irregular worlds predominate over worlds that in fact contain neither apparent nor non-apparent irregularities. I've yet to hear (or at least understand) anything that contradicts this intuition.

By assuming explicitly Church thesis, some amount of arithmetical realism, and the computationalist hypothesis, your question is amenable to a mathematical problem.

The part of that problem which I have been able to solve confirms your intuition on that last matter. Well QM also and more easily, but I don't use the "QM assumption" (for methodological reasons).

Bruno

Brian Holtzhttp://iridia.ulb.ac.be/~marchal/

blog: http://knowinghumans.net

book: http://humanknowledge.net