AP: The question of whether two chunks of matter are the same surely has little to do with specifications.
BH: 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: For souls and spirits, yes. Possible entities, however, are arguably not entities, because an entity, by definition, exists.
A logically possible entity, by definition, exists in at least one possible world. I suspect by "exists" above you mean something like "actually exists" or "exists in this world", and that the souls and spirits you have in mind are the ones that you think actually exist in this world. I'm talking more broadly about possible souls in their possible worlds. How do you decide whether two logically possible souls are the same if neither exists in this world? Presumably you do it by comparing what we (hypothetically) know about them -- i.e. their specifications or descriptions.
BH: If two specifications contradict each other, they surely specify different worlds, right?
AP: Well, on the account you have, a specification is a bitstring.
I haven't personally committed to a particular specification scheme, and I hesitate to do so before you do. :-) I suspect that any complaint you have about the best available specification approach is a problem that is shared by whatever technique you yourself use to distinguish e.g. similar possible souls. (You might claim that you don't need one because souls and chunks of matter etc. are such familiar things that we "surely" needn't resort to specifications to decide their identity. If so, I would again protest this invocation of our intuitions about our world to seemingly wave away questions about myriad other worlds.)
AP: Intuitively, an encoding method is a map between bitstrings and worlds. But that would be circular here.
Let me try to come up with an example encoding method that could break whatever circularity you're worried about. What I need is a collection of possible world that are both 1) simple enough that they can be mechanically mapped to bitstrings, and 2) not so simple that they can be canonically enumerated or have two specifications easily inspected to see if they specify what we would consider the same universe. How about reversible cellular automata with infinitely many past and future non-trivial states? A world could be encoded into a bitstring by encoding its transition rules and then encoding any one of its states. Since there is no distinguished state in such a world's infinite series of states, it's not necessarily tractable to test two worlds for the obvious form of identity involving shared transition rules and a shared state somewhere in their histories.
You asked earlier "What IS a world?" The problem with this question is that it can be too restrictive to try to define what worlds are by enumerating what they can be made of -- "chunks of matter", souls, substances, etc. A more general approach is to come from the other direction, and say that a world is any causal closure that doesn't involve a logical contradiction. When you approach worlds this way, it's more natural to think of descriptions and specifications as primary, rather than to think of the traditional ontological building blocks -- substances, "chunks of matter", etc. -- as primary.
The other problem with this question is that it can be misleading to think that the inhabitants of a world have a privileged or authoritative perspective about what counts as the ontological primitives of that (or any) world. We might think that Spirit or substances or quantum fields or 11-D strings are the fundamental building blocks of our world, but if our world turns out to be a simulation, then it's easy to see how an information-theoretic perspective could suddenly be recognized to be a better one. The way I think of it is that each possible world is just a possible simulation, and each has the same content -- i.e. inhabiting a world feels the same -- whether or not the simulation is ever "run" on some "actual" simulator. (For any claim that an actual simulator is in operation, then the simulator's world can itself be considered a merely-possible simulation. I'm assuming for the moment that "turtles all the way down" is not a sensible claim.)
Now let me get back to the problem of induction. My untutored 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'm guessing I would have this intuition even if weren't attracted to an information-theoretic approach to defining or specifying worlds. Are these issues independent, or is this predominance calculus sensitive to how one approaches the multiverse?
[Brian Holtz] 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.[scerir] Is that true? Isn't Reichenbach's common cause a possibility? Something like: future light cones of a and b do overlap within the future light cone of c, and c can act on this overlap ...
Sorry, I wasn't very clear. I'm talking about causal closure in the broadest metaphysical sense, in which causal relatedness is transitive and can relate events that in fact had no nomological ability to influence each other.