Title: Message
BH: 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.
AP: I take it that we agree that there are facts about the identity or non-identity of objects within this world that are independent of how we describe the objects. 
Yes, but only because we can find out more about this world's objects by virtue of our causal relatedness to them.
AP: Our difference is that you think that things are no longer so straightforwards if the objects are not worldmates.  I say that not being worldmates is no big deal, as long as we are dealing with a Lewisian framework where the different worlds all exist concretely. 
Where I think identity becomes less straightforward is not between entities that aren't worldmates with each other, but rather between entities that aren't worldmates with us. I don't see (or at least comprehend) here an answer to my question above.
I still don't know what work is being done by your use of "concretely" here. If you chase the meaning of the word "concrete" through any dictionary, all the paths you follow will end up at some notion of at least a potential causal relationship with some indexical base object. But if like me you define a world as a causal closure, then it's a category mistake to speak of a world as "existing" in this conventional sense of "concrete" existence, because by definition no other world can have a causal relationship with ours or anything in ours.
AP: Any two deterministic, reversible automata with state space of the same cardinality are isomorphic, no? 
If so, wouldn't that involve an isomorphism whose information content is potentially the same size as the state space itself?
AP: So, are they all one world, or is every different automaton a different world, even if isomorphic? 
I don't assume that there is a fact about whether two merely-isomorphic automata are the same world or not. (By "merely isomorphic" I mean they don't have the trivial isomorphism of having the same transition rules and a shared state somewhere in their state histories.) The point of my example was to try to make this assumption unavailable, so that the straightforward bitstring encoding of an automaton stands as a first-class instance of a world, and cannot be waved away as just one of the many ways that the "concrete" world in question can be described.
My answer to your question would be that every different automaton is a different world, except perhaps for the most trivial of isomorphisms. Note that for a given purpose, such as in considering the phenomenology experienced by the worlds' inhabitants, we might define equivalence classes across strictly different automata and consider them the same world. But such a perspective wouldn't necessarily be privileged, and wouldn't be the right way to think about how many worlds there are of the relevant kinds (which is the key to the problem of induction).

BH:  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.  

AP: It depends how the simulation runs.  If the simulation runs inside a computer that is itself a physical object, then a physicalistic ontology is perfectly fine--it's just that it doesn't apply to the "things" we think it applies to. 
Who can vouch that the simulator is physical and not itself in a simulated universe?  Surely not the inhabitants of the simulator's universe.  I repeat what I said after the above quote: "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."
AP: And of course if one thinks that consciousness cannot be a simulation, one will reject your example. 
Yes, I noted earlier that my perspective "depends on the thesis that physicalism is right and that qualia and consciousness are epiphenomena".

 BH: 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. 

AP: My intuitions come from analysis rather than information theory. :-)  Nice numbers (e.g., rationals, algebraics) are generally much fewer (meagerness, measure, cardinality) than non-nice numbers (irrationals, transcedentals).  Nice functions (e.g., continuous) are much fewer (e.g., cardinality, and in some contexts meagerness, and infinite-dimensional-zero-measure, if memory serves me) than non-nice functions.  Etc .

But all that is required to resolve the induction objection is that not-nice universes are usually not noticeable as such to their inhabitants. I guess I need to learn some more transfinite mathematics before I'll be able to understand how (whether?) you're responding to this point that irregularity doesn't undermine induction if the irregularity is unnoticed. Let me know if you can recommend any introductory texts in this area.

Brian Holtz
Yahoo! Inc.

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