Yes, but only because we can find out more about this world's objects by virtue of our causal relatedness to them.
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.
If so, wouldn't that involve an isomorphism whose information content is potentially the same size as the state space itself?
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).
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."
Yes, I noted earlier that my perspective "depends on the thesis that physicalism is right and that qualia and consciousness are epiphenomena".
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.
- RE: possible solution to modal realism's problem of induction Brian Holtz