Indistinguishable?
Re dense worlds, Dave Chalmers asks in what sense worlds that differ only in which intrinsic properties play which roles are indistinguishable. That's a very good question, and I'm afraid I don't have a good answer. He notes that those worlds differ in lots of respects, including their laws and quite probably the perceptions of their inhabitants.
What I want to say is that the worlds are somehow 'structurally alike', or 'isomorphic'. But that's hard to cash out. Is every Ramsey sentence that is true of one of them also true of the others? Then I would first have to restrict the 'old' terms of the Ramsey sentence. But that's a minor problem. What's worse is that this doesn't take care of more complicated rearrangements, where different parts of roles are played by different properties. Here the quantifiers of the Ramsey sentence would have to range over very gerrymandered (though intrinsic) properties. And given that gerrymandered properties are generally supposed to be causally inefficacious this is dubious. And finally, even if the Ramsey sentence account would work, I would still have to say why worlds that cannot be distinguished by Ramsey-sentences (or are otherwise 'structurally alike') are in any reasonable sense indistinguishable.
This leaves me with the intuitive idea that a world is indistinguishable from ours if it belongs to a class of worlds such that no possible experience and investigations could tell us which of them is ours. But that's very rough.
I could also try to avoid any appeal to indistinguishability. Thus: By the intrinsic nature of fundamental properties and the principle of recombination, there are lots of worlds, with completely different distributions of fundamental properties, in none of which Al Gore won the presidency. In fact, for virtually any redistribution of our fundamental properties, there is a world with that distribution in which Al Gore did not win the presidency. But there is also a world where Al Gore won the presidency which has exactly the same distribution of fundamental properties as one of the worlds just mentioned.