I deny that they will come to identical conclusions about everything.

The claim is merely that they will produce identical subsequent brain states and identical nerve impulses.

Your argument against my view seems to presume that my view is false. I deny that they will come to identical conclusions about everything. When I reason, I come to conclusions about things in my environment. For example, I came to the conclusion that Obama was born in Hawaii, based on evidence about Obama that was available to me. The Boltzmann brain cannot even refer to Obama, so it cannot come to this conclusion.

Do you deny that the Boltzmann brain thinks it can refer to Obama? I.e. that it has some mental representation of an external world that is indistinguishable from your own except insofar as it does not successfully refer to anything in an external world?

If your answer is "Yes, I deny it." Then I don't think you understand what it means to have identical brain states or your view presumes metaphysically spooky features that you haven't unpacked. But what I understand your position to be is that you don't deny it but that you think that the Boltzmann brain's representation of the external world doesn't can't come to identical conclusions about the world because it's representation doesn't successfully refer to anything.

If you want to say that a belief must have a causal connection to the thing it is trying to refer to: fine. We can call what Boltzmann brains have "pseudo-beliefs". Now, how can you tell if you have beliefs or pseudo-beliefs? You can't. Claiming that the subjective situations of the human and the Boltzmann brain are evidentially distinguishable is totally bizarre when they themselves can't make the distinction.

The reason people are focusing on the viability of the skeptical scenario in their responses to you is that it looks like the reason you think this is a viable evidential distinction is that you are unreasonably confident that your mental states successfully refer to an external world. Moreover, a solution to the argument that doesn't reject the SSA or the cosmological model shouldn't just play with the meaning of words-- readers should react with a sense of "Oh, good. The external world exists after all." If they don't it's a good indication that you haven't really addressed the problem. This is true even though the argument starts by assuming that we are not Boltzmann brains since obviously the logical structure remains intact.

You should to stop assuming that everyone is misunderstanding you. Everyone is giving you the same criticism in different words and your argument is not being upvoted. Update on this information.

This gets difficult, because there's a whole set of related terms I suspect we aren't quite using the same way, so there's a lot of underbrush that needs to get cleared to make clear communication possible.

When I'm trying to be precise, I talk about experiences providing evidence which constrains expectations of future experiences. That said, in practice I do also treat clusters of experience that demonstrate persistent patterns of correlation as evidence of the state of external systems, though I mostly think of that sort of talk as kinda sloppy shorthand for an otherwise too-tedious-to-talk-about set of predicted experiences.

So I feel reasonably comfortable saying that an experience E1 can serve as evidence of an external system S1. Even if I don't actually believe that S1 exists, I'm still reasonably comfortable saying that E1 is evidence of S1. (E.g., being told that Santa Claus exists is evidence of the existence of Santa Claus, even if it turns out everyone is lying.)

If I have a whole cluster of experiences E1...En, all of which reinforce one another and reinforce my inference of S1, and I don't have any experiences which serve as evidence that S1 doesn't exist, I start to have compelling evidence of S1 and my confidence in S1 increases. All of this can occur even if it turns out that S1 doesn't actually exist. And, of course, some other system S2 can exist without my having any inkling of it. This is all fairly unproblematic.

So, moving on to the condition you're describing, where E1 causes me to infer the existence of S1, and S1 actually does exist, but S1 is not causally entangled with E1. I find it simpler to think about a similar condition where there exist two external systems, S1 and S2, such that S2 causes E1 and on the basis of E1 I infer the existence of S1, while remaining ignorant of S2. For example, I believe Alice is my birth mother, but in fact Alice (S1) and my birth mother (S2) are separate people. My birth mother sends me an anonymous email (E1) saying "I am your birth mother, and I have cancer." I infer that Alice has cancer. It turns out that Alice does have cancer, but that this had no causal relationship with the email being sent.

I am comfortable in such an arrangement saying that E1 is evidence that S1 has cancer, even though E1 is not causally entangled with S1's cancer.

Further, when discussing such an arrangement, I can say that the brain-states caused by E1 are about S1 or about S2 or about both or neither, and it's not at all clear to me what if anything depends on which of those lexical choices I make. Mostly, I think asking what E1 is really "about" is a wrong question; if it is really about anything it's about the entire conjoined state of the universe, including both S1 and S2 and everything else, but really who cares?

And if instead there is no S2, and E1 just spontaneously comes into existence, the situation is basically the same as the above, it's just harder for me to come up with plausible examples.

Again, you're using the word "evidence" differently from everyone else. This only serves to confuse the discussion.

Tabooing "evidence", what I was saying is that a BB would have the same initial brain-state (what I termed "evidence") and therefore would achieve the same final brain-state (what I termed "conclusions"). The laws of physics for its brain-state evolution, and the physical causality between the two states, are the same as for your brain. This is trivially so by the very definition of a BB that is sufficiently similar to your brain.

I don't know what you mean by "externalist evidence" and I don't see how it would matter. The considerations that apply here are exactly the same as in Eliezer's discussion of p-zombies. Imagine a BB which is a slightly larger fluctuation than a mere brain; it is a fluctuation of a whole body, which can live for a few seconds, and can speak and think in that time. It would think and say "I am conscious" for the same reasons as you do; therefore it is not a p-zombie. It would think and say "Barack Obama exists" for the same reasons as you do; therefore what everyone-but-you calls its knowledge and its beliefs about "Barack Obama", are of the same kind as yours.