Boltzmann Brains and Anthropic Reference Classes (Updated)

Do you really think the assumption that the external world (as we conceive it) is real can't be used in reasoning and decision making performed by us? It is used all the time, to great effect.

Do you think Bostrom is wrong to use anthropic reasoning as a basis for disconfirming Boltzmann's model? After all, the assumption there is that Boltzmann's model goes wrong in predicting that we are Boltzmann brains. We know that we're not, so this is a bad prediction. This piece of reasoning seems to be something you deny we can actually do.

One way to see the difference between my representational states and the Boltzmann brains' is to think counterfactually. If Barack Obama had lost the election in 2008, my current brain state would have been different in (at least partially) predictable ways. I would no longer have the belief that he was President, for instance. The Boltzmann brain's brain states don't possess this counterfactual dependency. Doesn't this suggest an epistemic difference between me and the Boltzmann brain?

That's just how you're defining belief. If the brain can't tell, it's not evidence, and therefore irrelevant.

I don't think this is a mere definitional matter. If I have evidence, it must correspond to some contentful representation I possess. Evidence is about stuff out there in the world, it has content. And it's not just definitional to say that representations don't acquire content magically. The contentfulness of a representation must be attributable to some physical process linking the content of the representation to the physical medium of the representation. If a piece of paper spontaneously congealed out of a high entropy soup bearing the inscription "BARACK OBAMA", would you say it was referring to the President? What if the same inscription were typed by a reporter who had just interviewed the President?

Recognizing that representation depends on physical relationships between the object (or state of affairs) represented and the system doing the representing seems to me to be crucial to fully embracing naturalism. It's not just a semantic issue (well, actually, it is just a semantic issue, in that its an issue about semantics, but you get what I mean).

And I don't know what you mean when you say "If the brain can't tell...". Not only does the Boltzmann brain lack the information that Barack Obama is President, it cannot even form the judgment that it possesses this information, since that would presuppose that it can represent the content of the belief. So in this case, I guess my brain can tell that I have the relevant evidence, and the Boltzmann brain cannot, even though they are in the same state. Or did you mean something about identical phenomenal experience by "the brain can't tell..."? That just begs the question.

A Boltzmann brain that uses your logic would exclude itself from its reference class, and therefore conclude that it cannot be itself. It would be infinitely wrong. This would indicate that the logic is faulty.

The Boltzmann brain would not be using my logic. In my post, I refer to a number of things to which a Boltzmann brain could not refer, such as Boltzmann. I doubt that one could even call the brain states of a Boltzmann brain genuinely representational, so the claim that it is engaged in reasoning is itself questionable. I am reminded here of arguments against pancomputationalism. A Boltzmann brain isn't reasoning about cosmology for the same sort of reason that a rock isn't playing tic-tac-toe. The existence of an isomorphism between it and some system that is reasoning about cosmology (or playing tic-tac-toe) is insufficient.

I once ran across OP's argument as an illustration of the Twin Earth example applied to the simulation/brain-in-a-vat argument: "you can't be a brain in a vat because your beliefs refer to something outside yourself!" My reaction was, how do you know what beliefs-outside-your-head feel like as compared to the fake vat alternative? If there is no subjective difference, then it does no epistemological work.

How could it know its beliefs look like they are about Obama? How does it even know who Obama is?

Let's say you have a computer set up to measure the temperature in a particular room to a high precision. It does this using input from sensors placed around the room. The computer is processing information about the room's temperature. Anthropomorphizing a little, one could say it has evidence of the room's temperature; evidence it received from the sensors.

Now suppose there's another identical computer somewhere else running the same software. Instead of receiving inputs from temperature sensors, however, it is receiving inputs from a bored teenager randomly twiddling a dial. By a weird coincidence, the inputs are exactly the same as the ones on your computer, to the point that the physical states of the two computers are identical throughout the processes.

Do you want to say the teenager's computer also has evidence of the room's temperature? I hope not. Would your answer be different if the computers were sophisticated enough to have phenomenal experience?

As for your example, the criterion of ontological identity you offer seems overly strict. I don't think failing to eat the sandwich would have turned you into a different person, such that my duplicate's beliefs would have been about something else. But this does seem like a largely semantic matter. Let's say I accept your criterion of ontological identity. In that case, yes, me and my duplicate will be (slightly) evidentially distinguishable. This doesn't seem like that big of a bullet to bite.

Is it legitimate to hold that the possibility of being a Boltzman brain doesn't matter because there's no choice a Boltzman brain can make which make any difference? Therefore, you might as well assume that you're at least somewhat real.

Well, if you are a Boltzmann brain than your best bet may be to maximize enjoyment for the few fractions of a second you have before dissolving into chaos. So if you assign a high probability that you are a Boltzmann brain maybe you should spend the time fantasizing about whatever gender or genders you prefer.

You have misunderstood what I am saying. It is definitely not a consequence of my claim that there are no erroneous or unfounded beliefs. One can have a mistaken belief about Obama (such as the belief that he was born in Kenya), but for it to be a belief about Obama, there must be some sort of causal chain linking the belief state to Obama.

your Boltzman brain copy doesn't know it can't have beliefs about Barack Obama

Sure, but I do. I have beliefs about Obama, and I know I can have such beliefs. Surely we're not radical skeptics to the point of denying that I possess this knowledge. And that's my point: I know things my Boltzmann brain copy can't, so we're evidentially distinguishable.

Interesting article; and Motl's a well-known knowledgeable and sometimes correct debunker. I didn't disagree substantially with anything up until here:

It was the probability density for a brain creation itself, around exp(-10^{57}), that determined the "importance" of the effect of a spontaneous brain creation. If we multiply this small number by a huge volume, we obtain a huge result that has no physical relevance for any place of the Universe in the present, past, or future (because the factor of the "spacetime volume" transformed the quantity into some "statistics of events in the whole spacetime" i.e. a global quantity which can't possibly influence any observable phenomena in a region of spacetime, by locality and causality).

I'm not exactly sure what he means, but it seems like even if the brains are not local to anything else, they are the observers; so the objection seems moot.

I think most people here intuitively disagree with this, and assume your "evidence" (in the sense of the word that comes into Bayesian reasoning) includes only what you "know" in the subjective, introspective sense, not the externalist sense.

Yeah, I'm getting this now, and I must admit I'm surprised. I had assumed that accepting some form of semantic externalism is obviously crucial to a fully satisfactory naturalistic epistemology. I still think this is true, but perhaps it is less obvious than I thought. I might make a separate post defending this particular claim.

You're right that the BB-based skeptical argument you offer is a different argument for skepticism than brains-in-vats. I'm not sure it's a more serious argument, though. The second premise in your argument ("If current physics is not essentially correct, I know nothing about the universe.") seems obviously false. Also the implication that I am very likely to be a BB does not come just from current physics. It comes from current physics in conjunction with something like SSA. So there's a third horn here, which says SSA is incorrect. And accepting this doesn't seem to have particularly dire consequences for our epistemological status.

I think Bostrom's claim is that no matter what situation you're dealing with, all observers that are subjectively indistinguishable from you must be part of your reference class. Whether (and which) observers who are subjectively distinguishable get to be part of it will depend on what you're reasoning about.

Huh, you're right. I totally misremembered Bostrom's argument. Reading it now, it doesn't make much sense to me. He moves from the claim that proportionally very few observers would live in low entropy regions as large as ours to the claim that very few observers would observe low entropy regions as large as ours. The former claim is a consequence of Boltzmann's model, but it's not at all obvious that the latter claim is. It would be if we had reason to think that most observers produced by fluctuations would have veridical observations, but why think that is the case? The veridicality of our observations is the product of eons of natural selection. It seems pretty unlikely that a random fluctuation would produce veridical observers. Once we establish this, there's no longer a straightforward inference from "lives in higher entropy region" to "observes higher entropy region".

Later, he offers this justification for neglecting "freak observers" (observers whose beliefs about their environment are almost entirely spurious):

At the same time, the existence of freak observers would not prevent a theory that is otherwise supported by our evidence from still being supported once the freak observers are taken into account—provided that the freak observers make up a small fraction of all the observers that the theory says exist. In the universe we are actually living in, for example, it seems that there may well be vast numbers of freak observers (if only it is sufficiently big). Yet these freak observers would be in an astronomically small minority compared to the regular observers who trace their origin to life that evolved by normal pathways on some planet. For every observer that pops out of a black hole, there are countless civilizations of regular observers. Freak observers can thus, in the light of our observation selection theory, be ignored for all practical purposes.

But this is just false for our current cosmological models. They predict that freak observers predominate (as does Boltzmann's own model). So it seems like Bostrom isn't even really engaging with the actual Boltzmann brain problem. The argument I attribute to him I probably encountered elsewhere. The argument is not uncommon in the literature.

So the idea is that Boltzmann brains would form in smaller fluctuations, while a larger fluctuation would be required to account for us. Since smaller fluctuations are more common, it's more likely that a given brain is a Boltzmann one.

Your wording implicitly assumes you're not a Boltzmann brain. If you are one, the "us" is an illusion and no larger fluctuation is necessary.

But does this take into account the fact that one large fluctuation can give rise to trillions of brains? Enough so that it would be more likely that an observer would be in one of these larger ones?

Yeah, it does. The probabilities involved here are ridiculously unbalanced. The frequency of a fluctuation (assuming ergodicity) is exponentially related to its entropy, so even small differences in entropy correspond to large differences in probability. And the difference in entropy here is itself huge. For comparison, it's been estimated that a fluctuation into our current macroscopic universe would be likelier than a fluctuation into the macroscopic state of the very early universe by a factor of about 10^(10^101).

Under this idea, wouldn't the Boltzmann brain have an equivalent belief about "Barack Obama", which would correspond to some isomorphic thing in its environment? And then, wouldn't this be extremely unlikely, since by definition, the Boltzmann brain is in a higher entropy place (as it would observe a world isomorphic to ours, which has relatively low entropy)?

Not sure what you're getting at here. The belief state in the Boltzmann brain wouldn't be caused by some external stable macroscopic object. It's produced by the chance agglomeration of microscopic collisions (in Boltzmann's model).

Not everyone shares your extreme positivism, I guess.

ETA: Re-reading this comment, I see that it might come across as flippant or hostile. It's not intended to be either. I just think that you have a perspective on what questions are worth addressing (and how they should be addressed) that is unusual. Whether it is the right perspective (I don't think it is) is the subject of another discussion, one that I don't wish to have here.

What I don't get is why people even bother spending time discussing such nonsense seriously, let alone make meaningless claims like this.

Sure you do: the observed phenomenon that many things that philosophers consider major problems are artifacts of human cognitive psychology. c.f. p-zombies. The bad philosophy in question does not survive because it says anything about the physical universe, but because its proponents refuse to be convinced their claimed problem is not a problem.

tl;dr when philosophers claim they've come up with something that says something about physics, they've generally failed to realise that the ancient Greeks deciding to concentrate on pure thought and eschew experimentation was an error.