There is another reason to rule out you being a Boltzmann brain. BBs cannot validly reason about anything, and this makes them not you. Admitting any nonzero probability of being a BB makes valid knowledge and reasoning impossible. (How can you know that you can validly reason? Well, what do you think happens if you assume that you can’t?)
Slightly longer: if we admit some probability of being BBs, how can we bound that probability? This means assigning probabilities to different explanations of what we see. But an unknown proportion of reasoners-doing-the-quantifying are BBs and are working from false knowledge and false rules of logic! They might have come into existence with every possible conclusion already formed instead of reasoning from evidence! Eddington’s logic, that more complex fluctuations are exponentially less likely (thus giving us a prior distribution on which BBs exist), is still logic—reasoning based on observations—and if you allow yourself to use that logic, any logic, you have already decided you, personally, are not a BB. In which case, reasoning about the probability that some “yous” really are BBs—that you are a BB with some probability—makes no sense.
If some BB is is physically the same as your non-BB brain, why can’t you talk about the probability you are one? Because a BB used invalid reasoning to arrive at that conclusion, and so it cannot expect to arrive at any valid conclusions if it keeps on thinking.
Even longer:
A BB cannot perform valid reasoning because it does not contain validly-acquired knowledge. It spontaneously came into being containing some knowledge, and a BB containing different memories, priors or laws of logic might have been just as likely. And since it takes time to think through an argument, a BB is even more likely to come into being already convinced of the conclusion—any possible conclusion!
The above paragraph is still subtly wrong. Even the concept of valid reasoning would have come into existence as part of the BB. The claim that different BBs are equally likely was either invalidly-reasoned by a BB, or that simpler ones are likelier, probably came spontaneously into existence as part of the BB. BBs cannot reason about greater Reality any more than they can reason about their own worlds.
You cannot assume you are a BB (with some probability), any more than you can assume a contradiction because it makes all further reasoning impossible. It makes predicting the next second of sensory data impossible. So we might as well not do it, and behave as if that probability is zero.
Boltzmann’s original idea, that the whole universe might be an enormous spontaneous fluctuation from the Big Bang onwards (though Boltzmann didn’t know about the Big Bang), is less problematic. It’s still wrong, for the reasons Eliezer gave, but at least it wouldn’t require us to conclude we cannot reason about anything!
So what should we do if cosmology turns out to say that the universe will end in thermodynamic soup, long-lived enough to generate BBs? (It may or may not actually predict that, but we have to be able to reason in the event that it does.) Some people deny anthropics in various ways. Some think anthropics would thereby falsify such a cosmology. I just set the probability of me, personally, being a BB to zero. A (logical) probability which cannot only be reasoned forward from but which invalidates all past reasoning and knowledge is, at the very least, not a useful part of any possible decision-algorithm. So we might as well behave as if it doesn’t exist.
(Could it exist for others, even if not for ourselves? I think it logically could, but Boltzmann’s classical thermodynamics suggests we are incredibly unlikely to ever observe / interact with another fluctuation with a distinct origin from your own ordered part of the world.)
Doesn’t this argument prove too much? Why doesn’t similar reasoning rule out other mentally-impaired states like drunkenness, dreams, and brain injuries? In fact, why doesn’t it rule out being a flawed human being, rather than an ideal reasoner?
Even if all your memories are false, couldn’t you still reason validly about abstract concepts (like math) and hypothetical scenarios? This seems to show that BBs can do at least some valid reasoning.
Even if you might be in some state S that would totally prevent you from reasoning validly, if you conjectured you were in some state T that would permit you to reason validly, and your reasoning based on that conjecture leads to a contradiction, wouldn’t that allow you to rule out state T without ruling out state S? This seems to show that you can do at least some useful reasoning without completely ruling out that you are in an impaired state.
Some non-Boltzmann minds like most dreaming humans can’t do any useful reasoning, but normal humans can. We know we can because we use it to succeed at life, and we know we are succeeding at life because we trust our senses. You have to ground your belief in reality in something; if you fully distrust your senses then, yes, you cannot reason about reality, just as a Boltzmann brain can’t. And you can’t reason about logic either, because we learn about logic using our physical senses.
You could not because your definitions of those concepts, and your understanding of the rules of reasoning, and your memory of starting a single-sentence-long proof or chain of thought by the time you’re finishing it, would be as false as all your other memories. You can’t reason about 2+2=5 if you don’t know what + means.
Who is “you” in “if you conjectured”? You have to assume you’re able to reason at all, before you can reason about state T. You, Dweomite, can make an argument about T, because you’re not in an impaired state. A Boltzmann brain could not validly make the same argument, in the sense of arriving at a correct conclusion because the argument was correct. A Boltzmann brain which is considering your argument about T is equally likely to believe or disbelieve it, because it came into being thinking it just thought through it and either accepted or rejected it.
My dreaming brain isn’t entirely incapable of useful reasoning—sometimes I can recognize that I am dreaming and choose whether or not to wake up, although during a dream I also tend not to be capable of doing coherent reasoning for more than a short period of time.
I did say most dreaming humans. But the point isn’t how well dreamers can reason, that’s just an example and if it doesn’t serve it’s not essential. My argument was that imperfect reasoners can still be trusted because they can be evaluated empirically on their success, and their reasoning ability is caused by evolution and learning in an ordered environment; whereas Boltzmann brains are not grounded, and any correct reasoning they carry out will be an accident.
There is another reason to rule out you being a Boltzmann brain. BBs cannot validly reason about anything, and this makes them not you. Admitting any nonzero probability of being a BB makes valid knowledge and reasoning impossible. (How can you know that you can validly reason? Well, what do you think happens if you assume that you can’t?)
Slightly longer: if we admit some probability of being BBs, how can we bound that probability? This means assigning probabilities to different explanations of what we see. But an unknown proportion of reasoners-doing-the-quantifying are BBs and are working from false knowledge and false rules of logic! They might have come into existence with every possible conclusion already formed instead of reasoning from evidence! Eddington’s logic, that more complex fluctuations are exponentially less likely (thus giving us a prior distribution on which BBs exist), is still logic—reasoning based on observations—and if you allow yourself to use that logic, any logic, you have already decided you, personally, are not a BB. In which case, reasoning about the probability that some “yous” really are BBs—that you are a BB with some probability—makes no sense.
If some BB is is physically the same as your non-BB brain, why can’t you talk about the probability you are one? Because a BB used invalid reasoning to arrive at that conclusion, and so it cannot expect to arrive at any valid conclusions if it keeps on thinking.
Even longer:
A BB cannot perform valid reasoning because it does not contain validly-acquired knowledge. It spontaneously came into being containing some knowledge, and a BB containing different memories, priors or laws of logic might have been just as likely. And since it takes time to think through an argument, a BB is even more likely to come into being already convinced of the conclusion—any possible conclusion!
The above paragraph is still subtly wrong. Even the concept of valid reasoning would have come into existence as part of the BB. The claim that different BBs are equally likely was either invalidly-reasoned by a BB, or that simpler ones are likelier, probably came spontaneously into existence as part of the BB. BBs cannot reason about greater Reality any more than they can reason about their own worlds.
You cannot assume you are a BB (with some probability), any more than you can assume a contradiction because it makes all further reasoning impossible. It makes predicting the next second of sensory data impossible. So we might as well not do it, and behave as if that probability is zero.
Boltzmann’s original idea, that the whole universe might be an enormous spontaneous fluctuation from the Big Bang onwards (though Boltzmann didn’t know about the Big Bang), is less problematic. It’s still wrong, for the reasons Eliezer gave, but at least it wouldn’t require us to conclude we cannot reason about anything!
So what should we do if cosmology turns out to say that the universe will end in thermodynamic soup, long-lived enough to generate BBs? (It may or may not actually predict that, but we have to be able to reason in the event that it does.) Some people deny anthropics in various ways. Some think anthropics would thereby falsify such a cosmology. I just set the probability of me, personally, being a BB to zero. A (logical) probability which cannot only be reasoned forward from but which invalidates all past reasoning and knowledge is, at the very least, not a useful part of any possible decision-algorithm. So we might as well behave as if it doesn’t exist.
(Could it exist for others, even if not for ourselves? I think it logically could, but Boltzmann’s classical thermodynamics suggests we are incredibly unlikely to ever observe / interact with another fluctuation with a distinct origin from your own ordered part of the world.)
Doesn’t this argument prove too much? Why doesn’t similar reasoning rule out other mentally-impaired states like drunkenness, dreams, and brain injuries? In fact, why doesn’t it rule out being a flawed human being, rather than an ideal reasoner?
Even if all your memories are false, couldn’t you still reason validly about abstract concepts (like math) and hypothetical scenarios? This seems to show that BBs can do at least some valid reasoning.
Even if you might be in some state S that would totally prevent you from reasoning validly, if you conjectured you were in some state T that would permit you to reason validly, and your reasoning based on that conjecture leads to a contradiction, wouldn’t that allow you to rule out state T without ruling out state S? This seems to show that you can do at least some useful reasoning without completely ruling out that you are in an impaired state.
Some non-Boltzmann minds like most dreaming humans can’t do any useful reasoning, but normal humans can. We know we can because we use it to succeed at life, and we know we are succeeding at life because we trust our senses. You have to ground your belief in reality in something; if you fully distrust your senses then, yes, you cannot reason about reality, just as a Boltzmann brain can’t. And you can’t reason about logic either, because we learn about logic using our physical senses.
You could not because your definitions of those concepts, and your understanding of the rules of reasoning, and your memory of starting a single-sentence-long proof or chain of thought by the time you’re finishing it, would be as false as all your other memories. You can’t reason about 2+2=5 if you don’t know what + means.
Who is “you” in “if you conjectured”? You have to assume you’re able to reason at all, before you can reason about state T. You, Dweomite, can make an argument about T, because you’re not in an impaired state. A Boltzmann brain could not validly make the same argument, in the sense of arriving at a correct conclusion because the argument was correct. A Boltzmann brain which is considering your argument about T is equally likely to believe or disbelieve it, because it came into being thinking it just thought through it and either accepted or rejected it.
My dreaming brain isn’t entirely incapable of useful reasoning—sometimes I can recognize that I am dreaming and choose whether or not to wake up, although during a dream I also tend not to be capable of doing coherent reasoning for more than a short period of time.
I did say most dreaming humans. But the point isn’t how well dreamers can reason, that’s just an example and if it doesn’t serve it’s not essential. My argument was that imperfect reasoners can still be trusted because they can be evaluated empirically on their success, and their reasoning ability is caused by evolution and learning in an ordered environment; whereas Boltzmann brains are not grounded, and any correct reasoning they carry out will be an accident.