I can only skim most of this right now, but you’re definitely misconstruing what Bostrom has to say about Boltzmann. He does not rely on our having non-qualitative knowledge that we’re not Boltzmann brains. Please re-read his stuff: http://anthropic-principle.com/book/anthropicbias.html#5b
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 uncommonin the literature.
You’re right of course that Bostrom is not engaging with the problem you’re focusing on. But the context for discussing Boltzmann’s idea seems different from what he says about “freak observers”—the former is about arguing that the historically accepted objection to Boltzmann is best construed as relying on SSA, whereas the rationale for the latter is best seen in his J Phil piece: http://www.anthropic-principle.com/preprints/cos/big2.pdf ). But I’ll grant you that his argument about Boltzmann is suboptimally formulated (turns out I remembered it being better than it actually was).
However, there is a stronger argument (obvious to me, and maybe charitably attributable to Bostrom-sub-2002) that you seem to be ignoring, based on the notion that SSA can apply even if you can (based on your evidence) exclude certain possibilities about who you are. The argument doesn’t need the absurd inference from “lives in higher entropy region” to “observes higher entropy region” but rather needs Boltzmann’s model to suggest that “very few observers observe large low-entropy regions”. Since most Boltzmann brains have random epistemic states and can’t be described as observing anything, the latter sentence is of course true conditional on Boltzmann’s model. Most observers don’t observe anything (and even the lucky ones who do tend to have tiny-sized low-entropy surroundings) so virtually all observers do not observe large low-entropy regions.
Anyhow, if a Boltzmann-brain-swamped scenario is true, a very tiny fraction of observers make our observations, whereas if the world isn’t Boltzmann-brain-swamped (e.g. if universes reliably stop existing before entering the de Sitter phase), a much less tiny fraction of observers make our observations. The SSA takeaway from this is that our observations disconfirm Boltzmann-brain-swamped scenarios.
You can of course exclude Boltzmann brains from the reference class, but this doesn’t get you very far. Much more rarely but still infinitely often, there will arise observers with some surrounding environments and veridical observations about those surrounding environments. Still, it seems very plausible that the typical observations of such observers are different from the expected observations of evolved beings, so they dominate the reference class and again the SSA argument goes through. For your move against this argument to be successful, you have to have good grounds for excluding all de Sitter phase observers. And based on my rudimentary understanding it seems that the variety of de Sitter phase observers won’t allow you to do that with general considerations like externalism. Hope this helps.
A question: why do you think that your non-qualitative/external evidence should be taken into account differently than qualitative/internal evidence if SSA holds? At least for observers subjectively indistinguishable to ourselves, your choice is to exclude the one’s who don’t have our presumed external evidence from the reference class. Why not just include everyone in the reference class and then update based on both qualitative and external evidence?
I can only skim most of this right now, but you’re definitely misconstruing what Bostrom has to say about Boltzmann. He does not rely on our having non-qualitative knowledge that we’re not Boltzmann brains. Please re-read his stuff: http://anthropic-principle.com/book/anthropicbias.html#5b
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):
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.
You’re right of course that Bostrom is not engaging with the problem you’re focusing on. But the context for discussing Boltzmann’s idea seems different from what he says about “freak observers”—the former is about arguing that the historically accepted objection to Boltzmann is best construed as relying on SSA, whereas the rationale for the latter is best seen in his J Phil piece: http://www.anthropic-principle.com/preprints/cos/big2.pdf ). But I’ll grant you that his argument about Boltzmann is suboptimally formulated (turns out I remembered it being better than it actually was).
However, there is a stronger argument (obvious to me, and maybe charitably attributable to Bostrom-sub-2002) that you seem to be ignoring, based on the notion that SSA can apply even if you can (based on your evidence) exclude certain possibilities about who you are. The argument doesn’t need the absurd inference from “lives in higher entropy region” to “observes higher entropy region” but rather needs Boltzmann’s model to suggest that “very few observers observe large low-entropy regions”. Since most Boltzmann brains have random epistemic states and can’t be described as observing anything, the latter sentence is of course true conditional on Boltzmann’s model. Most observers don’t observe anything (and even the lucky ones who do tend to have tiny-sized low-entropy surroundings) so virtually all observers do not observe large low-entropy regions.
Anyhow, if a Boltzmann-brain-swamped scenario is true, a very tiny fraction of observers make our observations, whereas if the world isn’t Boltzmann-brain-swamped (e.g. if universes reliably stop existing before entering the de Sitter phase), a much less tiny fraction of observers make our observations. The SSA takeaway from this is that our observations disconfirm Boltzmann-brain-swamped scenarios.
You can of course exclude Boltzmann brains from the reference class, but this doesn’t get you very far. Much more rarely but still infinitely often, there will arise observers with some surrounding environments and veridical observations about those surrounding environments. Still, it seems very plausible that the typical observations of such observers are different from the expected observations of evolved beings, so they dominate the reference class and again the SSA argument goes through. For your move against this argument to be successful, you have to have good grounds for excluding all de Sitter phase observers. And based on my rudimentary understanding it seems that the variety of de Sitter phase observers won’t allow you to do that with general considerations like externalism. Hope this helps.
A question: why do you think that your non-qualitative/external evidence should be taken into account differently than qualitative/internal evidence if SSA holds? At least for observers subjectively indistinguishable to ourselves, your choice is to exclude the one’s who don’t have our presumed external evidence from the reference class. Why not just include everyone in the reference class and then update based on both qualitative and external evidence?