Adam Elga on Being Rational in a Very Large Universe | Mindscape 345
Quick Read
Summary
Takeaways
- ❖Bayesian reasoning, while quantitative, faces significant challenges when applied to cosmological models that predict vastly different scales or observer populations.
- ❖The 'prior self' method suggests evaluating peer disagreements by asking what your past self would have thought about the likelihood of being right given the disagreement.
- ❖Self-locating uncertainty arises when one's identity or position within a scenario is unknown, even if all objective facts are clear (e.g., teleporter paradox).
- ❖The Sleeping Beauty problem illustrates how different assumptions about self-locating uncertainty lead to conflicting probabilities ('thirder' vs. 'halfer').
- ❖Applying self-locating assumptions to cosmology can lead to 'presumptuous' conclusions, such as favoring theories with more observers.
- ❖The Boltzmann brain problem suggests that in eternal universes, most observers would be transient, randomly fluctuating brains, leading to a self-undermining dilemma about the reliability of one's own memories and observations.
- ❖A potential 'stable stance' against Boltzmann brains involves assigning intrinsic low plausibility to such 'predicaments' rather than relying solely on empirical evidence or internal consistency.
- ❖The simulation argument and AI's self-trust issues are analogous to Boltzmann brain problems, highlighting the pervasive nature of these philosophical challenges.
Insights
1The Cosmological Puzzle of Observer Existence
When comparing two cosmological models that predict similar local conditions but differ in overall size (e.g., closed vs. open universe), one might argue the larger universe is more likely because it's statistically more probable for an observer like oneself to exist within it. This reasoning, based on 'the data that I exist,' highlights a core challenge in cosmological theory choice.
Sean Carroll introduces the puzzle: 'What if you're a cosmologist? ... In one theory, the universe is bigger than in the other one.' ()
2Rationality in Peer Disagreement: Deferring to Your Prior Self
When encountering a peer (someone considered equally smart and well-informed) who holds a different opinion based on similar evidence, a rational person should defer to what their 'prior self' would have thought. This involves asking your past self how likely they would have considered you to be right, conditional on such a disagreement, rather than immediately splitting the difference or sticking to your guns.
Adam Elga explains: 'You basically should defer to what your prior self would have thought.' ()
3Self-Locating Uncertainty in Teleportation
The teleporter paradox, where a person is duplicated across multiple receiving stations, creates self-locating uncertainty. Even if all objective facts about the world are known, the individual wonders 'Which one am I?' This isn't about objective events but subjective location, and the intuitive response is often to assign equal credence to being any of the duplicates.
Elga details the Star Trek teleporter example: 'You wake up and you look around, but the receiving bays... look exactly alike. And so you're wondering, am I on the Enterprise or am I on the Pmpkin?' ()
4The Sleeping Beauty Problem and 'Thirder' vs. 'Halfer' Positions
In the Sleeping Beauty experiment, a coin flip determines if Beauty is woken once (heads) or twice (tails, on Monday and Tuesday, with memory erased). Upon waking, Beauty's credence in the coin being heads is debated: 'halfers' maintain 1/2, while 'thirders' (like Elga) argue for 1/3, because the 'tails' scenario has two possible awakenings, effectively boosting its probability from Beauty's subjective perspective.
Elga describes the problem: 'If it's heads, you're going to wake up sleeping beauty on Monday. If it's tails, you're going to wake her up on Monday and Tuesday.' () and concludes 'you end up forced to the conclusion that... you should be twothirds confident in uh tails and one-/ird in heads.' ()
5The 'Presumptuousness' of Self-Locating Assumptions in Cosmology
Applying 'thirder'-like reasoning (Self-Indication Assumption) to cosmology implies that theories predicting more observers or more instantiations of one's experience get a 'boost' in probability. This leads to the 'presumptuous' conclusion that one can favor certain cosmological theories from an armchair, simply based on the number of potential observers, without new empirical data.
Elga states: 'Someone who is attracted to the third type view... is committed to saying that theory B in this case gets a big boost and there they are sitting in their philosophers's chair and how presumptuous...' ()
6The Boltzmann Brain Problem and Self-Undermining
In an eternal, fluctuating universe, it's statistically likely that most conscious observers would be 'Boltzmann brains'—transient, randomly formed brains with false memories. If one concludes they are likely a Boltzmann brain, this undermines the reliability of their apparent memories and reasoning, creating an unstable, self-undermining loop. This challenges the very basis of scientific inquiry.
Elga explains: 'If the universe is really longlasting... the vast majority of them are Boltzman brains meaning piles of that just formed out of nothing out of pure random chance.' () and 'Boltzman brains should not trust their apparent memories.' ()
7A Stable Stance Against Boltzmann Brains: Intrinsic Low Plausibility
To escape the self-undermining loop of the Boltzmann brain problem, one can adopt a 'stable stance' by assigning an intrinsically low prior plausibility to 'radically diluted, randomly created creatures' (like Boltzmann brains). This is analogous to how one might assign low priors to skeptical scenarios (e.g., brain in a vat) in everyday epistemology, allowing for a rational, non-skeptical approach to scientific cosmology.
Elga proposes: 'Maybe there's just a rational prior that favors the first sort of predicament over the second.' () referring to 'normal human being' vs. 'completely randomly created Boltzman brain.'
Key Concepts
Bayesian Reasoning
A quantitative method for updating beliefs (credences) based on new evidence, using prior probabilities and likelihoods. It forms the foundation for scientific theory choice but faces challenges with self-locating uncertainty.
Self-Locating Uncertainty
Uncertainty about one's own identity or position within a given scenario, even when all objective facts of the world are known. Examples include the teleporter paradox, Sleeping Beauty problem, and observer selection in multiverses.
Self-Indication Assumption (SIA)
The view that one should give a 'boost' to possible worlds or scenarios that involve more instantiations of one's own experience or state of mind, effectively increasing the probability of being in such a world.
Self-Sampling Assumption (SSA)
The view that one should consider oneself a random sample from the set of all observers in the universe, often leading to favoring possibilities where a high fraction of observers are 'like me'.
Compartmentalized Conditionalizing (CC)
A Bayesian updating approach that imposes 'firewalls' between possible worlds, preventing probability from crossing world boundaries when new information is learned, often leading to 'halfer' positions in problems like Sleeping Beauty.
Self-Undermining Argument
A situation where the conclusion of an argument undermines the very premises or reasoning used to reach that conclusion, creating an instability (e.g., if you conclude you're a Boltzmann brain, you shouldn't trust the reasoning that led you there).
Externalism (Epistemology)
The philosophical view that the justification or knowledge of a belief can depend on factors external to a person's conscious awareness, such as reliable causal connections to the world, which can offer a way out of some skeptical scenarios.
Lessons
- When faced with a peer who disagrees with your conclusion, reflect on your 'prior self's' assessment of who would be more likely to be correct in such a scenario, rather than immediately assuming you are right.
- Recognize that in situations of self-locating uncertainty (e.g., 'Which copy of me am I?'), objective facts alone may not suffice for assigning probabilities; subjective factors about your 'predicament' may need to be considered.
- Be wary of cosmological or philosophical arguments that lead to self-undermining conclusions (e.g., if a theory implies your reasoning is unreliable, question the theory itself, or your initial premises).
- Consider assigning intrinsically low prior probabilities to radically skeptical or 'randomly created' scenarios (like Boltzmann brains) to maintain a stable and actionable framework for rationality, even if such scenarios cannot be empirically disproven.
Quotes
"I characterize myself as addicted to rationality... I've always been fascinated with probability, doing the rational thing, what's justified, optimizing."
"If I lived in one of these eternal universes with random fluctuations, then I would be a Boltzman brain. But I look around and I see I am not. Therefore, I do not live in such a cosmology."
"Boltzman brains should not trust their apparent memories. Boltzman brains never went to school. They never read a textbook. They have no reason to think that anyone has ever looked through a telescope or that any human being has ever existed. They're just random blobs."
"I cannot rule out on the basis of either reason or evidence that I'm a Boltzman brain. I cannot rule out that I'm a brain in a vat living in a simulation, being dreamed by an evil demon, all sorts of different things. Uh but they're not ways to go through life."
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