probabilities should correspond to expected observations and expected observations only
FWIW I think this is wrong. There’s a perfectly coherent framework—subjective expected utility theory (Jeffrey, Joyce, etc)—in which probabilities can correspond to many other things. Probabilities as credences can correspond to confidence in propositions unrelated to future observations, e.g., philosophical beliefs or practically-unobservable facts. You can unambiguously assign probabilities to ‘cosmopsychism’ and ‘Everett’s many-worlds interpretation’ without expecting to ever observe their truth or falsity.
However, there is another source of uncertainty: observational uncertainty. The other person might be uncertain whether they have all the facts that feed into their model, or whether their observations are correct.
This is reasonable. If a deterministic model has three free parameters, two of which you have specificied, you could just use your prior over the third parameter to create a distribution of model outcomes. This kind of situation should be pretty easy to clarify though, by saying something like “my model predicts event E iff parameter A is above A*” and “my prior P(A>A*) is 50% which implies P(E)=50%.”
But generically, the distribution is not coming from a model. It just looks like your all things considered credence that A>A*. I’d be hesitant calling a probability based on it your “inside view/model” probability.
Probabilities as credences can correspond to confidence in propositions unrelated to future observations, e.g., philosophical beliefs or practically-unobservable facts. You can unambiguously assign probabilities to ‘cosmopsychism’ and ‘Everett’s many-worlds interpretation’ without expecting to ever observe their truth or falsity.
You can, but why would you? Beliefs should pay rent in anticipated experiences. If two beliefs lead to the same anticipated experiences, then there’s no particular reason to choose one belief over the other. Assigning probability to cosmopsychism or Everett’s many-worlds interpretation only makes sense insofar as you think there will be some observations, at some point in the future, which will be different if one set of beliefs is true versus if the other set of beliefs is true.
Because the meaning of statements does not, in general, consist entirely in observations/anticipated experiences, and it makes sense for people to have various attitudes (centrally, beliefs and desires) towards propositions that refer to unobservable-in-principle things.
Accepting that beliefs should pay rent in anticipated experience does not mean accepting that the meaning of sentences are determined entirely by observables/anticipated experiences. We can have that the meanings of sentences are the propositions they express, and the truth-conditions of propositions are generally states-of-affairs-in-the-world and not just observations/anticipated experiences. Eliezer himself puts it nicely here: “The meaning of a statement is not the future experimental predictions that it brings about, nor isomorphic up to those predictions [...] you can have meaningful statements with no experimental consequences, for example: “Galaxies continue to exist after the expanding universe carries them over the horizon of observation from us.”″
As to how to choose one belief over another, if both beliefs are observationally equivalent in some sense, there are many such considerations. One is our best theories predict it: if our best cosmological theories predict something does not cease to exist the moment it exits our lightcone, then we should assign higher probability to the statement “objects continue to exist outside our lightcone” than the statement “objects vanish at the boundary of our lightcone”. Another is simplicity-based priors: the many-worlds interpretation of quantum mechanics is strictly simpler/has a shorter description length than the Copenhagen interpretation (Many-Worlds = wave function + Schrödinger evolution; Copenhagen interpretation = wave function + Schrödinger evolution + collapse postulate), so we should assign a higher prior to many-worlds than to Copenhagen.
If your concern is instead that attitudes towards such propositions have no behavioural implications and thus cannot in principle be elicited from agents, then the response is to point to the various decision-theoretic representation theorems available in the literature. Take the Jeffrey framework: as long as your preferences over propositions satisfies certain conditions (e.g. Ordering, Averaging), I can derive both a quantitative desirability measure and probability measure, characterising your desire and belief attitudes (respectively) towards the propositions you are considering. The actual procedure to elicit this preference relation looks like asking people to consider and compare actualising various propositions, which we can think of as gambles. For example, a gamble might look like “If the coin lands Heads, then one person comes into existence outside of our future lightcone and experiences bliss; If the coin lands Tails, then one person comes into existence outside of our future lightcone and experiences suffering”. Note, the propositions here can refer to unobservables. Also, it seems reasonable to prefer the above gamble involving a fair coin to the same gamble but with the coin biased towards Tails. Moreover, the procedure to elicit an agent’s attitudes to such propositions merely consists in the agents considering what they would do if they were choosing which of various propositions to bring about, and does not cash out in terms of observations/anticipated experiences.
(As an aside, doing acausal reasoning in general requires agent to have beliefs and desires towards unobservable-in-principle stuff in, e.g. distant parts of our universe, or other Everett branches).
FWIW I think this is wrong. There’s a perfectly coherent framework—subjective expected utility theory (Jeffrey, Joyce, etc)—in which probabilities can correspond to many other things. Probabilities as credences can correspond to confidence in propositions unrelated to future observations, e.g., philosophical beliefs or practically-unobservable facts. You can unambiguously assign probabilities to ‘cosmopsychism’ and ‘Everett’s many-worlds interpretation’ without expecting to ever observe their truth or falsity.
This is reasonable. If a deterministic model has three free parameters, two of which you have specificied, you could just use your prior over the third parameter to create a distribution of model outcomes. This kind of situation should be pretty easy to clarify though, by saying something like “my model predicts event E iff parameter A is above A*” and “my prior P(A>A*) is 50% which implies P(E)=50%.”
But generically, the distribution is not coming from a model. It just looks like your all things considered credence that A>A*. I’d be hesitant calling a probability based on it your “inside view/model” probability.
You can, but why would you? Beliefs should pay rent in anticipated experiences. If two beliefs lead to the same anticipated experiences, then there’s no particular reason to choose one belief over the other. Assigning probability to cosmopsychism or Everett’s many-worlds interpretation only makes sense insofar as you think there will be some observations, at some point in the future, which will be different if one set of beliefs is true versus if the other set of beliefs is true.
Because the meaning of statements does not, in general, consist entirely in observations/anticipated experiences, and it makes sense for people to have various attitudes (centrally, beliefs and desires) towards propositions that refer to unobservable-in-principle things.
Accepting that beliefs should pay rent in anticipated experience does not mean accepting that the meaning of sentences are determined entirely by observables/anticipated experiences. We can have that the meanings of sentences are the propositions they express, and the truth-conditions of propositions are generally states-of-affairs-in-the-world and not just observations/anticipated experiences. Eliezer himself puts it nicely here: “The meaning of a statement is not the future experimental predictions that it brings about, nor isomorphic up to those predictions [...] you can have meaningful statements with no experimental consequences, for example: “Galaxies continue to exist after the expanding universe carries them over the horizon of observation from us.”″
As to how to choose one belief over another, if both beliefs are observationally equivalent in some sense, there are many such considerations. One is our best theories predict it: if our best cosmological theories predict something does not cease to exist the moment it exits our lightcone, then we should assign higher probability to the statement “objects continue to exist outside our lightcone” than the statement “objects vanish at the boundary of our lightcone”. Another is simplicity-based priors: the many-worlds interpretation of quantum mechanics is strictly simpler/has a shorter description length than the Copenhagen interpretation (Many-Worlds = wave function + Schrödinger evolution; Copenhagen interpretation = wave function + Schrödinger evolution + collapse postulate), so we should assign a higher prior to many-worlds than to Copenhagen.
If your concern is instead that attitudes towards such propositions have no behavioural implications and thus cannot in principle be elicited from agents, then the response is to point to the various decision-theoretic representation theorems available in the literature. Take the Jeffrey framework: as long as your preferences over propositions satisfies certain conditions (e.g. Ordering, Averaging), I can derive both a quantitative desirability measure and probability measure, characterising your desire and belief attitudes (respectively) towards the propositions you are considering. The actual procedure to elicit this preference relation looks like asking people to consider and compare actualising various propositions, which we can think of as gambles. For example, a gamble might look like “If the coin lands Heads, then one person comes into existence outside of our future lightcone and experiences bliss; If the coin lands Tails, then one person comes into existence outside of our future lightcone and experiences suffering”. Note, the propositions here can refer to unobservables. Also, it seems reasonable to prefer the above gamble involving a fair coin to the same gamble but with the coin biased towards Tails. Moreover, the procedure to elicit an agent’s attitudes to such propositions merely consists in the agents considering what they would do if they were choosing which of various propositions to bring about, and does not cash out in terms of observations/anticipated experiences.
(As an aside, doing acausal reasoning in general requires agent to have beliefs and desires towards unobservable-in-principle stuff in, e.g. distant parts of our universe, or other Everett branches).