Suppose an answer appeared here, and when you read it, you were completely satisfied by it. It answered your question perfectly. How would this world differ from one in which no answer remotely satisfied you? Would you expect yourself to have more accurate beliefs or help you achieve your goals?
If not, to the best of your knowledge, why have you decided to ask the question in the first place?
I don’t know what you mean here. One of my goals is to get a better answer to this question than what I’m currently able to give, so by definition getting such an answer would “help me achieve my goals”. If you mean something less trivial than that, well, it also doesn’t help me to achieve my goals to know if the Riemann hypothesis is true or false, but RH is nevertheless one of the most interesting questions I know of and definitely worth wondering about.
I can’t know how an answer I don’t know about would impact my beliefs or behavior, but my guess is that the explanation would not lead us to change how we use probability, just like thermodynamics didn’t lead us to change how we use steam engines. It was, nevertheless, still worthwhile to develop the theory.
My approach was not helpful at all, which I can clearly see now. I’ll take another stab at your question.
You think it is reasonable to assign probabilities, but you also cannot explain how you do so or justify it. You are looking for such an explanation or justification, so that your assessment of reasonableness is backed by actual reason.
Are you unable to justify any probability assessments at all? Or is there some specific subset that you’re having trouble with? Or have I failed to understand your question properly?
I think you can justify probability assessments in some situations using Dutch book style arguments combined with the situation itself having some kind of symmetry which the measure must be invariant under, but this kind of argument doesn’t generalize to any kind of messy real world situation in which you have to make a forecast on something, and it still doesn’t give some “physical interpretation” to the probabilities beyond “if you make bets then your odds have to form a probability measure, and they better respect the symmetries of the physical theory you’re working with”.
If you phrase this in terms of epistemic content, I could say that a probability measure just adds information about the symmetries of some situation when seen from your perspective, but when I say (for example) that there’s a 40% chance Russia will invade Ukraine by end of year 2022 this doesn’t seem to correspond to any obvious symmetry in the situation.
Perhaps such probabilities are based on intuition, and happen to be roughly accurate because the intuition has formed as a causal result of factors influencing the event? In order to be explicitly justified, one would need an explicit justification of intuition, or at least intuition within the field of knowledge in question.
I would say that such intuitions in many fields are too error-prone to justify any kind of accurate probability assessment. My personal answer then would be to discard probability assessments that cannot be justified, unless you have sufficient trust in your intuition about the statement in question.
What is your thinking on this prong of the dilemma (retracting your assessment of reasonableness on these probability assessments for which you have no justification)?
Suppose an answer appeared here, and when you read it, you were completely satisfied by it. It answered your question perfectly. How would this world differ from one in which no answer remotely satisfied you? Would you expect yourself to have more accurate beliefs or help you achieve your goals?
If not, to the best of your knowledge, why have you decided to ask the question in the first place?
I don’t know what you mean here. One of my goals is to get a better answer to this question than what I’m currently able to give, so by definition getting such an answer would “help me achieve my goals”. If you mean something less trivial than that, well, it also doesn’t help me to achieve my goals to know if the Riemann hypothesis is true or false, but RH is nevertheless one of the most interesting questions I know of and definitely worth wondering about.
I can’t know how an answer I don’t know about would impact my beliefs or behavior, but my guess is that the explanation would not lead us to change how we use probability, just like thermodynamics didn’t lead us to change how we use steam engines. It was, nevertheless, still worthwhile to develop the theory.
My approach was not helpful at all, which I can clearly see now. I’ll take another stab at your question.
You think it is reasonable to assign probabilities, but you also cannot explain how you do so or justify it. You are looking for such an explanation or justification, so that your assessment of reasonableness is backed by actual reason.
Are you unable to justify any probability assessments at all? Or is there some specific subset that you’re having trouble with? Or have I failed to understand your question properly?
I think you can justify probability assessments in some situations using Dutch book style arguments combined with the situation itself having some kind of symmetry which the measure must be invariant under, but this kind of argument doesn’t generalize to any kind of messy real world situation in which you have to make a forecast on something, and it still doesn’t give some “physical interpretation” to the probabilities beyond “if you make bets then your odds have to form a probability measure, and they better respect the symmetries of the physical theory you’re working with”.
If you phrase this in terms of epistemic content, I could say that a probability measure just adds information about the symmetries of some situation when seen from your perspective, but when I say (for example) that there’s a 40% chance Russia will invade Ukraine by end of year 2022 this doesn’t seem to correspond to any obvious symmetry in the situation.
Perhaps such probabilities are based on intuition, and happen to be roughly accurate because the intuition has formed as a causal result of factors influencing the event? In order to be explicitly justified, one would need an explicit justification of intuition, or at least intuition within the field of knowledge in question.
I would say that such intuitions in many fields are too error-prone to justify any kind of accurate probability assessment. My personal answer then would be to discard probability assessments that cannot be justified, unless you have sufficient trust in your intuition about the statement in question.
What is your thinking on this prong of the dilemma (retracting your assessment of reasonableness on these probability assessments for which you have no justification)?