How do you determine the relevant probabilities? What if you’re looking for, say, the probability of a nuclear attack occurring anywhere in the world in the next 20 years?
Such as? I am probably unable to give you a wholly general prescription for P(X | nuclear war is going to happen) valid for all X; I have even no idea how such a prescription should look like even if infinite computation power was available, if you don’t want me to classify all sorts of information and all sorts of hypotheses relevant to a nuclear attack. Of course it would be nice to have some general prescription allowing to mechanically detect what information is relevant, but I think this a problem different from Bayesian updating.
“Apply Bayes’ rule anyway” is not a method of reasoning unless we have some way of determining what the numbers are. If we don’t have a method for finding the numbers, then we still have work to do before calling Bayes’ rule a method of reasoning.
I haven’t said we haven’t some way of determining the numbers. I have said that I can’t concisely formulate a rule whose domain of definition is the set of all possible information. What you are asking for is basically outlining a large part of the code of a general artificial intelligence. This is out of reach, but it doesn’t mean we can’t update at all. Some probabilities plugged in will almost certainly be generated by intuition, but I don’t think method of reasoning has to remove all arbitrariness to be called such.
What you are asking for is basically outlining a large part of the code of a general artificial intelligence.
Kind of! I’m asking for the best algorithm for human intelligence we can come up with. I guess that indeed, the phrase “apply Bayes’ rule” is significantly better than nothing at all.
What information you are updating from?
All information available to me.
Such as? I am probably unable to give you a wholly general prescription for P(X | nuclear war is going to happen) valid for all X; I have even no idea how such a prescription should look like even if infinite computation power was available, if you don’t want me to classify all sorts of information and all sorts of hypotheses relevant to a nuclear attack. Of course it would be nice to have some general prescription allowing to mechanically detect what information is relevant, but I think this a problem different from Bayesian updating.
“Apply Bayes’ rule anyway” is not a method of reasoning unless we have some way of determining what the numbers are. If we don’t have a method for finding the numbers, then we still have work to do before calling Bayes’ rule a method of reasoning.
I haven’t said we haven’t some way of determining the numbers. I have said that I can’t concisely formulate a rule whose domain of definition is the set of all possible information. What you are asking for is basically outlining a large part of the code of a general artificial intelligence. This is out of reach, but it doesn’t mean we can’t update at all. Some probabilities plugged in will almost certainly be generated by intuition, but I don’t think method of reasoning has to remove all arbitrariness to be called such.
Kind of! I’m asking for the best algorithm for human intelligence we can come up with. I guess that indeed, the phrase “apply Bayes’ rule” is significantly better than nothing at all.