The two are still locked in a debate which is ultimately the result of interpreting one question in two different ways, and then answering the two seperate questions as if they were exclusive answers to one question. Exactly as the two argue about sound being there in the absence of observers.
Not exactly. The real argument is about what should be used for inference (both scientific and otherwise). The debate about “what probability actually is” is just another case of debating semantics as a proxy for debating what’s actually at stake.
Yes, I think we agree. Except that i don’t think that the fact that there is meaningful argument to be had about bayesian inference v.s. frequentist inference, means that the debate has not been centered around arguing about what probability is, which is a mistake; the same class of mistake as the mistake being made by the realists and idealists arguing over sound. The bayesian and the frequentist have proposed ways to settle their debate. And there are observations which act as evidence for bayesian inference, or frequentist inference. But exactly what experience should i expect if i think “probability is frequency” as opposed to if I think “probability is subjective degree of belief” ? Arguing about which inferences are optimal, is perfectly reasonable, but arguing about what thing probability really is, is silly.
Yes, I think we agree. Except that i don’t think that the fact that there is meaningful argument to be had about bayesian inference v.s. frequentist inference, means that the debate has not been centered around arguing about what probability is, which is a mistake...
Did I give the impression that I thought the argument about what probability is wasn’t a mistake?
Not exactly. The real argument is about what should be used for inference (both scientific and otherwise). The debate about “what probability actually is” is just another case of debating semantics as a proxy for debating what’s actually at stake.
Quick edit: and your post helps make this clear.
Yes, I think we agree. Except that i don’t think that the fact that there is meaningful argument to be had about bayesian inference v.s. frequentist inference, means that the debate has not been centered around arguing about what probability is, which is a mistake; the same class of mistake as the mistake being made by the realists and idealists arguing over sound. The bayesian and the frequentist have proposed ways to settle their debate. And there are observations which act as evidence for bayesian inference, or frequentist inference. But exactly what experience should i expect if i think “probability is frequency” as opposed to if I think “probability is subjective degree of belief” ? Arguing about which inferences are optimal, is perfectly reasonable, but arguing about what thing probability really is, is silly.
Did I give the impression that I thought the argument about what probability is wasn’t a mistake?
I wasn’t sure.
Oh, well in rereading my comment I could see why it was ambiguous. Yeah, I think we agree.