I misread the Cauchy example since I was going too fast, nevermind the symmetry part. > then that’s the purely frequentist view and then you also agree that it

I misread the Cauchy example since I was going too fast, nevermind the symmetry part. > then that’s the purely frequentist view and then you also agree that it’s meaningless I'm saying that when you hit "meaningless" you can back up a step to where you actually had randomness and look at that distribution, which gets rid of a lot of these issues. But after looking at these examples I think it only makes sense in limited circumstances to do that. Like in the trivial example: your final distribution isn't based on the probability of the mean being any particular number. The only probability was back a step and that was 50%. At this point I still don't think it's objectively wrong to say a particular interval above is 95% likely, but there's too many ways to interpret the statement so nobody should say it is. The way we're calculating that these intervals are "wrong" is by looking at all the possible parameters that could have given us the samples we got, and checking how often the range contains the parameter. That's a useful calculation but is it the one people expect? I think that depends on the situation. Treating the parameter as being the thing we sample over is misleading, but treating it as fixed is also misleading.