Well, let’s not keep frequentism as a statistical method, cause bayes almost always if not always does better. But it is a theoretically interesting fact that komolgorov models finite frequencies, and our intuitions about infinite frequencies, and a fact that it does.
Understanding exactly what degrees of belief are, becomes a lot easier (I suppose) if you know that for some reason they are isomorphic to frequencies, and that for some reason they are also isomorphic to spatial measures. This not only allows us to solve problems of degree of belief by solving problems of frequency and area. But also, if we understand what degree of belief has in common with frequency and area, then we understand what it has in common with bayes.
Understanding exactly what degrees of belief are, becomes a lot easier (I suppose) if you know that for some reason they are isomorphic to frequencies
If probabilities were systematically wrong about the frequency of success in independent trials, there would be some other method of reasoning from incomplete information that was better than probabilistic logic. But since the real world obeys all the requirements for probabilistic logic (basically, causality works), there is no such method, and so frequencies match probabilities.
for some reason they are also isomorphic to spatial measures
Read a introductory chapter on set theory that uses pictures to represent sets, and you will understand why.
It’s certainly an interesting fact that these things behave the same. But it’s not an unsolved problem. We don’t have to keep a definition around that’s useless in the real world because of any lurking mystery.
Well, let’s not keep frequentism as a statistical method, cause bayes almost always if not always does better. But it is a theoretically interesting fact that komolgorov models finite frequencies, and our intuitions about infinite frequencies, and a fact that it does.
Understanding exactly what degrees of belief are, becomes a lot easier (I suppose) if you know that for some reason they are isomorphic to frequencies, and that for some reason they are also isomorphic to spatial measures. This not only allows us to solve problems of degree of belief by solving problems of frequency and area. But also, if we understand what degree of belief has in common with frequency and area, then we understand what it has in common with bayes.
If probabilities were systematically wrong about the frequency of success in independent trials, there would be some other method of reasoning from incomplete information that was better than probabilistic logic. But since the real world obeys all the requirements for probabilistic logic (basically, causality works), there is no such method, and so frequencies match probabilities.
Read a introductory chapter on set theory that uses pictures to represent sets, and you will understand why.
It’s certainly an interesting fact that these things behave the same. But it’s not an unsolved problem. We don’t have to keep a definition around that’s useless in the real world because of any lurking mystery.