Probabilities

[Towlie]

I invite all of you who are interested in probabilities to please join me in this thread, and to comment on the view I offered in my post #13.

Thank you.

 

[GreedyAlgorithm]

Probability is an absolute objective state of nature that can often, although not always, be approximated by experiment or determined by analysis. Probability itself is not subject to opinion or differing points of view, although degree of confidence in an assessment of probability is.
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Confidence is different. Confidence is a property of a person and is affected by the knowledge that person has and his ability to properly analyze that knowledge, so different people can have different levels of confidence about an existing state of nature, based on what they know and how they analyze it.
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Confidence is a measure of personal certainty about a state of nature.

Probability is a state of nature.

You're putting these two on very different footing, for no reason I can see. You can happen to have whatever confidence you like about a state of nature, no one cares - the laws of mathematics specify exactly what degree of confidence you should have, given the knowledge you are bringing to bear. And lo and behold, those laws are identical to the laws governing expected frequency. And why not? The degree of belief any prediction engine should have given the knowledge available to it should be the same as the expected frequency computed given that same knowledge (call it "laws of physics" and "environment" if you don't like the term "knowledge").

If you want some sort of "absolute" probability, well, tough. Anything we compute can be no better than our proper degree of belief given the aggregated background knowledge from all of humanity. Maybe some claim there is an ideal absolute probability we would compute, had we all the knowledge available, and maybe so, but that's even further removed from the practical than anything I've heard about Bayesians.

 

[Towlie]

You can happen to have whatever confidence you like about a state of nature, no one cares - the laws of mathematics specify exactly what degree of confidence you should have, given the knowledge you are bringing to bear.

Yes, I agree with that. The degree of confidence that a person should have, given what is known and shared, is an objective quantity that can generally be calculated.

And lo and behold, those laws are identical to the laws governing expected frequency.

Yes, and that's interesting. The root-mean-square (RMS) mathematics used to calculate AC voltage and current are very much like the mathematics used to calculate standard deviation, but just because we use the same calculation methods, that doesn't mean the two concepts are the same.

If you want some sort of "absolute" probability, well, tough.

It exists whether you or I want it or not. The probability of a fair coin landing heads up when flipped is 1/2, and that's absolute.

Anything we compute can be no better than our proper degree of belief given the aggregated background knowledge from all of humanity. Maybe some claim there is an ideal absolute probability we would compute, had we all the knowledge available, and maybe so, but that's even further removed from the practical than anything I've heard about Bayesians.

That's little more than a personal philosophical view and it's one that I don't happen to share with you. I believe the Universe is rationally intelligible.

 

[GreedyAlgorithm]

Okay, sounds like we agree on everything then. I find your insistence that there is some fundamental difference between probability and degree-of-belief-given-that-we-know-everything to be distasteful, and I'm sure you think my insistence that they are the same is absurd, but that doesn't mean we have any disagreements about facts about the world.