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16th July 2009, 08:15 AM | #41 |
ancillary character
Join Date: May 2009
Posts: 1,474
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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.
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16th July 2009, 09:25 AM | #42 |
Muse
Join Date: Aug 2005
Posts: 569
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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. |
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16th July 2009, 09:47 AM | #43 |
ancillary character
Join Date: May 2009
Posts: 1,474
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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.
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16th July 2009, 10:03 AM | #44 |
Muse
Join Date: Aug 2005
Posts: 569
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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.
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