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AstraSequi comments on [LINK] Common fallacies in probability (when numbers aren't used) - Less Wrong Discussion
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Comments (9)
To throw out an idea I never followed up on, I think the "probability of a model" is a category error. Most models we deal with, and particularly in the context of assigning probabilities to models, are not propositions that are true or false, but maps that are more or less accurate.
I'm not sure what the implications to model testing and generalization theory would be in that, but I expect there would be some, and it always just irked me to see things like P(M1).
I think 4 generalizes better as
Remembering Jaynes' "background information I" is often helpful.
Another way to generalize 4 is
I don't think "changes the issue" is the best way to say this, because there is always a probability that your model won't work even if it doesn't say something is impossible.
I don't know about this being a category error though. I think "map 1 is accurate with respect to X" is a valid proposition.
I think that's good too - Jaynes advocated including a "something else that I didn't think of" hypothesis to your hypothesis to avoid accepting something strongly when all you've done is eliminate the alternatives you've considered.
"Is accurate" isn't much of a proposition in itself, as it leaves out the level of accuracy.
Probability of a proposition. Propositions are true or false. Level of accuracy of a model. Models are more or less accurate.
Maybe "Is accurate enough that it doesn't change our answer by an unacceptable amount"? The level of accuracy we want depends on context.
How would you measure the accuracy of a model, other than by its probability of giving accurate answers? "Accurate" depends on what margin of error you accept, or you can define it with increasing penalties for increased divergence from reality.