Anyway, I think you're getting the direction of the argument wrong. It's not that you have probabilities and force an interpretation of them as degrees of belief.
You start with real numbers representing degrees of belief (with an ordinal meaning only, a larger number means more plausible) and some "common sense" properties they should have to be "rational":
- having identical information should result in the same degree of belief
- the degree of belief in "not A" should be a function of the degree of belief in A
- the degree of belief in "A and B" should be a function of the degree of belief in "A given B" and the degree of belief in B
p(A) + p(not A) = 1
p(A and/or B) = p(A) + p(B) - p(A and B)
p(A and B) = p(A|B)p(B) = p(A)p(B|A)
In pages 5-9 he derives the rules of probability as a "reasonable expectations" extension to symbolic logic.
Of course you're right that this is a description of how rational thought should be and not necessarily a description of how people think. Actual beliefs can be inconsistent in the same way that one can believe things that go against the laws of logic.
It's always fun to discuss the foundations of probability. Thanks.
Do the rules make sense? The rules don't have to make sense, they're axioms. They're assumed to be true whether they make sense or not. We are not discussing the axioms. We are discussing interpretations of probability. In my opinion a good interpretation of probability must provide a context in which these axioms (kind of) make sense. And that's one of the problems I have with the interpretation of probability as a degrees of belief, the rules don't make sense in the provided context, at least to me, because I don't know how to make sense of arithmetic operations involving degrees of belief. (But that doesn't mean that I think the rules themselves don't make sense.)
Finally, even if you think that the human mind doesn't work in the way degrees of belief are hypothesised to work, you may still find the concept useful as a means of giving an interpretation to probability. Personally, I don't think that the mind works like that, nor that they're useful as an interpretation of probability. This is basically my position.