[kgwgk]

Fine. I was trying to answer your question "what do people mean when they say they're 33% sure that tomorrow it will rain". They mean that they find twice as plausible that it will not rain. It's just that you don't understand it as they do.

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

The rules of probability _are_the_consequence_ (once the value of certainty is fixed to 1)

    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)

and the use of probabilities to represent degrees of belief is not something you come up with. It is derived from the assumptions above (which don't involve probability at all).

[lottin]

Alright, thank you. I don't think that this is right at all, but I will give it a further thought when I have the time. Nice talking to you.

[kgwgk]

Depending on your background, you may find this paper interesting http://jimbeck.caltech.edu/summerlectures/references/Probabi...

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.