Yeah, the position in academic philosophy as I understand it is: Dutch book arguments aren’t really about betting. It’s not actually that we’re so concerned about bets. Rather, it’s a way to illustrate a kind of inconsistency. At first when I heard this I was kind of miffed about it, but now, I think it’s the right idea. I suggest reading the SEP article on Dutch Book arguments, especially Section 1.4 (which voices your concerns) and Section 2.1 or section 2 as a whole (which addresses your concerns in the way I’ve outlined).
Note, however, that we might insist that the meaning of probability is as a guide for actions, and hence, “by definition” we should take bets when they have positive expectation according to our probabilities. If we buy this, then either (1) you’re being irrational in rejecting those bets, or (2) you aren’t really reporting your probabilities in the technical sense of what-guides-your-actions, but rather some subjective assessments which may somehow be related to your true probabilities.
But if you want this kind of “fully pragmatic” notion of probability, a better place to start might be the Complete Class Theorem, which really is a consequentialist argument for having a probability distribution, unlike Dutch Books.
Yeah, the position in academic philosophy as I understand it is: Dutch book arguments aren’t really about betting. It’s not actually that we’re so concerned about bets. Rather, it’s a way to illustrate a kind of inconsistency. At first when I heard this I was kind of miffed about it, but now, I think it’s the right idea. I suggest reading the SEP article on Dutch Book arguments, especially Section 1.4 (which voices your concerns) and Section 2.1 or section 2 as a whole (which addresses your concerns in the way I’ve outlined).
Note, however, that we might insist that the meaning of probability is as a guide for actions, and hence, “by definition” we should take bets when they have positive expectation according to our probabilities. If we buy this, then either (1) you’re being irrational in rejecting those bets, or (2) you aren’t really reporting your probabilities in the technical sense of what-guides-your-actions, but rather some subjective assessments which may somehow be related to your true probabilities.
But if you want this kind of “fully pragmatic” notion of probability, a better place to start might be the Complete Class Theorem, which really is a consequentialist argument for having a probability distribution, unlike Dutch Books.