[nieve]

Isn't declaring "the raison d’être of probability theory is to explain the decision-making of individuals facing uncertainty" basically a claim that the sole purpose of probability theory is an economist's approach? It's entirely possible that much more work in probability is done without a bet or payoff in sight than is done for the sake of decision-making models. It seems like basing epistemological arguments about all probability theory on a framing friendly to very specific groups of non-mathematicians.

[glial]

What is a probability? Nearly always, a probability isn’t a statement about the world, it’s a statement about your knowledge and the information you have. Even for frequentist statisticians, equating probabilities with proportions of outcomes is an admission that you only have partial knowledge about the outcomes.

Of course it also has mathematical structure and properties that may be interesting to people for their own sake. And there may be interesting things to say about quantum physics using probability, but I think a historian of mathematics would not claim that quantum physics was the driving force for the development of probability theory.

Anyway, the “raison d’être” != every conceivable use.

[alisonkisk]

Can you give an alternate definition for probability than "decision making under uncertainty?" I've never heard one. Sure there are mathematical real-analytic "theories of probability" but that's abstract analysis of measure, until it's applied to answer how... probable something is