You’re correct that probability still works in a hypothesized deterministic universe. It’s a point that’s often too often forgotten, causing discussions to go d

You’re correct that probability still works in a hypothesized deterministic universe. It’s a point that’s often too often forgotten, causing discussions to go down unnecessary rabbit holes debating foundations of quantum mechanics when discussing the roll of a six sided die. Statisticians and mathematicians have gone very far down the path you’re discussing, and you might be interested in some sets of axioms that have come up around probability and relaxations of true/false logic. The Kolmogorov axioms [0] are the “standard” probability axioms, and are phrased in terms of set theory and measure theory (not requiring any mention of physics or a physical universe!). There are other ways to quantify degree of belief, however, and they are very interesting. Apparently Cox’s theorem [1] justifies a popular probability framework for Bayesians. But there are many more interesting ways to do degree of belief, like Dempster-Schafer theory [2], which I understand to be a plausibility calculus. Everybody seems to find a single system and decide it’s the only one out there, [0] https://en.wikipedia.org/wiki/Probability_axioms https://en.wikipedia.org/wiki/Probability_axioms [1] https://en.wikipedia.org/wiki/Cox's_theorem https://en.wikipedia.org/wiki/Cox's_theorem [2] https://en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory https://en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory