Justification of probability theory

The axioms of Euclidean geometry( AEG) are true because every statement( or derivation from axioms) and axioms made in AEG corresponds to a true statement in a flat 2-D world. Thus, every statement in AEG are true because they correspond to something we can see, or visualize. We can conceivably imagine a 2-D world. This is the approach to geometry by 19 century mathematicians. This is also the modern approach to the nature of truth as statements corresponding to a particular model.


How do we justify Probaility theory? There are 2 formulation to probability theory. One is the frequency formulation of probability. This is a outdated formulation. No one use it, and i don` t care for it. The modern approach to probability theory is formulated into 3 axioms in the 1930 s by a russian mathematician. The whole of probability theory expand on this three axioms. Here is the problem. The advanced formulation incorporate normative component to probability. Probability no longer need to be about the odds of doing something infinite many times. It could be about degrees of believe in a propositions, or occurence. For a physical occurence A, and epistemic agent is supposed to assign a number between 0 and 1. Similarly, a agent could assign a number between 0 and 1 to the believe of the proposition "the moon is bad of chease" etc. This is a problem, because we cannot justify probability theory in the way we justify Euclidean geometry. There is no model for each statements in the theory to "correspond to". Probability seems to be more of a "tool" used to express our state of belief. According to alot of modern philosophers, this is how we ought to interpret probability. What do you guys think?