Cox’s theorem proves that probability theory is the unique consistent framework for reasoning under uncertainty.[1][2] Any system satisfying basic consistency requirements must be isomorphic to probability theory.
This framework is compositional over viewpoints: you assign probabilities over models/hypotheses and update via Bayes’ rule. Aumann’s Agreement Theorem shows that rational agents with common priors who update on shared evidence converge in their beliefs.
[1] Cox, R. T. (1946). “Probability, Frequency and Reasonable Expectation”. American Journal of Physics. 14 (1): 1–13.
[2] Cox, R. T. (1961). The Algebra of Probable Inference. Johns Hopkins University Press.