“Constructing a Logic of Plausible Inference: A Guide to Cox’s Theorem”, 2003 (; similar):
Cox’s theorem provides a theoretical basis for using probability theory as a general logic of plausible inference. The theorem states that any system for plausible reasoning that satisfies certain qualitative requirements intended to ensure consistency with classical deductive logic and correspondence with commonsense reasoning is isomorphic to probability theory.
However, the requirements used to obtain this result have been the subject of much debate.
We review Cox’s theorem, discussing its requirements, the intuition and reasoning behind these, and the most important objections, and finish with an abbreviated proof of the theorem.