Colin Howson, talking about how Cox's theorem bears the mark of Cox's training as a physicist (source):

An alternative approach is to start immediately with a quantitative notion and think of general principles that any acceptable numerical measure of uncertainty should obey. R.T. Cox and I.J. Good, working independently in the mid nineteen-forties, showed how strikingly little in the way of constraints on a numerical measure yield the finitely additive probability functions as canonical representations. It is not just the generality of the assumptions that makes the Cox–Good result so significant: unlike some of those which have to be imposed on a qualitative probability ordering, the assumptions used by Cox and to a somewhat lesser extent Good seem to have the property of being uniformly self-evidently analytic principles of numerical epistemic probability whatever particular scale it might be measured in. Cox was a working physicist and his point of departure was a typical one: to look for invariant principles:

To consider first ... what principles of probable inference will hold however probability is measured. Such principles, if there are any, will play in the theory of probable inference a part like that of Carnot’s principle in thermodynamics, which holds for all possible scales of temperature, or like the parts played in mechanics by the equations of Lagrange and Hamilton, which have the same form no matter what system of coordinates is used in the description of motion. [Cox 1961]