I think the point is that
a) The reals are most convenient for representing plausibility.
b) Any results that hold under the transitive and universal comparability laws will still apply if we represent plausibility with reals, so you might as well use them.
So axiom 1 of Cox’s theorem is just “plausibilities can be represented using reals”, not “plausibilities must be represented using reals”?
I think the point is that
a) The reals are most convenient for representing plausibility.
b) Any results that hold under the transitive and universal comparability laws will still apply if we represent plausibility with reals, so you might as well use them.
So axiom 1 of Cox’s theorem is just “plausibilities can be represented using reals”, not “plausibilities must be represented using reals”?