[Question] Jaynes-Cox Probability: Are plausibilities objective?

[Haziq Muhammad]

Is the objectivity of plausibility assignments assumed in the Jaynes-Cox formulation of probability theory?

This is what I mean by “the objectivity of plausibility assignments”:

$A$ and $B$ are propositions.$\left(A|B\right)$ is the plausibility of $A$ given that $B$ is true and is represented with a real number as a result of our desiderata. Is the quantity $\left(A|B\right)$ uniquely determined by $A$ and $B$?

If this is the case, is this one of the assumptions that we make (implicitly or explicitly) or can this be derived from our desiderata?

If not, then in what sense is the plausibility of $A$ given $B$ objective?

Thank you