The state postulate is as follows: The state of a simple compressible system is completely specified by two independent, intensive properties.
My first question is whether there is any justification for this postulate or whether it is simply an empirical law? That is, why is it not the case that 3 intensive variables are required to fix the state or even 4? If it is an empirical law with no justification and just happens to be a law our universe abides by, then why is it not one of the laws of thermodynamics as it clearly provides foundational value to the field of thermodynamics?
My second question pertains to how we can know whether 2 intensive variables are in fact independant. Say temperature $T$ and specific volume $v$ for example. If we are given a thermodynamic problem, how would we know whether these are independent or not? or perhaps specific internal energy $u$ and pressure $P$. Are there certain combinations that are simply always independent of each other or does independence between intensive variables vary from problem to problem and require a full understanding of the problem at hand? Let us take a phase change for example. From my understanding of phase changes, I know that the boiling temperature is dependent on the pressure and hence I won't be able to use $T$ and $P$ as 2 variables to completely specify the state. But how would I know know what combinations of intensive variables will be independent in this case or any other case for that matter? Does it simply require rote memorization of all independent pairs of intensive variables for all thermodynamic problems or is there a more simple way to figure out what is independent and what isn't?
I hope this question makes some sense and any help would be most appreciated!