science

Right you are putting words in my mouth.

I never said that you derive it from axioms first, although I'm sure there exist theories which were derived from previous work especially some classical theories. The point I'm making is that a set of equations has to be self consistent, and sovlable, both of which are provable properties of those equations. That says NOTHING about the physical validity of the equations. However if you can't prove those properties on some level, you have a pretty nonsense set of equations.

Like I said you aren't "proving" that the theory is what governs whatever phenomenon, rather that it is consistent with itself.

As for finding the range of validity, again I agree with on that point, although I'm 100% sure there exists cases where you can predict the theory breaks down - just from looking at the equations, or deriving the bounds. But like I said, the equations still have to be non contradictory and solvable. In fact if they aren't solvable you cannot begin to verify them.

I completely appreciate that you are right about unable to prove a theory like you said. I'm pointing out that most people use proof to refer to showing that the equations aren't contradictory, again that doesn't prove the theory, but we know a good theory doesn't contradict itself, and hopefully it doesn't contradict other stuff, although relativetivity contradicts quatuam, indicating something else is going on.