The scientific principle operates in the context of objective reality, which basically means two things:
1. The assumption that the observer and observed are completely separate.
2. The assumption that if many observers look at the same thing, it will still look/be the same thing.
Within this context, the scientific method operates as follows:
First we create a set of axioms; things and rules which we will assume to be present, true and valid.
Then we use these axioms on themselves, creating and unfolding a mental, abstract structure. When we're done unfolding, we have a comprehensive scientific theory.
We now have the axioms and the theory, and two choices lie ahead of us: either we do nothing further with it (then it's mathematics) or we do something (then it's the rest of science).
If it's not mathematics, we take a good look at our human world around us and see how well our theory fits the world we see.
If our theory fits well enough, we apply and use it to achieve something we wish to achieve.
If the theory doesn't fit well enough, we adjust the theory, fold it back, and try to find a new set of axioms which would unfold the abstract structure of the adjusted theory.
And so on and so forth.
The scientific principle is surprisingly useful unless you ignore its deficiencies.