Principle of Worldviews and Pragmatism
As you will see, some axioms are twofold principles, wherein two related assumptions or beliefs are tied together.
Note: an assumption is an idea tentatively accepted as true or likely prior to any testing or examination. It is similar to a belief held in faith but ultimately more flexible and changeable. A belief, in the context of magic, is a utility of attention and intention mixed with expectation, which does not require faith because it is wielded as steel rod against the fabric of causality and the turbulence of fate or chance.
The World View
Your worldview is your understanding of reality, from outer space and nature to politics, biology, and everyday physics. Much of this is learned though instincts and intuition also play a formative role.
It is the worldview that allows you to form paradigms, or models for how reality works, and the worldview that provides all the raw materials for constructing those paradigms. Your worldview is the more concrete set of beliefs you hold about what this life is about, what our universe is and how it operates, while the paradigm can be more abstract and experimental (this will make more sense when you read the about principle of belief).
Regardless of what you claim to believe, or even what you want to believe, your worldview is what you actually believe to be true. While this is subject to change, such change may take time and effort.
Please also be aware that your worldview is simply the interface between yourself and the unknowable, objective reality, or the noumenal world from which the phenomenal world emerges or is drawn forth.
Enter Pragmatism
By itself, the principle of pragmatism states if it works, it is true. If a method gets the desired results, the underlying beliefs or explanations can be assumed true. Similarly if reality behaves as if angels and demons are real when the same are used in magical work, it then follows that angels and demons are real. In the world of empiricism and mechanism, indeed neither the precepts of a method nor the existence of spiritual beings may prove to be true, yet the efficacy and veracity demonstrated by affirmative magical results files them in the true/real category regardless of their ontological standing.
Ideally a magician seeks to reconcile with a worldview that can support his or her goal structure. Else he or she must resign to a goal structure the present worldview is capable of supporting.
There is nuance here, you are correct. I will not diagram it nor spell it iout for you on this occasion however, as it is important that you interpret the words above and navigate the path they lay out of your own makeup and nature.
The ire supportive of your goal structure in terms of tangible results, the more valid a worldview can be stated as being.