Thank you OP for this very good and nice text!
I often do my best to make people aware of the topic, which really goes to the core of our "being here". I’ve studied philosophy and science for many years, and have been practicing spirituality for decades (with the term spirituality I don’t mean metaphysics, esoteric teachings, or any of that nonsense. To me, spirituality is the most stringent, and also the most empirical, science there is). I am also a professional musician and a professional sound engineer.
I would say that an approach increases its value insofar as you know the limits of that approach. And the limits include unquestioned assumptions, world views etc.
Each and every approach is a choice, an exclusion, a decision. This starts long before you make a measurement etc.
If you measure, and know exactly what the limitations of that measurement are - including the whole approach, the hypothesis that stands behind it, your world view, etc. -, then your measurement gives you valuable data. If you don’t know the limitations, or see them incorrectly, or expand them inappropriately in your imagination, your measurement is becoming less and less meaningful.
Good scientists are aware of that. Many of the great scientist went deeply into epistemology. For clear reasons.
And yes, you can prove that a lot of the concepts with which we approach the world cannot be true. And this isn’t something "subjective", this is strong science, logic, reason etc. Many (most, if not all) philosophers failed in that regard. Kant’s "Ding an sich" is absurd, but a correct outcome of his approach (which *could* mean that the whole approach is incorrect). Descarte’s "prove" of an outside world is hilarious, but very revealing. They took the mind to its limits, and failed there. Seeing how and why they failed is very illuminating. It tells us a lot about the mind and its inherent limitations.
Hegel critizised a lot of the mind’s approach, in a very good manner. His deconstruction of the approach "a thing is a bundle of characteristics" for example is marvellous, and very appropriate. A thing cannot be constituted of properties, and cannot be recognized through properties. Hegel’s analysis is stringent, rational and correct.
Good scientists are aware of the strong and profound limitations of the scientific approach. Unfortunately, a lot of people who use science to fortify their mind and their assumptions are not.
And to return to my first statement: If you know the limitations of an approach, you can make good use of the approach. If you don’t know the limitations, or misjudge them, you are out in phantasy land. And it is not possible to recognize the limitations of a system from inside that very system (Goedel).
Subject and object are not two. Which also means that you can’t keep the opposition between them, but choose only one of them. If you do so, you’re again out in phantasy land.