I agree that analysis of concepts is sometimes necessary to get to the bottom of disagreements, especially if people are talking past each other. Those end up being semantic disagreements, or differences in how we're using our symbols.

But if you're saying that we often mistake the map for the territory, or reify our concepts, your mathematical analogy might be reinventing the wheel.

There are roughly two views of our representations of reality. We can be realists or pragmatists. Realists say that a statement is true if it agrees with the facts. That means there might be one best characterization of the facts, and all the other ones are wrong.

Pragmatists say there's no metaphysical agreement or correspondence between fact and symbol. Our symbols are tools that perform certain jobs. Some tools work better than others, depending on the conditions. We can explain why our tools work by positing the truth relation between facts and adequate statements, but the pragmatist will insist that that explanation is justified more by its utility than by any known metaphysical agreement between our minds and the rest of reality.

I side more with the pragmatists here, although I'm wary of the extreme, "postmodern" forms of relativism and subjectivism. Our use of symbols shouldn't be arbitrary, because there is a knowable external reality out there. But there's no magical, absolute fit between a human mind and the world that that mind encounters.

All of our conceptions are all-too human and mammalian to be adequate to nature's monstrous, inhuman reality. With the likes of philosophy and science, we're doing the best we can and we are indeed in some kind of progressive relation with reality, given the success of our technological applications of our most rational theories. But we should remain humble and grounded in an appreciation of our relative smallness and of the vanity of our inclinations.