"The question whether objective truth can be attributed to human thinking is not a question of theory but is a practical question. Man must prove the truth — i.e. the reality and power, the this-sidedness of his thinking in practice, …"is echoed, I think, in the difference between the pragmatism of James (truth is what works) and that of Peirce (truth is what inductively prevails). Since diagrams are essentially fictions and all kinds of fictions — illusions, wishful thinking, etc. — may work but hardly comply with our notion of truth, it is hard to say the Jamesian sort of pragmatism works. But with Peirce's sort of pragmatism what is true must not only work, it must continue to work through different applications. A diagram or theory must "prove" its "reality and power … in practice."
But let's take this a step further and hypothesize that it is this inductive rigor — not mathematics, empiricism, or even experimentation per se — that constitutes the truth and objectivity of science. This opens all kinds of diagrammatic thinking, even philosophy, to the possibilities of science. There may be problems with exactness, expanding the range of applications, or maintaining a community of investigators, but all diagrammatic thinking can submit itself to further applications, assess the consequences of doing so, and adapt itself to the results.