Of course we have not proved our view of the goal of thought. There can be no question of proof where the nature of proof itself is in question. All we can say is: Here is the standard and ideal that we actually use in thinking.
When we understand, it's always through a system. As our understanding grows more complete, it's always through a system of greater unity.
If the ideal seems unconvincing and artificial, consider its alternatives. Do they formulate better or worse what we mean by understanding? When we read a famous book called Ethics Geometically Demonstrated, most of us feel we are getting insight.
In the end this illumination is merely following associations.
But that explanation of understanding cannot itself be verified.
If we deny all degrees to necessity, and confine it to a set of the barest abstractions, not much insight remains. The genuineness of insight does not depend on ensuing changes in practice. Perhaps in a poem, a piece of music, or some religious experience an insight is gained that one hesitates to call understanding, because understanding has become so identified as something abstractly intellectual. But such insight is understanding, unique, limited in degree, but still with rights of its own. And to reject it as understanding on the ground of its concreteness is absurd.
If I accept the ideal of concrete necessity, these varying insights are legitimized, ordered, and appraised. If I accept any other, some insights must be excluded.