WHY believe reality is intelligible?
The total is intelligible only if it's a system, all-inclusive, and perfectly integrated.
And perfect integration assumes that no two parts can each be different from the other without each entailing a difference in the other. Hence, perfect integration is possible only if all the parts are internally related by difference.
And without the constant influence of the implicit ideal of thought in the scientific search for connection beyond apparent irrelevance, that belief would probably have been dismissed a long time ago as fanaticism or even atheism.
Proof of the rationality of things is not logically possible, since it would assume that same supposedly independent rationality whose applicability is in question in trying to prove it.
But the question is not whether logic is applicable to some unexperienced object. It's whether our known world of persons and things can be understood or intelligibly construed.
If the known world of things and persons cannot be understood or intelligibly construed, then thinking is useless from the start, since the conditions of understanding could not possibly, in that case, be fulfilled. The question "Why?" would simply have no answer when it is asked about various arrangements in the system.
Even uncertainty about the answer would leave us permanently ignorant, not just about whether we can know reality, but whether there is any knowledge about reality.
Science and theory assume we can know reality. And at each successive step in thought when I ask why, I assume there's an intelligible answer, whether I find it or not.
But the desirability of something does not prove it exists. Any evidence that the world I'm trying to construe is a set of internally related parts must come from other more basic sources.