The universe cannot possibly be illogical, because epistemologically it makes no sense to suppose it’s illogical if there’s no way, even in principle, of observing something illogical in the universe.
You cannot possibly observe an illogical event or combination of events. You may think, for example, of observing something violating any rule we know of or intuit about reality (such as two solid things taking up the same space, or maybe the superpositions known to actually occur in quantum mechanics), but any such instance would only necessarily indicate a previously unknown or counterintuitive aspect to the laws of physics.
To observe something that’s actually illogical, you’d have to observe something tantamount to, for example, a square circle. And you can never manifest or observe a square circle by definition. The concept of perceiving a square circle is logically self-contradictory, and hence it can’t happen.
The fact that the universe cannot possibly be illogical, for the above logical reasons, means that the “data” of the fact of the universe’s not being illogical isn’t “out there” in the universe, but necessarily follows from our own epistemology or logic. So, the universe cannot be intrinsically illogical.
If the universe cannot be intrinsically illogical, then it cannot be intrinsically logical either. The opposite of illogical is, of course, logical, and, if the universe could not have been anything but logical, then, again, the “data” of the fact that the universe is logical wouldn’t be “out there” in the universe, but would necessarily follow from our epistemology or logic.
If the universe were logical, then it would be, on some suitably deep metaphysical level, incidental that that it’s logical, so that it could hypothetically have been observed to be some other way. But, as we’ve already demonstrated, it cannot be observed to be any other way. Hence the universe is not, itself, logical.
Logic is therefore only in our minds and how we choose to assimilate, or at least synthesize an understanding/mental model of, the universe. It seems to the semantic organizing principle of our minds, or one important, overarching aspect of it.