> I think it's perfectly valid and necessary to make sense of reality. If existing things are something specific, then claims about them, if they make sense, must be true or false. If reality can be in some 'undetermined' state then... things get messy.

First, reality is messy. It's a whole lot more fucked up than your everyday intuition leads you to believe. This is an important lesson of modern physics. It is sadly lost on most people, for the simple reason that modern physics is quite inaccessible, and popularizations of it are too simplified to communicate any of the real concepts involved, or just plain wrong.

But even without invoking reality as such you can easily see that not all statements are true or false. Paradoxes like "this statement is false" are neither, obviously. You qualify your statement with "if they make sense", but if you do that, I can easily claim that any statement about the future does not "make sense".