TL;DR: A glass drinking vessel filled halfway to its brim with water in a room at standard temperature and pressure at sea level on Earth is mostly empty.
Is the glass half full or half empty?
The immediate snarky answer is that it's entirely full, but only half of it is full of water; the other half is full of air.
Further snarky thought will however lead one to remember that most of the volume of a given substance is empty space, sparsely dotted with atoms jostling about within it. Further thought along that line brings to mind the supposed fact that atoms themselves are mostly empty space, so the glass is definitely mostly empty.
Still further thought, however, reminds one that the fundamental subatomic particles are all infinitesimal points, interacting with each other through forces, which forces prevent other things from occupying some volume, but still in the end, the stuff "filling" the glass is a spattering of zero-volume points interacting with each other through empty space. So really, the glass isn't just mostly empty, it's entirely empty, and so is the whole universe.
But, still further thought will lead one to remember that those forces, and the point-particles themselves, are really all just excitations in energy fields, most of which usually have a nonzero value most places you might find glasses of water, and one of which, the Higgs field, definitely has a nonzero value everywhere. So, in a sense, the glass is again entirely full, and so is the whole universe.
At this point though, it's worth considering what exactly we mean by "full" to begin with. We say the glass is full of water when, upon trying to pour more water into it, that water just ends up on the table and not in the glass. In other words, the glass is full when you can't put anything more into it. But we can definitely put a lot more into that glass than is in there right now.
To start with, yeah, we could pour more water in, and then it will be more full.
But that water is still "mostly empty space". Under normal circumstances water, like any liquid, is mostly incompressible, but
Squeeze enough more water into there hard enough and the water will eventually become solid instead of liquid, but even solids can still be compressed, you just have to squeeze even harder. Thanks to adiabatic heating the glass itself might (temporarily?) become a liquid somewhere along the way here too, I'm not sure of all the specifics of the phase diagrams of glass and water.
In any case at some point you're going to end up with a hot dense plasma of hydrogen, oxygen, and silicon long since dissociated with each other. Keep squeezing more and more "water" (hydrogen-oxygen plasma) in there and some of those atoms will start to fuse together into denser and denser elements. Keep squeezing more into the glass and eventually even the electrons will start to fuse with the protons and you'll have a "glass"(-shaped magic force field) full of nothing but neutronium.
But it's still not full! Keep squeezing more and more into that "glass" until it contains enough mass that its self-gravitation makes it impossible for anything inside of it to escape from it... and congratulations, not only if your glass finally full, but you no longer need your magic force field to contain it! Because it's a black hole now. Anything more you want to add to it, you're going to need a larger volume, and you'll automatically get one real soon now, so yeah, now it's definitely full.