A paradox is self-contradictory. It proves that itself cannot be true. The glass half full/glass half empty arguments are merely contradictory viewpoints. Each viewpoint is trivially self-consistent.
One could try to argue that there's a paradox in claiming the glass is simultaneously half empty and half full, and trying to argue that that is a self-contradiction there. However, it is mathematically completely sound, so there's no mathematical way to argue that a paradox can form.
So if we have to contort the original meaning of the phrase and leave behind the well accepted rules of mathematics, at some point we're really inventing a new phrase all together. We'd probably want to start from the question of "what should the paradox teach," and come up with a new phrasing.
A joke I remember from my Boy Scout days:
An optimist says the glass is half full.
A pessimist says the glass is half empty
A realist knows that if they sit around arguing long enough, eventually they're going to have to wash the glass.