Let me say at once I don’t know how to think about things that I like to think about without invoking existence. Our logic seems to demand things to talk about, and properties of those things. Reification is the habit we have as we make sense of the world. It is perhaps necessary to make a living in this universe.
I recall my horror when I learned that the Pauli exclusion principle was a result of the fact that the description of two fermions involved a function f(x, y) where x had to do with where the first particle was and y the second. Because f(x, y) = −f(y, x) meant that f(x, x) ≡ 0 which implied that the two particles could not be in the same state. This was given as the ultimate reason that everything in the world couldn’t be at the same place. I knew at that point that physics would not provide enlightenment about things in the world.
Another crunch came when it came to my attention that there were real numbers that could not be identified, let alone named. This is merely because only denumerably many things can be named, and that is not enough for the uncountable reals. The recent book “Naming Infinity” traces this urge more generally in mathematics. A friend of mine felt better when she learned the name of her affliction: “idiopathic hypogeusia’ until she translated it from the latin as “You can’t smell and we have no idea why.”. We feel better when we have names for things, as if that puts us in control.