Two Perspectives One Cup

I think I've figured this out now.

The glass is entirely full of equal parts air and water.  Unless it's in a vacuum in which case it is truly half empty.  Although it may be half full of undetectable dark matter and therefore it is entirely full again.

No actually I think this is how it is.

If the glass starts empty and you fill it half way, it's half full because the process is filling it.  If the glass begins full and you empty half of it out, it is half empty because the process is emptying it.