When the question is merely posed as "Is the bottle half empty or half full", we have no more information than that. We don't know whether it has been filled or emptied, we don't know if the environment is the same as ours right now. All these are assumptions. As I told Matt, we can just as well assume that the rest of the bottle is a vacuum.
In an environment such as ours the bottle is never half empty. Half of it will be filled with various gases while the rest will be filled with some other substance, most likely some sort of liquid.
The terms "Half full" and "Half empty" are idiomatic expressions, they're not ment to refer to the gases contained within the container.
Given that it is irrelevant whether or not you describe the state of the bottle as "half full" or "half empty", both are idiomatic expressions that accurately describe the state that the bottle is in. Namely that half of the bottle contains the relevant substance. Arguing that either descriptions are "incorrect" is purely pedantic as is perfectly clear what anyone using either description means.
Language is a medium, it is a means to describe reality to someone else. If multiple descriptions describe the same thing that isn't necessairily a problem. There isn't one that must be false and in this case, both are valid.
Missed breakfast- ½ empty
Rebuffed flirtation at the market- ½ empty
Failed attempt D: to do a wheelie on the bike I used to ride when I was 8- ½ empty... ...you get the idea
Unless something like^ happens, it's ½ full.