According to quantum theory, empty space is, well, not that empty after all. Rather it is full of virtual particles – particles that quickly blip in and out of existence. Theory states that a mirror can absorb energy from some of these virtual photons, and re-emit it as actual photons. Of course, this only works if the mirror is traveling through the vacuum at nearly the speed of light, making it difficult to prove, to say the least.
http://www.popsci.com/science/article/2011-06/quantum-first-light-created-vacuum
Ryan S covered the cognitive bit quite thouroughly so I'll say this about physical vacuum: its "non-emptiness" has been pretty much demonstrated 60 years ago by the Casimir effect, which I think is really cool but I might be a nerd.
If we still have a concept of vacuum in science, it's only as a reference, an ideal case, like the absolute zero (which is basically the same thing, i.e. the lowest possible energy state).
Still, in everyday life saying that your glass is empty is less confusing than stating that it is full of air.
Well why didn't you say so sooner. You know how much time I've wasted wondering if nothing was really something, when all the while I just needed to hear you say how it is.
Nothing is something in your imagination.
In the real world, nothing is nothing.
When scientists put bonobos (one of the words from the spelling bee) or macaques into a room that is alight with a tint, be it green or red, they see habituation occur in the occipital lobes of the apes. Eventually their brains stop reacting to the colored-light, it merely becomes as if it was white light. The brain habituates to the most common features in it's environment. White-light is defined by the contrast with incidental light. So it is with us, that which is most common in our environment and our experience is made transparent, invisible, undetectable. The old saying goes; we are like fish trying to find water. Because we spend our entire lives in water, and because to see water clearly would seriously impede our lives, we never experience the water except as negation.