An entity cannot not be and the definition of nothing is not being. Can we include "nothing" among the abstract entities or should we differentiate nuances of nothing, eg. the mathematical nothing, the idea of nothing and nothing itself? My main concern here is not "nothing" but the consistency of basic ontological axioms.
Any possible entity, whether concrete or abstract, exists only in our minds. In addition, our mind can create entities from nowhere (e.g. a gift, the infinite number, a consequence, a hole, a set of pending tasks). Nothing is just a mental entity representing an idea, the idea of the lack of entities. Exactly like the number 0, a hole in the ground (is there something physical as a hole?) or the infinite (it is something that doesn't exist, but we can use such idea even in physics).
In fact, any possible entity, abstract or concrete, is just a system (cf. systems theory), which is just a set of interrelated parts, and parts are also systems. A "family" is a group of individuals with certain features, related by certain events in the past, etc.
It is clear that abstract entities -a marriage, a hole, chaos, political preferences, exist only in our minds. But also physical systems. They exist only in our minds.
My favorite physical system example is a rainbow. It has exactly the same features as all other physical systems (think of a rock), but since parts are bigger and visible, they allow understanding the volatile concept of thing our mind has:
- A rock, nothing, and a rainbow are sets of smaller parts. The parts of nothing are the missing parts of a thing. Think of nothing in space or nothing in your room. Even if you think of a dark space in your room, you are essentially thinking on the lack of light in such space. And space itself is also a thing.
- Parts are related: clouds and rainbows have electromagnetic links inbetween, which gives them temporal cohesion. Just like rocks. Rainbows are just "easier" to be "broken" by us. A thing, or nothing is the same. A dark space is made of the lack of contiguous possibilities of displacement; or the lack of photons having specific properties that relate them in our minds.
- Rocks, rainbows or nothing exist only as perceptions in our minds. On nature, there are no boundaries on rainbows and rocks. Rocks are constantly mutating and exchanging fundamental particles with the rest of the environment. Just like rocks. And nothing in the floor? You will perceive it after your nose gets broken!
- We can interact with them. Perhaps we can throw an atomic bomb, creating changes on the set of parts and the rainbow; perhaps it moves as a whole. Exactly the same as interacting with the rock. Or a hole in the ground. When your finger interacts with the rock, atoms are just exhibiting repulsive forces. You never really touch a rock.
- There are no boundaries of things. Everything is just atoms, which are not particles, but moreover interaction probability clouds. You can see the sky, a hole or a rock, but everything is a network of "connected" atoms.
- Our mind and our bodies have the habit of interacting with groups (systems), not parts (elementary forces, at the end). Can you drink energy? No. You need energy converted to a system, a thing, a set of parts. Would you move a pile of sand by moving grain after grain? No. You take groups: systems, precisely of the size and form adequated for you to interact with them.
Conclusion: all things exist only in our minds. Nothing is also a thing. You can categorize ideas (things) as you like (phenomenon, noumenon? Existing, not existing? Occupying space or not?...).
Nothing is such a fundamental concept that it would certainly be helpful to have a definition of ontological nothingness that could be agreed upon and used in propositions about being, even if just to deny its possibility.
Such a nothing, I would suggest, is not just an empty set, not just an empty universe, it is the absence of all systems that could potentially define any particular kind of nothingness.
Such a nothing must mean, no space, no time, no numbers, no God, no Set Theory. Simply nothing. A nonentity, a state of non-being, that we could usefully refer to, if we had a name for it that didn't get confused by other ideas of nothings that are actually empty somethings.
Is it an entity? No. Is there an entity that is an abstract of nothing, one that we can usefully use as an idea? Yes.
Aside from the comment about linguistic entities, if we mean "physical nothingness"--what is left when everything is removed, as they say--then we're left with what nothing means to physicists.
In that case, philosophical nothingness is impossible as what the nothing of physics entails is virtual particles, fields, forces.
As far as I know, all other meanings of nothing about well-defined and generally owing to context.