There is at least one sort of nothingness which is impossible. Take the set of all possible worlds, including the actual world (supposing there is such a set). Now imagine that instead of that, there were nothing. Or again, imagine that every possible world were empty. Then nothingness would be necessary and the existence of anything at all impossible. Given that there actually is something, this sort of nothingness is evidently impossible.
Are other sorts of nothingness also impossible? It is often thought that the impossibility just described entails that it is necessary that something exist, even if no single thing exists necessarily. A common argument to this effect focuses on possibilities. It goes like this: if there were nothing at world w, then at w no proposition would be true or false, hence nothing would be possible or impossible. But e.g. it is possible at w that I exist, since I actually do. Hence it is false that there is nothing at w.
This is an argument about truthmakers – things which make propositions true. Thus there are several options for responding to it. First of all, we could try denying that truths need to have truthmakers at all. Of course, we needn’t go this far. A weaker variant would deny only that possible truths require their own truthmakers. This too seems like strong medicine. Yet weaker, and more palatable, is the following: even if possible truths require truthmakers of some sort, it remains doubtful whether, if it is possibly true at w that I exist, there must be something in w which is the truthmaker supporting that possibility. The alternative, which is prima facie viable, is to let possibilities at w be supported by truthmakers at other possible worlds.
A different sort of strategy for using possibilities against the possibility of nothing is this: regardless of whether a possible truth needs a truthmaker, if it is possibly true at w that I exist, then this truth, this proposition, must itself be something, i.e. it must exist in w. This strategy focuses on the truthbearers rather than the truthmakers of propositions. The proponent of this argument could accept (arguendo) that the truthmaker of the proposition that I could exist needn’t exist in w, but she denies that this gets the nihilist – the defender of the possibility of nothingness – off the hook. The reason, she says, is that the truthbearer of that proposition must exist in w.
How ought we to respond to this? Supposing we want to keep believing that there are various things that are true at the empty world w, it follows that we must deny that a proposition must exist in w in order to be true there. This is the distinction between truth at a world and truth in a world. The idea is that various things are true at the empty world, but nothing is true in the empty world. If this distinction works then neither the objection from truthmakers nor from truthbearers will pose a problem for the nihilist.