I have read that someone defined nothingness as the empty set. Is this true? Is nothingness the empty set?
Sometimes the empty set is defined as the set of true contradictions, of which there are none, or as the set such that x: x≠x, for there is no such x. Or it might be defined operationally, as the empty inset operation. There's probably a way to define it as the -ness of nothing, but unless "empty set" isn't already a useful enough description, I don't see that we would have reason to call this thing "nothingness" also, except maybe as a paraphrase of "nothingness" ("that which we call by the name of 'nothingness' would be more aptly called 'the empty set' since otherwise it is hard to refer to something by referring to nothing").
EDIT: Note that we can use several descriptions here that could taxonomize our talk of "nothingness" better (Kant does something like this at one point). Let absolute nothingness be x that is neither an element nor a set. An ur-element is only an element, an ur-set is only a set (it is not an element of another set also). One might wonder about the propriety of talking about a necessarily empty set (is a box that always forces objects out of itself really a box?). Or, assuming strong well-foundedness, one might have it that the empty set is not said to be the set of true contradictions but the set of ill-founded sets (of which there are none, or this set is itself ill-founded). The list goes on...
" Nothingness is the same thing as the empty set" sounds like a piece of " badiology" ( from Badiou, the french philosopher ).
Maybe "nothingness = empty set" is a good approach to nothingness.
But I don't think the reverse, namely " empty set = nothingness", is a good approach to the empty set.
Just in th same way as 0 is not nothing, it is a number, the empty set is not nothing, it is a set.
Just for fun : https://www.youtube.com/watch?v=I1G_SI1-W-4
But maybe the thesis rests on a distinction ( parallell to the " ontological difference") between " nothing " and " nothingness". In that case my answer would be nullified.