Nothing is an object. We can, for example, think about it. (What things were like before God created the world.) Heidegger, indeed, claimed that one can have a direct phenomenological experience of nothing in a rather pessimistic way:22
Does such an attachment, in which man is brought before the nothing itself, occur in human existence?
This can and does occur, although rarely and only for a moment, in the fundamental mood of anxiety (Angst) . . .
Anxiety reveals the nothing.
This does not, of course, entail that nothing exists. One can have direct phenomenological acquaintance with non-existent objects. (Try thinking of Zeus!) Indeed, nothing does not exist since, presumably, it is impossible for it to enter into causal interactions with things.
Of more importance is that nothing is a contradictory object. Since it is an object, it is something.23 But it is the absence of all things too; so nothing is nothing. Everything is the mereological sum of the universal set. Nothing is the mereological sum of the empty set. (We will see how this idea can be articulated in the Interlude on Nothing, Section 6.13.) But there is nothing in the empty set, so nothing is absolute absence: the absence of all objects, all presences.24 It is no thing, no object.
The Chinese/Japanese character for nothing is 無 (Chin: wu; Jap: mu). Using this for ‘nothing’, we therefore have: 𝔖x x = 無 and ¬𝔖x x = 無. Nothing both is and is not an object. In this respect, it behaves exactly as does a proper gluon. In fact, it is a gluon. For nothing can have no parts (other than itself): if it did, it would not be the absence of every thing. Hence, it is a simplex, and so is its own gluon. Nothing is the gluon of nothing. In particular, then, improper gluons may be and not be objects.
There is much more to be said about nothing in later parts of the book. But before we even get to the second part, there is one final matter to be dealt with: the issue concerning SI, which I raised and set aside in Section 2.6. That is the topic of the next chapter.
22 Heidegger (1977), p. 102f. I certainly do not endorse his pessimism.
23 Philosophers often wonder why there is something rather than nothing. However, even if there were nothing—even if everything would be entirely absent—there would be something, namely nothing.
24 And even all absences.The absence of an absence is not a presence!