On Larval Subjects, Levi discusses three mereologies in a description of the relations between objects in subtractive OOO. To summarize (though you should read it yourself), when talking about a couple, there are three objects (the two individuals and the couple). As Levi lays out the basic theory:
Insofar as all objects are necessarily aggregates of other objects, it follows that objects cannot exist without their parts. However, while subtractive variants of OOO concede that objects cannot exist without their parts and that, indeed, one way of destroying an object is through the destruction of its parts, nonetheless objects are independent of the parts that compose them. In other words, objects cannot be reduced to their parts. The parts of an object are themselves objects that have their own autonomy and life. The larger object composed out of these parts is another object that has its own autonomy and life.
I understand this, but I also want to push on it somewhat and then comeback from the edge. As we think about parts and aggregates, at the limit we encounter two kinds of strange, conceptual singularities. I say they are "conceptual" because no human can or at least has experienced the universe or quantum foam directly. Quantum foam is theoretical physics. In theory (and based on my obviously non-expert understanding of such matters), a philosophy of objects doesn't really work on the quantum level unless it has a kind of Deleuzian virtuality.
In a different way, the universe, while a more familiar concept, is equally problematic. Following the OOO line of thinking where an object is independent of its parts, the universe is something in excess of what makes up the universe. But where would that excess come from if not from the aggregate relations of the objects? Perhaps the universe is one of many. Energy and matter get sucked into black holes; maybe these are passages beyond the universe. Maybe. However, what this points to is the problem of thinking about totalities or wholes. Now this is certainly addressed in OOO where we understand "the withdrawal of objects."
Objects in the mirror of subjectivity are other than they appear.
What quantum foam and the universe might present are virtuality and absolute exteriority. If quantum foam is real, then all objects emerge continually from an immanent, undecided sub-atomic turbulence that exists both inside and outside our conventional notions of time and space. This is the virtual as I understand it.
On the other hand, a totalizing object, like the universe, demands the recursivity that exteriority offers. That is, in a more local example that Levi uses, I am a citizen of the US, and as such I am part of the object. But at the same time, being a citizen is part of me. The US is part of me. Inasmuch as the US as a nation is an object, aggregated from other objects but also in excess of the expressed characteristics of those objects, and I am similar aggregate, we are both exposed, exteriorized, to one another. I am part of the US; the US is part of me; and the relation (the coupling of the US and me) is a third.
There were three in the family, and that's the perfect number.
Of course, in a Deleuzian spirit, we might mount an anoedipal response to such a calculation: rather than the three points that define a plane, there are always n – 1 dimensions to relations.
It is not the One that
becomes Two or even directly three, four, five, etc. It is not a multiple
derived from the One, or to which One is added (n + 1). It is composed not
of units but of dimensions, or rather directions in motion. It has neither
beginning nor end, but always a middle (milieu) from which it grows and
which it overspills. It constitutes linear multiplicities with n dimensions
having neither subject nor object, which can be laid out on a plane of consistency,
and from which the One is always subtracted (n – 1). (ATP)
The "it" in this blockquote is the rhizome. If the universe is One, it is composed of directions in motion from which it grows and overspills. I am a part of the universe; the universe is part of me; the universe and I have a relation, which is three, but n -1 dimensions laid out on a plane of consistency, the virtual, the turbulent sub-atomic non-spacetimes of quantum foam. Given these recursive, exteriorized relations, it is not possible to say where the universe or I begin/s or end/s anymore than it is possible to count the dimensions of a fractal.
As I understand it, the issue for OOO is to say that object relations do not need to travel "all the way" down to the sub-atomic and back up. I agree. Furthermore, the realm of quantum foam might suggest a degree of randomness and mutation in the universe which, at least, is not locally observable in our light cone. As always, Newtonian physics remains good enough for predicting my experience of the world. This is what I meant earlier when I said I want to come back from the edge of reality. I see concerns like the virtual and totality as being taken up by OOO in a way that is not unlike the philosophy's address of correlationist concerns with ideology and representation. That is, to address these things as matters of degree. Yes, my coffee mug arises from the virtual, from quantum foam, I suppose. And yes, the fact that it is a "coffee mug" indicates it has some semiotic dimensions, and even ideological ones. But let's not forget that it is also a mug, with characteristics that are quite obviously different from sub-atomic particles, and that exceed capture within semiotic and ideological apparatuses.
Still "the mug" that I grasp (physically and mentally) is the one that is subtracted from the n. Perhaps this is what is meant by the "subtractive variants of OOO."