What is the smallest possible number of objects an object-oriented world can contain? It seems as if it has to be either a small integer greater than one, or infinitely many.

It has to be more than one, because you need at least two for any object to make a difference to another object: a single object not making a difference to anything (and not withdrawing inscrutably from relation with anything) doesn’t really exist as an object. A dyad of two discrete objects, each acting as existential foil for the other, is enough for the basic dialectic of objecthood to get going. But you then need a third object to localize (stage, witness, encapsulate, emplace etc.) their interactions. And possibly a fourth object, after that, to stand apart from the third. For any given object, there must be an object it makes a difference to (and is not exhausted in the difference it makes to it), an object that localizes this pair, and an object that is “outside” the theatre of its interactions. If four objects can all reciprocally be these required collaborators for each other, then four’s all you need; otherwise, you may well end up with an ever-ascending hierarchy.

If any object, considered as a black box (or theatre for the interactions of other objects), can be opened out into multiple sub-objects, and if there is no halting point to this downwards proliferation of nested sub-objects, then any object-oriented world must contain infinitely many objects. But I think it may be a mistake to think of localization (or “being a theatre for”) as strict containment. In other words, I think the “black box” metaphor is suspect - it sets up, as if by magic, a clean-cut and interminable Russian-doll hierarchy, in place of the strange loops and leaky abstractions with which we are acquainted by experience.

Suppose we have three objects, A, B and C. A is a theatre for the interactions of B and C, B hosts A and C, C hosts A and B. If you “open up” any of these three objects, you find that “internally” they articulate two others; but if you drill down through A into B, you find A again on the “inside” of B. The black box metaphor suggests that this should be impossible: you don’t find a box inside itself (unless that box is a Tardis that has materialized around another that has materialized around it…). But the figure knotting together these three objects is scarcely unthinkable…so perhaps we don’t have to commit ourselves to an infinitely-descending containment hierarchy after all.