ALL ob-ject-als are assemblages, but NOT ALL assemblages are ob-ject-als. (And I’m sorry you had to repeat yourself, but it does help.)
I like the example of the desk parts that are not yet a desk but (and perhaps I read this wrong) are you saying that every aggregate has the availability (and I like this word instead of potentiality because potential carries with it a notion of motive or purpose – but, as I see it, if no one put together the desk, that purpose or potential would never come to fruition) to become an assemblage? If so, this means that in order for an aggregate to become an ob-ject-al, what is needed is the inter-action with an actor that responds directly to this availability. Or, to put it another way,those desk parts (ob-ject-als and assemblages in their own right, as you pointed out) which now form an aggregate are available for forming an assemblage that is an ob-ject-al (a desk); however, what is needed is an actor (in this case someone who can put together the parts of the desk) who responds directly to this availability.
This is a crucial issue for my ontology and one that I am still working through, so it is worthwhile to comment on it further. The desk example is probably not the best example because, as you point out, it requires a maker to pass from being an aggregate to an assemblage. While this is certainly a common way for aggregates to become assemblages, I don’t think we want to presuppose this for all aggregate to assemblage processes.
Take, for example, the process of group formation. You have all of these people that are themselves individual assemblages. These individual assemblages or persons might themselves have network relations of various sorts among one another forming larger-scale assemblages. For example, there might be friends and lovers among this population. The question then becomes that of how we pass from a mere aggregate of people and assemblages to a global assemblage composed of all the people in the population.
The film The Mist can be read as depicting the morphogenesis of groups or as being a study of the process of groups-in-formation making the transition from the status of aggregates to the status of assemblages. At the beginning of the film you have people belonging to the same town but in such a way as to primarily be an aggregate. That is, any unity or One among these people is minimal and weak, consisting of being members of the same town without these members thinking of themselves as an assemblage or One. As the film progresses and the people trapped in the store encounter more and more of the creatures in the mist, polarities begin to form within the population. The process here could be analogized to one similar to the process an egg undergoes as the yoke gets progressively differentiated over the course of development. Eventually fairly well defined assemblages are produced, consisting of secularists on the one side and the religious on the other side, as well as racial divides. These identities did not pre-exist the formation of the assemblages– or if they did it was only with a low degree of intensity. The people that side with the ultra-fundamentalist religious woman were not themselves ultra-fundamentalist at the beginning of the film. Likewise, the people that form the secularist assemblage were not significantly related to one another in any particular way. Rather, the identity that forms the aggregates instead emerges from out of the Brownian motion of this nebulous population of the city and reinforces itself as a One or Unity as it comes into being.
In this respect I’m inclined to say that every object is a split-object written as
A, such that it is divided between its elements and its unity or status as One in such a way that there is a tension between parts composing an ob-ject-al and the Unity or One of the ob-ject-al that constantly needs to be reproduced in time. That is, because an assemblage or ob-ject-ile is itself composed of assemblages or other ob-ject-iles, it follows that there is a tension between the adventures of the assemblage as a One and the sub-assemblages that compose this assemblage-as-one (think of herding cats and then apply this to ob-jects).
That aside, the key point would be that here we have a transition from aggregate to assemblage(s) that is not the result of an agent or a designer, but is rather the result of an emergence. Once the assemblage has come to be as a unity of parts and One, of course, we can, for social systems and psychic systems, get self-reflexivity that directs ongoing unity among its elements in an intentional way, but we can have unities for these systems that aren’t the result of intentional design. Here the mist and the creatures in the mist function as a catalyst, inequality, or disequilibrium within the aggregate that is the occasion for the formation of the assemblage(s), without being the cause of the assemblages (i.e., we have a complex causality involving a number of factors in addition to the catalyst or disequilibrium that leads to new ob-jects).
Similarly, if we think about the United States, we see that this forms an assemblage or a One but only as split (
A or Assemblage). On the one hand we have the assemblages that belong to and are included in the United States (i.e., in set theoretical terms there are elements that are included– illegal aliens –without belonging). These elements form complex assemblages among themselves. Thus we have all the persons in the United States, families, amorous relations, relations of friendship, classes, ethnicities, genders, discourses, network relations pertaining to business, religion, political groups, and different occupations, occasional networks that form as people are thrown together in a variety of ways, and so on. This multiplicity of assemblages is constantly bubbling and shifting, such that all of these assemblages, like cats, are moving about in different directions and according to their own aims. On the other hand, we have the One or Unity of the United States that counts all of these other assemblages as belonging to it. Between this One and all these [now] sub-assemblages, there is a perpetual tension where the One (whatever that may be) struggles to maintain itself as One in terms of all these sub-assemblages and these sub-assemblages mill about in their own directions and for their own aims. The Unity of the assemblages consists in various mechanisms through which Identity is maintained in time as an ongoing problem rather than a property (i.e., there are processes of “one-ification” that constantly need to take place for the aggregate to form an assemblage).
I am disinclined to claim that all aggregates can form an assemblage or an ob-ject-ile. As Spinoza points out in Book III of the Ethics, philosophically we can minimally say that one object can either be combined with another object, or destroys another object (think poison), or one object is simply indifferent to another object. If this is about all we can say from an ontological perspective, then this is because the principles of connection among ob-ject-iles must be surveyed in each domain or for each type of ob-ject (material objects, societies, organisms, psychic systems, and so on).