In my development of the ontology of objects within the framework of onticology I have tried to argue that objects are not their local manifestations or actualizations, but rather a virtual endo-relational structure composed of relations among attractors, singularities, powers, or generative mechanisms. It is this virtual dimension of the object that, in my view, constitutes the proper being of an object. This virtual dimension of the object, I argue, constitutes its substantiality. Consequently, it follows that no object ever directly encounters another objects, but rather objects only ever encounter one another as local manifestations of their virtual proper being. The proper being of the object, its virtual structure, is always in excess of any of its local manifestations.
This model of objects is proposed, in part, to account for the identity of an object throughout its variations. Objects continuously vary or change as their conditions change, yet there is something of the object that remains the same. But what is this something? Certainly it can’t be the local manifestations or actualizations of the object because those local manifestations change with shifting conditions or changes in exo-relations to other objects. It is this insight that leads many, I think, to overmine objects by reducing them to their relations to other objects. Yet as Harman has compellingly argued, this line of thought fails to provide the conditions for the possibility under which these variations are possible. As a consequence, it follows that the identity of an object cannot be something in the appearance (to the world, not to humans), local manifestation, or actualization of an object, but must reside in another dimension of the object. And because the object can undergo variations while remaining that object, it follows that the proper being of the object, its substantiality, must be something that does not manifest itself. It is there everywhere in the object, without ever becoming present in the world. It is the “principle” of the object, its “essence”, its “style of being”, without being something that we could ever find in the local manifestations of the object.
One way of fruitfully thinking of the endo-relational structure of an object is by analogy to the mathematical discipline of topology. Already I had been moving in the direction of conceiving objects in this way in Difference and Givenness (cf. especially pages 64 – 72, but the theme runs throughout the entire book). Unlike Euclidean geometry that treats of fixed figures that are thought of as distinct from one another (like the triangles depicted to the left above), topology thinks forms dynamically as undergoing continuous variations. As described by Wolfram Math World:
Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be embedded in two-dimensional space), the set of all possible positions of the hour and minute hands taken together is topologically equivalent to the surface of a torus (i.e., a two-dimensional a surface that can be embedded in three-dimensional space), and the set of all possible positions of the hour, minute, and second hands taken together are topologically equivalent to a three-dimensional object.
The definition of topology leads to the following mathematical joke (Renteln and Dundes 2005):
Q: What is a topologist? A: Someone who cannot distinguish between a doughnut and a coffee cup.
From the standpoint of Euclidean geometry the scalene, equilateral, isosceles, right, obtuse, and acute triangles are distinct entities. From the standpoint of topology, by contrast, these triangles are all the same structure because they can be transformed into one another through a variety of dynamic operations.
In my language, each of the triangles described by Euclidean geometry would be a local manifestation of this particular virtual structure. The structure preserving features across these variations would be the virtual endo-relational structure of the object as such. This clip thus gives a sense of how I think about the being of objects undergoing variation in their local manifestations:
The variations that these various figures undergo (the cone, tubes, mug, and torus) are local manifestations of the virtual object. The local manifestations change, but the virtual structure defined by a set of relations and singularities remains the same. The local manifestations are thus subsets of the proper being of the object that necessarily belong to the object. The singularities or attractors preserved across these variations constitute the endo-relational structure of the object. And, of course, the variations that structure can undergo are infinite in character which is why the proper being of any object never itself manifests itself or is “withdrawn” from any of its variations.
Now like all analogies, this analogy is imperfect. First, it deals with a particular sort of object, abstract objects, rather than individuals. OOO certainly has room for abstract objects like all possible variations of a triangle, but we would have to think of individuals like the tree outside the window of my study as having a topology as well. Second, topology only allows us to think variations in shape or spatial form. However, we need to imagine topological variations not only for spatial individuals like the bubble undergoing continuous variations as it floats through the air, but also of other qualities such as color. Take the rotating vase in the clip below:
Pay special attention to the band about the lip of the vase as it rotates. Notice how the color of each point on band surrounding the top of the vase changes color as it rotates. This is a sort of topology defined by an endo-relational structure and set of attractors pertaining to color. It would be a mistake to claim that the band about the lip of the vase is blue. No, the band is now silver, now blue. Any suggestion that the band is blue is an approximate statistical claim pertaining to averages and optimal conditions defined by an observer, not pertaining to the being of the vase itself. And how do these variations take place? In this case the color variations in the endo-relational topology of the vase are a consequence of its endo-relational structure and attractors entering into exo-relations with other objects (photons of light) that produce certain local manifestations as a consequence. One of the key things onticology seeks to investigate are how these variations are produced as a consequence of internal motions of the object and external relations among objects. Time for dinner.