In my last post I proposed “Ø” as the matheme of the object. In fact, this, I think, is not quite accurate. The complete matheme of the object would be O1/Ø, where O1 refers to the manner in which an object is actualized in terms of properties at any given point in time, and where Ø refers to the divided, split, abyssal, or withdrawn object, beyond any of its actualizations. I have referred to Ø as the hidden, “interior world” of the object. This reference to “interiority” risks being misleading insofar as it has spatial connotations suggesting that Ø can be found by “opening up” an object. However, no matter how thoroughly we look into an object, now matter how carefully we dissect an object, the interior of an object is never found. This is because the interiority of an object is not any of its properties or qualities.

Already, in this formulation of the objectness of objects, I believe it becomes clear just how radically different this conception of objects is from that of representational realism. For representational realism, there is no doubt that the object consists of its properties. The whole issue is whether we are able to represent those properties, or whether our representations transform those properties such that we can never reach the “real” properties of the object. For onticological realism, by contrast, the object is never its properties. The object is not barred or split for us, but in itself.

read on!

There are at least three ways in which the object is split or divided (Ø). First, as I tried to argue before I got caught up in all this onticological nonsense, objects are acts, verbs, or processes. Insofar as objects are acts, verbs, or processes, they necessarily differ from themselves. One connotation of the matheme Ø would thus be that of an object in a relation of non-identity with itself. Like Frege’s concept of zero as the number that is non-self-identical to itself (cf. Frege’s Foundations of Arithmetic, but also Jacques-Alain Miller’s “Suture“), the object is not what is identical to itself, but rather is that which, first and foremost, differs from itself. If this is the case, then this is because the object can only exist as act through self-differing. An entity that did not self-differ, that did not withdraw from itself, would be a void that never manifested itself in the world.

The word “manifestation” here is dangerous, as manifestation immediately calls to mind someone for whom the manifest manifests itself. However, manifestation should not be thought as “manifestation-to” or “manifestation-for” anyone. The manifestness of manifestness is a pure manifestness without a manifestee or a recipient of the manifestation. Were there nothing else to regard the manifestation of an objectile, this objectile would still be manifest. And what it it that manifests itself? Certainly not Ø, for in differing from itself Ø can never manifest itself. Rather, Ø perpetually withdraws without ever appearing or manifesting. No, what manifests itself is O1, or a property or quality. In differing from itself Ø passes out of itself and produces a quality. Often these qualities are confused with the object, such that we ask ourselves, “does this quality belong to the object itself, or is the property the result of our practice, representation, engagement, etc.?” The answer to this question is “yes”. The objectness of the object is in excess of whatever qualities it might actualize, but were it not for Ø, O1 would not be possible. Consequently, Ø cannot be reduced to O1, but there is nonetheless an internal link between Ø and O1.

It is in this regard that onticology is unconcerned with questions of whether or not the blue mug is really blue. No, the blue mug is not blue. Why, because the mug, like any other object, is a barred or divided object that is always in excess of any of its predicates or properties. Onticology is not even bothered by the suggestion that blue might only be a property that occurs in the brains of certain animals and humans, for this is precisely what onticology predicts in its account of the onticological dialectic. However, in recognizing that the blue of the blue mug might only exist in the brain of the animal regarding the blue mug, the onticologist nonetheless rejects the thesis that the brain makes the blue mug blue. The brain is a necessary condition for the manifestation of the blueness of the mug, but the brain is not free to make the mug whatever color it might like. No, the mug must already possess a certain endo-consistency or endo-structure that enables it to produce these differences under these circumstances. Would the mug be blue independent of the animal regarding it? Who knows? Does it matter? No, because we have already begun from the premise that objects are barred or Ø, such that they are never identical to themselves. As a consequence, what is interesting from the standpoint of knowledge or epistemology is not the representation of an object as it is in itself independent of its relations, but rather the discovery of dispositions to produce particular types of differences when placed in certain exo-relations with other objects. Knowledge does not represent objects at all, but rather mines relations among objects.

This, then, is the second way in which objects are split. In entering into a field or into relations with other objects, differences (O1) are evoked in the object in different ways. These are phases of the object, manifest as a consequence of the conditions under which the object is evoked by other objects it relates to. Water has phases of steam, liquidity, ice, and many other phases in between. These are all O1’s of water, point-attractors in a phase space, that themselves have very different differential powers in relation to other objects. As an object, $, who would I have been had I been born in Paris? I do not know. This would have been an entirely different field, evoking very different O1’s in my being. I outlined this dimension of objects long ago in a post on Hegel’s critique of Kant’s “in-itself” (warning pdf). The point is that the object will be actualized differently depending on the field in which it is thrown. Again, this is why the onticologist is not particularly interested in anti-realist narratives about how we produce objects. From the onticological point of view, this is not because the anti-realist is wrong, but because the anti-realist is trite. If the anti-realist is trite, then this is because the anti-realist is simply drawing attention to a general ontological feature of all objects or the manner in which one object evokes a difference in another object. Here the object provoking the difference is the investigator.

Finally, if the interiority of the object is nothing that can be found in the object, no matter how carefully it is dissected, then this is because the interiority of an object is not its “inside”, but rather the set of attractors defining the phase space of which the object is possible. These attractors are not themselves “properties” of an object and are purely virtual. They can only be inferred through the production of differences in an object over time, and these attractors, which make up the internal world of the object (Ø), are never exhaustively actualized as this would require the object to be embedded in all possible inter-ontic relations or exo-relations within the universe or the pluriverse. The actualizations (O1) of which an object (Ø) is capable are never exhaustively manifested. All of this is a rough thumbnail sketch of where I’m trying to go. Hopefully it will lead somewhere interesting.