Morton has an interesting post up discussing the relationship between OOO and Goedel. As Tim observes:

So I was wondering whether there was a deep congruence between Gödel’s Incompleteness Theorem and the notion of withdrawal in OOO. Thinking as Levi Bryant does of objects as systems, and coherent ones at that (otherwise they couldn’t be operationally closed, in the lingo), would this not imply that there is at least one genuine element of any object-system that we can’t account for? In other words, objects are systems that we, or any other object, can’t “know” everything about, PRECISELY to the extent that they TRULY exist.

(This comes from a discussion of Xavier Zubiri with Graham Harman, who as I’m sure you know has opened up a treasure trove of philosophy old and new. Zubiri talks a little about Gödel in On Essence. Thanks Graham and forgive me if I made any errors here. And please correct.)

Might this not be a way to account for the beautiful symmetry between the fact that objects do seem to relate in some sense, yet in some deeper sense are totally withdrawn from one another? Objects are vulnerable and withdrawn simultaneously, and I wonder whether this is just a coincidence.

Morton’s thesis here revolves around Hofstadter’s idea of strange loops. The idea is that formal systems contain the possibility of auto-destruction by virtue of containing a self-referential strange loop that can cause their own destruction. As Tim puts it,

There is at least one entity out there (it could be lurking in your genome) called something like “If Tim Downloads This, He Will Auto-Destruct.” That’s what mortality MEANS. Life forms exist precisely to the extent that they are fragile. I kind of concur with Martin Hägglund on this point, via a different route.

Then I got to thinking about OBJECTS in general (see my previous post—yay, I am an object oriented ontologist). Not just living, but all objects. There is an EVEN LESS metaphorical sense in which the record player story is true for objects. I mean, we were just talking about record players a minute ago. There is at least one other object out there that could bring it about so that a certain object was annihilated.

In part, Tim is riffing on my account of objects. In chapter four of The Democracy of Objects, I treat objects as systems, drawing on the resources of Luhmannian autopoietic theory. Here I’m deeply influenced by Graham’s treatment of objects as structures in Tool-Being (which I find to be one of the most adrenaline inducing bits of writing in Harman’s work). If objects are systems or structures, then they will have certain formal properties (and perhaps this allows OOO to get around certain common criticisms directed at Badiou and Meillassoux concerning the applicability of maths to existence?).

read on!

Tim’s line of reasoning seems to be that if objects have these formal properties, then we can also think of them in Goedelian terms. Goedel showed that every formal system contains at least one proposition whose membership is undecidable. We are unable to decide whether the proposition does or does not belong to the system. Adopting Badiou’s language from Logics of Worlds, let’s call this element of systems or objects a “point” or “site” within objects.

It seems to me that Tim is groping towards two things in the concept of points or sites. First, I think Tim is suggesting an account of how to produce a relation out of non-relation. Insofar as objects are withdrawn, they are non-relational. It is the withdrawal of objects that leads Graham to resurrect the subterranean tradition of occasionalism in his account of vicarious causation. How can objects relate when they’re withdrawn from one another? For Harman, this requires what he calls a “sensuous vicar”. In Tim’s discussion of Goedel we get something similar. The point contained within an object would be akin to a sensuous vicar. Insofar as the point is a site of undecidability whose membership as belonging or not belonging to the object cannot be decided, the point would be a sensuous vicar that allows for the relation of the non-related. Points would be strange elements, like Hegel’s “bone in the throat”, that simultaneously belong to the object and don’t belong to the object, affecting transport or relations between objects.

This would also be why points are sites where the destruction of objects can occur. I’m not quite sure I agree with Tim’s thesis that there must be at least one object in the universe that can destroy an object. When Tim cites self-referential or strange loops, the image I get is not so much one of one object destroying another, so much as an object completely withdrawing into itself. Here the appropriate image or analogy is that of a black hole. A strange loop is a form of withdrawal so complete, so thorough, so total that the object has become entirely withdrawn and solipsistic. In chapter two of The Democracy of Objects, I argue that the structure of objects is such that they are simultaneously withdrawn and self-othering. Their virtual proper being is withdrawn, but they are self-othering in the form of producing qualities. Strange loops or self-referential processes would be a state of objects in which no self-othering takes place, but rather the object is completely withdrawn. In a sense, objects in a state of strange loopiness would be a bit like Leibniz’s slumbering monads. However, where Leibniz’s slumbering monads seem to be in a state of inertness, objects caught in strange loop would be caught in a troubled dream, endlessly pulsing about the paradox generated by their point without being capable of othering themselves. Like a black hole, nothing comes out. Here I suspect there are important consequences for certain pathological mental states and social systems that degenerate into a state of decay.

On the other hand, the strange membership characterizing sites or points would contain the possibility of death within objects because they would harbor either the possibility of generating new objects or of bringing about the undoing of the existing object. There are certain relations an object can enter into where new objects are formed (I’m not willing to say that all relations generate a new object). The possibility of such a linkage would lie in the points belonging to objects (and also not belonging). In many instances, these object generating linkages also spell the destruction or death of the objects linked. Likewise, strange elements are such that they can bring about a state of decay throughout an existing object, pulverizing it into a plurality of objects. This is what often happens in the case of viruses and cancers.

All of this brings me back to the theme of distinction as articulated by G. Spencer-Brown. Spencer-Brown argues that it is impossible to indicate anything without first drawing a distinction. Distinction precedes indication or reference. A window in your home, for example, is a sort of distinction. Once that window is made you can indicate what appears within the window. Every distinction contains a marked space and an unmarked space, such that the unmarked space becomes invisible. The unmarked space is what falls outside of the space of indication.

Recently Cogburn and I had a back and forth in email over this concept of distinction that’s helpful in clarifying Spencer-Brown’s concept of distinction. Cogburn pointed out that when asking whether we should get lunch with Jim or Steve we are employing a distinction yet neither Jim nor Steve become invisible. In other words, Jim and Steve are distinguished yet neither become invisible or fall in the unmarked space of the distinction.

Jon’s counter-example is it nice because it allows me to clarify how Spencer-Brown’s concept of distinction differs from how we ordinarily think about distinction. Spencer-Brown’s concept of distinction is not distinction between entities, so much as that which opens up the space of sensual objects on the interior of a real object altogether. When I was a young boy my grandfather used to take me to a walking trail in Virginia. Along this trail was an old train tunnel that you could walk through. Never, in my life, have I experienced such darkness. I was always terrified of that tunnel because the darkness would engulf you so thoroughly that you had no idea what was about you, what your feet were touching, whether that sound was another person or animal or just rocks skittering across the floor, etc. Indeed, this darkness was so thorough that it even seemed to devour the light of our flashlights.

This play of darkness and light is a helpful analogy for thinking Spencer-Brown’s concept of distinction. My flashlight would create a circle of light on the ground bounded by absolute darkness. Within that circle of light we encounter the space of indication. The rest falls into darkness. Consequently, in my response to Jon, distinction is not the distinction between Jim and Steve. Jim and Steve both fall in the space of the indicated, even though we’re talking about a disjunction (lunch with Jim or Steve). What falls in the unmarked space here is everything else in the world.

Luhmann argues that distinction lies at the ground of every system. Every system draws a distinction between itself and its environment. Now, distinctions have rather Goedelian properties in that they’re self-referential. Distinctions are self-referential in two senses. First, they are self-referential in the sense that they are drawn by the system that employs the distinction, but distinguish the system from an environment. Second, they are self-referential in that the distinction applies to the system itself.

Suppose, for example, that we take the example of the distinction between good and evil. Evil is everything that belongs to the environment of good. It is that which good strives to eject from itself so as to be good. The distinction between good and evil opens the space of indicating the good. Here we can get the gist of how this distinction functions through a reference to Plato. In the Meno Socrates objects to Meno’s list of examples of virtue, saying that he wasn’t asking for an example of this or that virtue, but for virtue itself. One way of thinking Socrates’ point is that he wants the distinction that allows for these indications (examples) to be made in the first place. Virtue itself would be the distinction, whereas instances of virtue would be the indicated rendered possible by this distinction.

Now, there’s a very real sense in which every distinction is unstable precisely because distinctions are self-referential. We can always ask “is the good good?” Here the distinction becomes self-referential and thereby falls into paradox as we no longer have a criteria allowing us to determine whether the distinction itself can be indicated as good. All we can do is ape the tautology “the good is the good!” In higher order systems capable of reflexivity, we thus find an additional reason for withdrawal. If the point of each system must withdraw, then this is because withdrawal is the only way in which the object can avoid falling into paradox or a self-referential strange loop. The distinction itself must become a blind spot and the system must take measures to ensure that the distinction is never applied to itself. I’ll halt here for the moment.

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