last night I fell asleep thinking about Russell's Paradox but I had it wrong. I was thinking "the class of all classes that belong to themselves" which doesn't turn out to be very paradoxical and so I was wondering what the fuss was and then this morning I look it up and it's the class of all classes that do not belong to themselves.
it took me some time to get this paradox because no one ever states it beyond that, as though it is perfectly clear stated that way. well if you think about it it becomes clear but why don't they go on to say this: the class of all classes that do not belong to themselves is paradoxical because if this class belongs to itself, then it can't belong to itself according to the rule; but if it doesn't belong to itself, then it must belong to itself, according to the rule.
this led me to look up one of Godel's Incompleteness Theorems which states that within any axiomatic system one can generate propositions that that system cannot prove true or false using its own logic. the example used to show this is simple and it again revolves around the impossibility of negating a negative criterion for belonging and still having a statement that is logically consistent. excluding the exclusion that stipulates inclusion is logically dicey.
I kind of knew these things already but from a completely different angle wherein propositional logic must be founded upon a statement that lies outside the dichotomy of true and false, and that this is the paradox that grounds both logic, language, and sense in general. the answer, if there is an answer, seems to lie outside of binary logic, which I never see these systems questioning; if you move outside of the region where statements are unambiguously true or false, where are you? and accordingly, if language can be said to operate through a process of delineation, is this the same as saying that language operates through a process of classification? are delineation and classification the same? I wonder. I wonder if différance is the counterpart of conceptual thought, or if concepts only proceed via différance, delineation, articulation.
it seems in any case that the event of articulation, or as Deleuze might put it, sense itself, is supposed to be that moment prior to truth and falsity, being both its ground and, paradoxically, the effect of drawing the distinction.
the point isn't to surround good and evil with a concept that leaves no residue, but to let the question go on indefinitely without condemning it as indistinct and perverse.
I guess I'm writing my dissertation now.
the logically dicey part, the "excluding the exclusion that stipulates inclusion," leads me to believe that the ethics of this whole thing rely upon an incomplete gesture of exclusion which thus leaves undecidable the status of any particular potential member--but further than that, if Agamben is trying to say something about all this, it must be that the state of riding upon that paradoxical line, of being exposed upon it, rather than being included or excluded, is the ethical situation and is the ultimate criterion of belonging outside of any conceptual group.
it's interesting to me, the way that logic always falters upon the binary distinction. isn't it possible to come up with a method--or maybe it cannot be a method--that does not rely upon this very simple model?