The Politics of Logic: Chapter 4 Notes and Comments

Chapter 1 Notes
Chapter 2 Notes
Chapter 3 Notes

Derrida and Formalism

Livingston states that an aim of this chapter is looking at the extent to which elements of Derrida’s deconstruction are a reflection on formalism and a parallel to metalogical results that arise from reflection on the structure and limits of language. He suggests that several of Derrida’s key terms can be understood as metalogical consequences of reflections on the implications of formalism. This provides a clear understanding of the textual praxis of deconstruction and its contemporary political implications.

Derrida suggests an anology between what he calls the “undecideable” and the incompleteness discovered by Godel. Juxtaposing Plato and Mallarme, he says that the issue is one of mimesis, the relationship between a representational text or image and the original that it represents. Godel’s theorum, essentially, shows that an assertion cannot be proven within the system it was asserted in. There is a truth in a consistent system that cannot be proven by the system. A popular example would be “This statement is false.” For Derrida, the undecidable is not a matter of a single term having mutually contradicting meanings but rather is a consequence of the total structural relationship. A word exists in a particular position in a text but the position of the undecidable, what the text itself, and the logic that governs it does not give us the resources to decide.
Derrida uses the neologism “differance“, in relation to Saussure’s view of language as a system of differences without positive terms, to express the general condition for the possibility of presentation itself, given that linguistic presentation is only possible in a system of signs. Differance expresses the total, systematic, and differential condition for presence but because it does so it cannot be presented or named within any system that is structured by it or it falls into a paradox. So, Derrida argues, differance is neither a word nor a concept. By being incapable of naming it, it exceeds the order of truth at a certain point. It is connected to the undecidable. The undecidable results from a complication of the relationship between the inside and the outside of a total system which occurs due to the combination of two operations:

1. The structural principles determining the meaning and value within a total system are defined and described as if from a point outside the system
2. This definition is recognized as taking place within the total system whose structural principles are defined and delimited.

This is also what is occurring in Godel’s system and in Saussure’s structure. For Derrida, all language is is a system of differences or of writing (even when it is spoken). This is left out when meaning is taken as the origin of it and is complete itself. Some critics of Derrida cite the generality of his system as not aligning with the deconstructive emphasis on the irreducible plurality of contexts and textual sites. Livingston suggests that Godel’s analogy holds up, there is no opposition. Despite a variety of formal systems and specific Godel sentences (GS) in them doesn’t prohibit Godel’s results showing the structures of proofs, truths, and meaning. Deconstruction functions the same way.

Livingston notes that Derrida’s undecidable takes two forms: one concerning truth or provability, the second concerning meaning and meaningfulness. While they are not directly analogous, there is a deeper analogy identified by looking closer at the Godel sentence. The Godel sentence, without an outside position commenting, is a completely insignificant formula. It is meaningful in an intra-systematic sense but it doesn’t have the meaning of “asserting its own unprovability. The sentence itself is undecidable between two meanings: one, an intra-systematic meaning that is coherent but undistinguished and an extra-systematic meaning that cannot be formalized within the system itself but which is responsible for the sentence’s unique status. It is only in a metalanguage that allows for the interpretation of the undecidability. This undecidability has to do with inconsistency rather than incompleteness for Derrida.

So, both Godel and Derrida’s arguments are similar in two respects. The first is a self-referential coding where the systems logic becomes formalized at a single point. the second is that both suggest a generalization of this result making a system either incomplete or inconsistent. Livingston then argues that there is actually a third connection that is essential for any deconstructive strategy. He says that the undecidable always results from a semantical effect of syntax that cannot itself be excluded from any system. This crossing of semantics and syntax suggests an analogy to diagonalization (see the notes from chapter one) which underlies Godel’s results. The GS diagonalizes the set of all decidable sentences of the system. So, the undecidable within a system depends on an intervention on syntax where the syntactical rules are encoded at one specific point (just like Deleuze). Thus, for Derrida, the terms invoking the undecidable are located at the point where syntax situates a semantic gap which is essential to the text. Differance, while expressing the total structural logic, does not name anything that can be named by terms within the system. So, if we gave differance a semantic value, we could only say that it names the void of non-being. This void is marked syntactically and this syntactical spacing is necessary because it opens the syntactic possibility of signification. Differance articulates the possibility of such spacing, so in this sense it does signify.

Agamben and Derrida

Agamben, paying homage to Derrida, emphasizes that deconstruction isn’t a hermeneutic of meaning. It is grounded on the undecidability of the reflection of syntax upon itself and the problematic topology of criticism that this implies. This is similar to the paradox of the absence of a name for the name or of the other paradoxes mentioned earlier in the book. Its topological structure is what Agamben calls the “threshold”. It is not the limit of a fixed line between inside and outside, such as the line of a circle marking a stark boundary between the area inside and the area outside. Instead it is of the threshold of in-closure that by being closed opens to the exterior, and in being open, encloses itself, similar to the mobius strip. This results from the confusion (in a technical sense) between syntax and semantics, the inside and the outside. So, Agamben says, the response of deconstruction is to trace the undecidable and document its syntactical necessity. By doing so it inhabits the complex topology. And, by tracing the boundary of thought and language it is an inscription of a limitative trace that erases itself the moment it inscribes. This tracing is the operation of paradoxico-criticism.

Derrida and Ethics

The structure of the undecidable that Livingston argues for has important consequences for what we should take the deconstructive response to the undecidable to actually be he says. This has significance for the ethical structures of hospitality and the gift.  For example, Derrida says the statement of the only possible gift is an impossible gift, is meaningful. Where I can give only what I am able to give, what is possible for me to give, I don’t give. So, for me to give something, I have to give something I don’t have. I make an impossible gift. So, I can only gift what I have, but once gifted I no longer have it so I cannot actually gift it. The ethical structure of the gift is dependent on the structurally necessary confusion between an inside (an intra-systematic and regular) and an outside (extra-systematic and unregulated) meaning. This paradoxical structure of confusion or crossing renders it undecidable and so makes it an example of an ethical concept in Derrida’s sense. This example can be generalized to many things that are regular and structured systems of practice and action. Wherever there are structures or rules that regulate and phenomena that are determined by the very possibility of jumping out of the system, undecidability appears. This calls for a deconstructive response. This is the case in systems of law, justice, and normatively regulated behavior among other things. In all of these cases where possibilities of action are predetermined by the prevailing system the point or meaning of what is “ethical” cannot be determined in intra-systematic terms. Derrida sees all these intersubjective systems of law, justice, politics, economics, etc. as fundamentally linguistic and as such are susceptible to the logic of the undecidable.

So, how do we deconstructively inhabit these spaces and respond to the dilemma of undecidablilty? One part of the answer, because there isn’t a rigorous constitution of these concepts outside of the undecidable (which depends on the crossing of the inside [syntactic] and outside [semantic] meaning) is to pursue decisions/solutions outside of the logic of any given system. But, “leaping outside the system” is not simply breaking with it or leaving one particular system for another. The undecidable is an essential precondition for the possibility of responsibility. If we can only decide from what is in the system we operate then there is no responsibility in our decisions. But, for Derrida, the responsible decision is only so because the singular other is not simply outside the system but inhabits the paradoxical space of in-closure or threshold itself, one that occupies the space of undecidability.