Derrida's Points of Departure
It occurred to me that some points Jacques Derrida notes in his Structure, Sign and Play in the Discourse of the Human Sciences* as phenomena where categories and structures -- that is, metaphysics itself -- deconstruct themselves, are explicable away inside logic and metaphysics. Naturally, this might be the consequence of the nature of metaphysics itself, that it is what makes language possible, and thus nothing can be said / written that would point outside its jurisdiction.
Sign
On sign, Derrida writes:
[T]he metaphysics of presence is shaken with the help of the concept of sign. But, as I suggested a moment ago, as soon as one seeks to demonstrate in this way that there is no transcendental or privileged signified and that the domain or play of signification henceforth has no limit, one must reject even the concept and word "sign" itself -- which is precisely what cannot be done. [...] If one erases the radical difference between signifier and signified, it is the word "signifier" itself which must be abandoned as a metaphysical concept.
Continuing by citing Lévi-Strauss and introducing the opposition between the sensible and the intelligible which is to be transcended, Derrida continues:
The concept of the sign, in each of its aspects, has been determined by this opposition throughout the totality of its history. [...] But we cannot do without the concept of the sign, for we cannot give up this metaphysical complicity without also giving up the critique we are directing against this complicity, or without the risk of erasing difference in the self-identity of a signified reducing its signifier into itself [...] For the paradox is that the metaphysical reduction of the sign needed the opposition it was reducing. (85)
I interpret these passages along the following lines: while sign would present itself as a point where the opposition it is based on (metaphysics) deconstructs itself, it cannot be done, for by erasing the opposition the sign is also erased or is reduced to a chain of signifiers. The sign lives on this opposition and cannot exist outside it.
Far from trying to refute this argument, I would merely like to call attention to a phenomenon that might be paralleled to the evolution of the sign.
Somewhat echoing Baudrillard's notion (see Simulacra and Simulations) that an image evolves first by referring to a thing and at the end referring to nothing but itself (a simulation of nothing), let me consider the notion of the mathematical set and its possible representations.
On the first level, a set is a collection of things. We could consider a set of my pony horse, that ant over there, and Aunt Margaret. I could create many sets this way. Next, I realize that I might want to consider the collection of all my sets made so far. For the sake of convenience, I might term such a collection a class. I may, therefore, consider the sets of animals of the same species and the class of invertebrate species. Realizing, however, that sets are just things like my pony horse, I might see no reason to distinguish between sets and classes any more, and so I decide to refer to collections of sets as sets, too. This makes me able to consider a set containing Aunt Margaret and another set containing all the ants around the house. Making it this far, I will also allow a set to contain nothing, inventing the empty set.
The next step is the trickiest one. I might -- in a delusional state of mind -- decide that there is nothing but sets. The world will not be poorer this way. There will, for example, be the empty set, the set containing the empty set, the set containing the previous set and the empty set, etc. Using brackets instead of circles for the sake of convenience, such a series of sets might be represented this way:
{}, {{}}, {{},{{}}}, {{},{{}},{{},{{}}}}, {{},{{}},{{},{{}}},{{},{{}},{{},{{}}}}}, etc.
Or, we may assign points (vertices) to each such set and draw an arrow (edge) from set A to set B if A contains B. This way, sets as such are represented not by things "containing" other things, but by a directed graph. The set, in other words, has ceased to be a representation of a collection of things. It now exists by its own right; a set is defined solely by other sets in a system in which identity is given by relation, immediately calling Ferdinand de Saussure and the idea of difference-defined signifiers and signifies to mind.
Now what I propose is to see sign as undergoing the same process as the set above, to acknowledge the possibility of seeing it not as rooted in the dichotomy of signifier-signified but as one that "transcends" it. It might be interesting to muse on the possible consequences of cutting the ground from under the feet of sign: would then it continue to be a singularity around which metaphysics is torn along the seams? If yes, would such a deconstruction really lead to the circle Derrida described?
Nature and Culture and Incest Prohibition
Derrida talks of decentering, which takes place when it is revealed that structures have been deprived of their centres and thus they cease to be structures -- in other words, when they, in a sense, get deconstructed. Ethnology, in Derrida's view, occupies a special place among the "human sciences" as it has
been born as a science only at the moment when a decentering had come about; at the moment when European culture -- and, in consequence, the history of metaphysics and of its concepts -- had been dislocated. (86)
He suggests that ethnology / ethnocentrism, like the sign, is another point which is indestructible by the nature of metaphysics, as "the ethnologist accepts into is discourse the premises of ethnocentrism at the very moment when he denounces them." (86) The way I see it, if one attempts to do away with the presuppositions propping up the structure of ethnology, they return as repressed content from the unconscious, forcing us back into metaphysics.
To illustrate his point, Derrida cites the opposition between nature and culture, natural and cultural (learned) behaviour. Lévi-Strauss, Derrida argues, having introduced this dichotomy, encounters "what he calls a scandal," namely, incest prohibition. For incest prohibition presents itself as being natural and cultural at the same time, and thus it questions the assumedly self-evident difference the dichotomy is based on. In other words, it cannot be grasped using the concepts nature or culture. From this observation, Derrida jumps to the conclusion that this fact is because incest prohibition precedes these concepts; that it is actually what made the concepts possible; that it is subsequently obscured (deferred) by the opposition (difference).
As I interpret this train of thought, I see incest prohibition as a reverse of sign inasmuch as sign was presented as being based on an opposition the erasure of which would lead to its destruction; incest prohibition, by contrast, precedes an opposition it generates. However, both things (I dare not say concepts) are, I think, points where the impossibility of getting rid of a dichotomy enables us to peer behind the scenes of metaphysics, which, in short, deconstruct (or show the need and the impossibility of the deconstruction of) metaphysics.
But how does Lévi-Strauss define natural and cultural? Derrida paraphrases the definitions in The Elementary Structures of Kinship the following way:
[T]hat which is universal and spontaneous, and not dependent on any particular culture or on any determinate norm, belongs to nature. Inversely, that which depends upon a system of norms regulating society and therefore is capable of varying from one social structure to another, belongs to culture. (86)
It is then hardly surprising that
The incest prohibition is universal; in this sense one could call it natural. But it is also a prohibition, a system of norms and interdicts; in this sense one could call it cultural. (87)
(Let me not consider the fact that while incest prohibition may be universal, the specific set of relatives it prohibits one from forming a sexual nexus with appears to vary from culture to culture.) The phenomenon of finding a thing belonging to more than one category is hardly surprising to one who has ever tried to give formal definitions for, for example, sets of phonemes, lexical items or types of soil. If one aims at creating an all-inclusive pair of disjoint categories, the safest way of doing it would be to say: something is A if this and this, and B if it is not A. Lévi-Strauss' definitions, however, do not follow this pattern. They define both categories independently of the other. His belief that he created disjoint categories simply points to a hidden presupposition which turns out to be untrue. Nothing more happens; Logos, Logic and, in my view, metaphysics stay unshaken.
One could imagine a linguist trying to categorize phonemes. At the moment, he considers unvoiced consonants, and, following common sense, tries to draw a distinction between sounds during the formation of which there is an air flow (for example, sh as in shiny) and sounds without an air flow (for example, t as in toil). The former category s/he names fricatives, for there is some friction in them, and the latter plosives, for there is a(n ex)plosion of air at the end of those sounds. Now our linguist considers the unvoiced consonant at the beginning of choose. It starts as a t and ends as an sh, and -- as other considerations show -- it is still one sound. In a sense, it fits both categories s/he established. Does this mean that this strange tsh sound precedes the plosive / fricative opposition? that it is what actually makes the two categories possible? that it is hidden as an oblique centre that can never be reached by the infinite chain of signifiers opened up if we tried to do away with our inaccurate categories? that it decenters Linguistics? I don't think one can whole-heartedly answer 'yes' to any of these questions. The fact that Lévi-Strauss' definitions are inaccurate, in itself, shows something not about metaphysics but about the definitions.
I, however, would not like to appear as one who thinks by showing the possible erroneousness of one example he thus deconstructed the deconstruction of metaphysics (or its impossibility). Still, I would like to argue that such examples have probably been magnified out of proportion in order to show us something about an all-inclusive (or, at least, an all-Western-culture-incluse) structure. It is, admittedly, an interesting, important, and hard question that is raised by the inaccurate categories of Lévi-Strauss, namely, whether anything formalized can successfully describe the world we live in or we will inevitably run into counterexamples to any number of and however refined categories, scientific models, etc. It is, however, a question that can be posed on the level of physical phenomena, measurement, mathematical models, computing and comparison. The "concept" of the metaphysical need not be introduced, and the examples cited by Derrida do not necessarily refer to it in any way. Unless in a way similar to the attempt of (re)presenting the existence / workings of a transcendental entity by listing a number of examples rooted in materiality.
And there's still the possibility that I constantly drag these phenomena back into Logic and Materialism precisely because concepts metaphysics made possible obscure from my sight the primeval things that ultimately generated the logical categories I operate in. As language is rooted in these concepts, everything said can be interpreted under metaphysics. I do not "see" beyond it because I can choose not to, and, out of a yearning for the comfort of concepts I think I know, I choose not to. But then the beyond-metaphysics becomes frighteningly similar to another entity that exists only if I believe in it, and would we really like to regard the possibility of a beyond to the Western history of metaphysics a kind of religion?
* Hazard Adams and Leroy Searle, eds. Critical Theory Since 1965, Tallahassee, Univ. Presses of Florida, 1986. 83--94.