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THE UNCONSCIOUS AS SURFACE NARDI Marta Lacan considers the unconscious as surface in an attempt to replace the geometry of the sac that is present in the second Freudian topic. Work with the topological surface allows us to reconsider the idea of surface, present in Freud´s work, without slipping towards the conception of layers or depths. On the other hand, we have to realize that the Lacanian preoccupation for the topological surface answers, in part, to the concern for finding a writing – and a writing implies putting it on a geometrical plane, in two dimensions, - a mathematical writing, in the "matema" sense, a writig to the letter. But the letter for this writing first specifies its phonemics. In order for the unconscious to have the effect of a writing it is necessary for the unconscious to speak, that it exist as discourse, making a social connection, with the analytical discourse being that which makes it exist. Now, the unconscious articulates as discourse by way of a process, negation, that in the context of the L´Ethique seminary is characterized by a particularity in the French language: ne explëtif or ne discordance. This negation, that is not complementary, is a symbolic operation for which a subject consists in the cut between that stated and the statement itself. Although Freud tells us that negation does not exist at the level of the unconscious, he immediately shows us that there are many ways to represent it metaphorically, except with this ne, because this negation is in the order of discourse. It is my intention to establish a relationship between the logical process and the topological process. I will start by considering the phrase by Lacan in Radiophonie: The unconscious, for the subject is that which reunites the conditions in him that either he is not or he does not think. They are reunited in a particular way that I will consider in the following. In the course of the seminary La Logique du Fantasme, Lacan works with the cartisian cógito by making use of the propositional logic and the conjunctivist logic. The principal process is articulated negation via the laws of De Morgan (logical) and the symmetric difference (set theory). Instead of cogito ergo sum we have two sets "either I think or I am not", that with the previous emptying of the ergo, the emptying of the interection, remain as disjunct sets. This pure and simple alienation, present in the field of language, is read by the unconscious under the regimen of the bedeutung and while ruled by it the intersection remains empty: "I do not think (think thing), I am not" , are presented together. This is another way of saying that the unconscious is the real of the symbolic. Working under this logic the unconscious is not allowed to articulate "Therefore I am". Each time the subject speaks, it will do so under the sign of negation, under the form of "It is not me who says it" or under the form of a lie. "You ask who is the person in the dream. It is not my mother". This is the same structure of the ...you will think that my intentions are hostile...(1) What is the logic that governs these uttering in an analysis? You think; I do not think and meanwhile I suppose that it is you who thinks – and this is a necessary moment in all analyses – I take shelter in the "it is not me who says it". The two expressions of the forced choice are presented together but without any possible connective logic. This is what Freud indicated to us as the impossibility of analytical intervention, of an intervention that makes it possible for a saying to touch the real. Following the process of propositional logic, for example the double negative as an afirmation, the only thing we would get, maybe, is an intelectual acceptance. What resource can we implement to understand the stating of "I do not think or I am not" in the act of speaking, since the symbolic logic is presented to us as insufficient? We can take the topological surface that Lacan uses to resolve the problem of the double inscription in Freud: the Moebius strip, that is to say the cross-cap with a hole(2). We can say that when we speak, we pass from the "I do not think" to the "I am not" in a continuous way, and unless there is an analytical action the choice is not made and if it is not made there is not alienation; that is to say we maintain the illusion that we can speak rejecting the mark (le trait). It is as if the patient would have actually said: "with respect to that person it occurs to me, really, that it was my mother; but I do not want that to happen." But that was not what he said, because if he says that we can consider that all the phrase is the effect of a cut, of an interruption. As a matter of fact the analyst can say that because for one instant, in one of the passages for the "I do not think" something happens, it happens by chance. In the Seminario...ou Pire, the ne explétif is considered as a negation corresponding to the pas- tout, the contingency, the negation discordance, negation that leaves the universal sense of the language incomplet. The unconscious becomes discourse by the negation and the subject is left divided between what he says and the rejection of what he says. The unconscious becomes discourse because of the middle cut of the Moebius strip, and at the moment in which the moebian structure is undone, the unconscious shows itself as the cut. The strip that we now have is cylindrical, that is to say it has a front and a back and it can return to being moebian by means of a seam. What I am interested in demonstrating in this work is that by means of the cut it is revealed that the discourse has a back side; the psycho-analytical discourse is the back side (l`envers) of the discourse of the unconscious. As a hypothesis we could consider that the cut in the strip is equivalent to the pas-tout in modal logic.
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