EDITORIAL by J. A.

Elements of Epistemology
Jacques-Alain Miller

Author’s Bio

This is the last of three lectures which I have been invited to deliver. In my first lecture here I introduced the work and style of Jacques Lacan, and although time constraints did not allow me to go beyond half of what I had planned to tell you, I think I was able to give an idea of the theoretical principles whose uninterrupted development started more than thirty years ago.

In my second lecture I attempted to use the example of the piropo or flirtatious message, which I improvised, as a paradigm, in order to transmit some truths which are fundamental and yet unrecognized about language; in particular, about the function of language in sexual separation, the fading of the reference, the equivocation of language (langue), the misunderstanding of communication.

I am going to dedicate this third lecture to the question of science, and more precisely to respond, as far as I am able, to Professor Cardenas, to whose invitation I owe my presence here (I have already thanked him, and I now thank him again), and whose reaction, after my last exposition, was to say that, in the way in which I presented it, the Lacanian theory appeared to conclude in the impossibility of knowledge. Fair enough. After all, the impossibility of knowledge does not scare me, since knowledge is not science. The difference between knowledge and science appears to me to be fundamental in Lacan’s epistemology. and acceptable well beyond the strict field of psychoanalysis.

For greater convenience, I shall divide this lecture into ten points which I shall cover successively. This means that this lecture will have a style and a tone different to the previous one.

I. One can postulate that throughout the history of thought the theory of knowledge has always upheld the ideal, which has been formulated in various ways, of the union of subject and object. More precisely, the classical theory of knowledge assumes a co-naturality of subject and object, a pro-established harmony between, the subject who knows and the object known. The theory of knowledge has always commented on the miracle of the adequation of knowledge, reserving a place for the-thing-in-itself which, in Kant’s terms, would be unknowable.

From its beginnings, science has been distinguished from knowledge, if only because the former constructs its object. This principle, let it be understood, is not specifically Lacanian. It is also the principle of Bachelard, for example, for whom the object and the scientific instrument are an incarnated theory – that is his expression. I point out that the same thing happens with the Freudian unconscious: in so far as this is apprehended in the novel device of Freud’s practice, it also realizes a theory.

Which theory? This is the whole question. This is a first and brief point which is open to discussion, and I should say that it is not specifically Lacanian.

II. The second point is more precise. It is pertinent to notice that all knowledge is fundamentally illusory and mythical, in so far as what it does is to comment on the “sexual proportion,” a term with which David Mauri has very appropriately translated the French expression rapport sexuel used by Lacan. All theory of knowledge has sexual connotations. You can take as an example Aristotle’s complementarity between form and matter. You can also think of that very elaborate form of knowledge, ancient Chinese astrology, which is a whole discourse about the male and the female and which organizes not only the gods but also the entire society. These are examples that Lacan considers in his seminar The Four Fundamental Concepts of Psycho-analysis. Similarly, one can recall the theory of phlogiston, so compelling and present during the seventeenth and eighteenth centuries, before the emergence of scientific chemistry. I would say since I cannot expose all the historical examples, that knowledge, in so far as it is distinguished from science, sings indefinitely the imaginary wedding of the male and the female principles. I believe it would not be an abusive generalization to state that all the “primitive forms” of knowledge are erotic. In the last analysis, they even get mixed up with the sexual techniques’. That is why Lacan’s thesis that The woman does not exist – which, in the way I presented it, appeared to be somehow abrupt, astonishing – is certainly a fundamental thesis for epistemology as well. Since the object, which in the theory of knowledge is meant to be complementary to the subject, represents also a way of taming the woman. Science – and by science I mean what was born as mathematical physics in the seventeenth century, and also mathematics proper, born well before that time. the gap between the birth of mathematics and the birth of mathematical physics being a big problem of the history of sciences – science, then, in this strict sense, assumes on the contrary that there is no co-naturality between subject and object, that there is no aesthesia of the opposite sex, that there is no natural sexual tropism. This is, furthermore, demonstrated by that structure which is fundamental to psychoanalysis and which introduced Freud to his practice, that is to say, hysteria. It is certainly one of the most surprising theses of Lacan’s epistemology – which I may not have enough time to develop here – that the structure of scientific discourse is not without relation with the structure of the discourse of hysteria. In this respect, Lacan’s proposition that there is no sexual rapport (or ratio) may be considered as a sort of secret condition for the emergence of the discourse of science. In a certain way, the men who developed the discourse of science in the seventeenth century must have posed the proposition that there is no sexual rapport. Those who are familiar with the texts from the Renaissance, for example, and the texts which have been preserved from the seventeenth and eighteenth centuries produced by astrologists and philosophers, know about that evident and sudden break in style and in the very approach to problems. One could say, in this sense, that the scientific approach assumes a de-sexualization of the view of the world, and to use a philosophical expression, a de-sexualization of being in the world. Psychoanalysis is not at all a pan-sexualism. Pan-sexualism is, for example, the theory of Schopenhauer, which places life at its start; or, more precisely, which places at its start the sexual instinct, which would animate the entire nature as well as all human creations. Freud, awkwardly perhaps, but in a very significant manner, introduced the paradoxical term of death instinct, and he discovered, through the angle of hysteria, that the other sex is the Other sex, written with the big 0 of exteriority. I restrict myself to mere allusions to the works of epistemologists. Those who know such works will be able to judge the pertinency of this summary.

III. One can ask what it is that generates the pan-sexualist illusion. It seems to me that this illusion, which falls precisely with the emergence of the discourse of science, but not before, is, in this connection, something recent. What gives birth to the pan-sexualist illusion is that all signification, being imaginary, is fundamentally sexual. All which is said and which makes sense always reveals that, in the end, it aims at a unique signification that occupies the place of reference – reference which does not exist in natural language, in the maternal tongue, in vulgar language; and this signification, which occupies the place of the reference which is lacking, is fundamentally phallic. This is what confers interest and value on that very ancient exercise of discourse called comedy, which has always consisted in making one laugh while revealing the imaginary object which all discourses surround and at which they aim, namely, the phallus. There is a paper by Lacan in this respect which he delivered in Germany in the 1950s, entitled Die Bedeutung des Phallus (The signification of the phallus). Indeed, it is necessary to understand that the phallus is the fundamental Bedeutung or signification. This idea may appear to be somehow excessive; but not if one considers that for instance Frege, who is at the origins of mathematical logic, proposed the theory that all that is said can be classified in two ways: first the expressions which have the true as reference and then those expressions which have the false as reference. He imagined that language has everyday objects as reference. Now then, the simplification of the formulation provided by Lacan states that the sole reference is the signification of the phallus. And there is a discourse for this malediction, which could well be called a benediction. In any case, there is a law of diction, according to which the phallus is always there; it always reveals itself in a pertinent way in the lapsus or in the joke. One could say: “Look for the phallus, it is never very distant. “ There is, however, a discourse which escapes this law of diction, and that is the discourse of science. But this is precisely, and I stress this point, because this discourse constitutes itself only from the moment of the extinction of signification, from the construction of systematic networks of elements which are in themselves. This is the thesis which can be discussed, and which does not require a detailed knowledge of the Lacanian phraseology: science supposes the extinction of signification. It is a mistake to believe that measurement is constitutive of science. Mathematization does not mean measurement. Evidence of this is to be found for instance in topology. Topology is a geometry without measurement where there is no question of distances, where only the schematic network of the signifier supports the objects. These objects do not have any consistency; they do not possess any substance other than the network of signifiers itself. Evidently, at the beginnings of topology objects were represented; for example, that singular object called the Moebius strip was represented. It is possible to construct this object before one’s eyes: one takes a ribbon, and instead of joining its ends to form a cylinder, one joins its ends after making a twist through 180 degrees. This object is obviously curious: if one slides a finger on its edge, the finger appears on the other side of the ribbon, without having passed through any frontier. In the case of a cylinder, the finger remains always on the same side; there are two sides: a back and a front. With the Moebius strip one can, without interruption, move from the back to the front. It is a very singular object which had to wait until 1860 to be discovered by the mathematician Moebius. This is rather extraordinary, one wonders why this simple, small operation could not be performed before that date. This is the first topological object which Lacan has utilized to explain that one should not be contented with the thought-that things always have a front and a back, that the unconscious is at the bottom and language is at the surface. There is, on the contrary, a relation of Moebius strip which makes it possible that correlation and continuity between the right side out and the reverse become conceivable in a scientific manner. In this respect, Lacan has taken advantage of these topological objects derived from scientific discourse in order to structure the analytic experience. One should not believe that because in the analytic experience one is faced with phenomena which appear to be paradoxical from the point of view of common sense it is impossible to analyze them scientifically. That what is in the exterior is at the same time in the interior is not simply a witticism. For example, there is an object called a Klein bottle, which was invented by the mathematician Felix Klein soon after the invention of Moebius’ strip. The Klein bottle materializes, mathematically, a relationship between inside and outside which places the outside, if I may use the expression, inside the outside. I would need more time to give you a’ summary of the works by Lacan which located the main terms of the analytic discourse in topological figures. I should say that this is only the ABC of topology, since these objects can be designed. You can have a Moebius strip in front of your eyes. You can have a Klein bottle in front of your eyes, in three dimensions, only in an approximate form; but it can still be drawn. Then, with algebraic topology, the objects can no longer be drawn: what is called an object is a pure creation of mathematical discourse.

Therefore, we should not take as a criterion of science what experimental science has believed it can define as scientific in its own case. I must tell you that all that we accept as scientific disciplines in the schools of humanities, that is sociology, psychology, medicine, is very often a joke in the eyes of a mathematician or a physicist. I say this only to make it clear that the concept of science is more complex than simply trying to be objective. As Hamlet has it:

There are more things in heaven and earth, Horatio.
Than are dreamt of in your philosophy.

The fate of science is tied to formalization, not to measurement. It is tied to the number in so far as the number represents in an enigmatic way the presence of the signifier in the real. I shall return to this point later. Lacan represents an attempt to formalize the structure which supports the phenomenology of the analytic experience. It is evident that this is a complex structure, since the phenomena which occur in the analytic experience induce, in a first approach, the feeling that they cannot be structured. Yet metaphor can be structured; metonymy can be structured; equivocation can be structured; the function of the Other in the determination of sense can be structured. This is, in a sense, an amazing feat. The feat consists in grasping, with the discourse of science, a Held that science was prepared to leave to obscurantism, that is to say, to leave as the refuge of fantasies of sexual knowledge.

This is why I was able to say, in my first lecture, that Lacan’s teaching was a critical and epistemological teaching, opposed to all obscurantist discourses which have found refuge, in the era of science, in the psychotherapeutic game.

IV. Once again, I am going to formulate a thesis which in my opinion has consistency outside the Lacanian phraseology, and which I submit for the consideration of teachers and students who are not specialists in Lacan.

Science assumes the disjunction of the symbolic and the imaginary, of the signifier and the image. Lacan has often commented on the works of Alexandre Koyré, one of the greatest French epistemologists, on Galileo, Kepler and Newton. Professor Cadenas told me that science is something which gives birth, for instance, to the equation of gravitation. This is also the example that Lacan uses as a model. But the emergence of the key equations of gravitation theory required – Lacan, on the basis of Koyré’s studies, points this out – the disappearance of all the imaginary values attributed to the movements of the stars. It required, according to Lacan’s expression, the extermination of all imaginary symbolism from heaven. What was. at bottom, the “epistemological obstacle” – to use Bachelard’s now famous expression – which opposed a barrier to the formulation of the equations of Newton’s theory? Let us consider Kepler’s example. Kepler could still think that. given the eminent dignity of the stars and their superior value, the orbits of planets should have a perfect form. Given that requirement of perfection, the movement of planets could not possibly be elliptical, but circular. This imaginary theory assumed that the circle, is more perfect than the ellipse; hence the requirement, I would say, of an aesthetic and imaginary character, that the movement of the planets be circular. Newton’s equation could only be formulated from the moment when there was a renunciation of the attribution of any imaginary signification to heaven; from the moment when thinking of the dignity of the planets ceased; when there was a renunciation of the requirement of perfection and one could be contented with those small symbols which can be written on a sheet of paper and which are valid for the entire creation.

In this sense, scientific theory has demanded. an adherence to the signifier in so far as this is separated from all imaginary signification is amusing that this did not prevent Newton from scrutinizing The Book of Daniel and The Apocalypse of John, in an attempt to decipher in the sacred text the future of creation and God’s plan. As with many other attempts at that moment of birth of scientific discourse. Newton could on the one hand exterminate the celestial signification, and on the other he looked for it, as a cabalist, by scrutinizing the biblical text. This is something which is not very well known. It is not to be found in Koyré. but in Lacan, who read Newton’s text on The Book of Daniel. Lacan has a copy of the edition of that time. It happened, then, as if signification, which had been excluded from heaven, found refuge in the sacred text. Newton is not, in this connection, the man one usually thinks he is. Someone wrote a beautiful article on Newton. He was a rather extraordinary scholar, and not simply an economist: Lord Keynes, John Maynard Keynes, who was very interested in Newton. Soon after the war he wrote an article in which he called Newton the last of the astrologists. That was the paradox which existed at the origins of the discourse of science: simultaneously with his construction of mathematical physics, Newton was passionately fond of astrology. A thesis published by MIT in 1975 or 1976 has revealed a number of papers by Newton concerning his research on physics. This presents to us Newton the individual as crossed by the epistemological cut. This is a remark aimed at avoiding any confusion between the individual and the subject of science, in so far as the latter is tied up with the discourse of science.

V. You must know Pascal’s sentence, which irritated Paul Valéry so much: “The eternal silence of these infinite spaces frightens me.” Valéry was bothered by this sentence; he considered it to be a beautiful verse, but he thought it was rather melodramatic. Pascal was also one of those traversed by the epistemological cut. I would say something different to what Valéry said. Pascal’s sentence on the silence of the infinite spaces reveals a very modern affect, since heavens, the creation, were not at all mute before the advent of science. On the contrary, (he spaces, heavens, the creation, the earth I sung the glory of God and the grandeur of His plan. It is precisely the discourse of science, since the emergence of mathematical physics, that makes the world become silent. Lacan sums up this proposition, which I believe is unquestionable, by saying that science assumes that there exists in the world the signifier which means nothing – and for nobody. That the signifier can be found in the world, a signifier which is organized and which responds to laws, but which is not linked with a subject who would express himself through it—this is an entirely modem and scientific idea. The signifier may exist independently of a subject who expresses himself through its mediation. This is a signifier separated from its signification; a signifier without intention. The mathematization of physics answers to this requirement. But the Freudian invention of the unconscious also responds to it: the signifier exists independently of the consciousness that the subject might have of it or its expression. It is rather the subject who is the effect of the functioning of signifying laws. This is why Lacan says, and history seems to confirm it, that psychoanalysis was not possible before the advent of the discourse of science.

The scientific context where the Freudian discovery was born was very significant. Freud was the disciple of Brücke and Helmholtz, German scientists who did not want to know anything but the discourse of science. Freud himself remained faithful to that inspiration for the rest of his days. In this sense, psychoanalysis can be considered as the manifestation of the positive spirit of science in a domain which has been specially resistant to the conceptual grasp of science. In a way, this has always been known. One cannot confuse Freud and Jung. If Jung broke with Freud – and, incidentally. it cost him three years of serious depression, apart from all the vicissitudes of history – it was because he returned, with his book The Transformation of Libido, to what in ancient times was called the soul of the world. This is an old theory which has continued to be present in the history of thought, and which treats nature in its entirety as a being. It is a fundamental intuition which German romanticism, for example, developed fully: it found a new youth with the Naturphilosophie and even in our days something of the same order has made Teilhard de Chardin fashionable. There have always been, and specially in the era of science, people who search for what they call a complement of soul in these forms of knowledge (savoirs) which are not scientific and yet are knowledge, that is to say, are organized. The soul of the world: this is precisely what the discourse of science has put aside; this is a movement which in history is incarnated by Descartes. Through this movement the scientific spirit separated from the spirit, which should be called obscurantist, of the Renaissance. The omega of Father Teilhard de Chardin was the grand signified which was supposed to arrange the whole of human history. Furthermore, you must know as I do the part of the theology which still remains in Marxism-Leninism. The separation between Bossuet and Marx has not been completely achieved.

VI. With the discourse of science, God ceases to speak. He is silent, even hidden, as Goldmann said when discussing Racine’s tragedies in The Hidden God. He is silent and hidden and he calculates, as somebody who is also at the emergence of the discourse of science, Leibniz puts it. Koyré and Kojève have analyzed the relation between science and Judaeo-Christian monotheism. Their thesis is that the discourse of science was only possible in a religious context, where something totally new and singular was postulated: the creation of the world ex nihilo by a divine grand Other. The creation ex nihilo constructed by the discourse of religion permitted to trust the natural experience, since through the natural experience one can find the traces of a logical creation. This is why science is not. perhaps, as atheist as is generally believed. On the other hand, in the discourse of science, the signifier means nothing within nature; on the other hand, the signifier is there, in nature, in order to organize according to laws. This is why science is always linked with the idea that there is already knowledge (un savoir) in the real: an articulated network of signifiers which function in the real independently of the knowledge that we may have of it. Once again, the history of science teaches us something, this time in connection with Newton. Cartesians were scandalised by Newton. They considered that Newton represented a return to obscurantism, since – and this is something that Lacan as epistemologist has underlined – they wondered how was it possible that the planets knew Newton’s laws of gravitation. How could the planets obey those laws? This constituted a return to the hidden qualities which Descartes has dismissed. In this respect, Newton says that he did not forge hypotheses that would have only fictional existence. With his small signifying articulation, he verifies that they function in the real. Many things are verified like that, which after all there is no need to comprehend, and which evidently place God in the horizon of science. One can verify, for example, that certain plants arrange their leaves according to the series of Fibonacci, which is a regular order of numbers in a series discovered in the thirteenth century. Do plants know mathematics? All that mathematical physics teaches us is the verification that there is a knowledge (savoir) which functions in the real. In this sense, science assumes God in two forms. In the first place, it assumes God as Descartes recognised him, as the guarantor of truth, that is to say, as an element which does not deceive. There is a very precise demonstration by Descartes in this respect. As God is perfect, it would constitute an infraction to his perfection that he lied; therefore, and although this is a limit to his power. God cannot lie. Not being able to lie does not constitute an impotence, but, on the contrary, an excellence of power. This conviction about an element which does not deceive is completely decisive in science. Avicenna said something similar: “God is shrewd, but He is honest.”

The idea of God’s honesty is not simply a joke of Avicenna’s, and although it is believed that one does not believe in God, perhaps the belief in God nevertheless persists. This is, besides, what Lacan said one day in his seminar, where there were approximately four times the number of people present here: that he was certain that there was not one person in the audience who in fact did not believe in God. In God as the element which does not deceive. In the beginning, that had the appearance of an act of faith, and the philosophical elaboration of divine perfection was an essential component of the discourse of science. One should not think that philosophy consists simply of stories floating in the air. Philosophy has had a decisive importance in the clarification of the discourse of science. This concerns the first aspect of God which I have evoked: God as the guarantor of truth; God who does not deceive.

There is a second aspect, which refers to God as supposed subject of knowing. This is something against which there is no possible defence. When there is a signifying intention which assumes a concrete form and develops, one cannot defend oneself against the idea that that signifying intention has always been there. This is why we frequently have difficulties in apprehending past epochs or different principles of thought, since the categories within which we are captured often appear to us to be so valid that we believe that they have always existed. But, for example, there is nothing to prove that Plato had at all the sense of I (le sentiment du moi) that we have since the emergence of the discourse of science. There is nothing to confirm the view that the idea that we may have of sexual enjoyment (jouissance) is the same that the Epicureans and the Stoics had. The same thing happens with scientific inventions. I shall consider an example which is more simple: that of Cantor, who invented the uncountable infinite. He developed this invention in mathematics, not through experimentation or measurement. He invented it, undoubtedly, in a subjective experience for which he paid, one could say, with his reason. It is known that Cantor had a number of admissions to psychiatric clinics. What was the source of Cantor’s references when he invented the uncountable infinite? This is not to be found in a manual of mathematics, but it is mentioned in the works of Bourbaki on the history of mathematics. Those references are contained in the works and letters of Cantor. Cantor looked for references in theology. There is, as well as his mathematics, a theology of Cantor. For him the uncountable infinite and set theory were means of approaching God. He thought that at the moment of his invention of the uncountable infinite he was God’s administrative employee.

Cantor’s abuses are of little interest to us. There is. however, a natural movement which consists in projecting a signifying invention onto a supposed subject of knowing. It has obviously become more and more true, and a real thing for us. Cantor’s uncountable infinite is more true now than at the moment when Cantor invented it. Now it has been grasped, absorbed and developed by the discourse of mathematics. Developments like this have always required, obviously, the consensus of the community of mathematicians. It is apparent that in their case the function of transmission is essential. It is regrettable that instead of conceiving of itself according to the model of the community of scientists, the community of psychoanalysts conceive of itself as an ecclesiastical community. This has been to a great extent responsible for the delay in the diffusion of the positive spirit of science in psychoanalysis, such as Lacan has developed it after Freud.

It is worthwhile to consider Cantor’s scientific invention again. You may know the way in which Cantor demonstrates the existence of the uncountable infinite. He starts off by building a chart which, by hypothesis, would comprise all numbers between 0 and 1. Then, following what is known as Cantor’s diagonal method, he changes the symbol which appears in the place corresponding to each number of the diagonal in his chart. He reverses each of the symbols of the diagonal chain. He thus demonstrates that, each of the lines being infinite, the diagonal number cannot appear in the list, and that, in the mathematical sense, there exists an infinite as uncountable, as not being in the list of numbers. This is the paradigm of the mathematical real: the real constructed on the basis of a purely signifying experience. It is a real which emerges from the impossible, determined by a network of signifiers; it arises as a form of impasse in formalization; it is a sort of residue of the signifying operation. I hope that through this example, which obviously assumes some knowledge of mathematics, you grasp the sense of Lacan’s apparently paradoxical proposition: “The real is the impossible.”

When I say that this example requires some knowledge of mathematics, I mean that in fact it can be explained on the blackboard in half an hour, even to people who know nothing of mathematics. I have not talked about this example to make you think that it is something very complex: it is, indeed the ABC of the signifier.

VII. Descartes developed what one could call the subject of science. We know that the emergence of the Cartesian subject, the subject who says “I think, I am,” constitutes a cut in the history of ideas. This cut has been identified as such, at any rate, in the history of philosophy. It is an error to think that the Cartesian cogito establishes the identity I=I. The Cartesian cogito is something different to the ego as function of synthesis which psychologists test It is an abuse to extend the specific identity of the Cartesian cogito to the whole psychical sphere – psychical acts, movements and representations. The Cartesian cogito is, at the time of its emergence, correlative of a very distinct moment. Lacan, following the Cartesian text very closely, and in a way which is not contradictory with the most rigorous reading of The Meditations so far, that of the philosopher Martial Guéroult, deciphered the first Meditation in this direction. You may know, even if it is only from having heard its being mentioned, about the function of the hyperbolic doubt in Descartes. This function is nothing else than the emptying of the universe of representations, of everything which is imaginary. The cogito in its identity only emerges as the ineradicable residue of this operation of emptying. It we follow Lacan’s witticism in this connection, the evidence is of an emptied subject (sujet évidé) who does not exist at all as a sphere which would contain lots of representations, qualities and a diversity of properties, but as a simple, vanishing jlot. Descartes says: “I am, I think” – but for how-long? I am only during the instant when I think.

This is a subject who at the moment of his emergence is not a substance at all; on the contrary, he is an entirely desubstantialised subject, who is not a soul in any way, who is not in relation with any nature; a subject for whom all natural adherences have been undone. This subject who has broken with all those adherences and with all signification apart from that punctual and vanishing residue where thought and being become one, is structurally the agent of the discourse of science. This is the subject who then makes the signifier work in its relation with the other signifiers. It is on the basis of this subject that one can simply trust the small letters of algebra. These, small letters are not words; they are not captured by metaphor and metonymy; they are separate from signification. This is also the subject who is correlative to Cartesian extension, that extension which is so singular that is entirely external to itself (as Merleau-Ponty used to say, “without shadow and without hiding place”), that extension which is entirely manipulable and which is effectively the foundation of the discourse of science. I must point out that Descartes does not remain in this point of the subject, because he immediately discovers that the subject is correlative of the divine big Other, supposed subject of knowing who guarantees the automatic manipulation of those small letters.

VIII. Lacan postulates, and this may appear to be paradoxical, that the subject of the Freudian unconscious. that subject which is ostensibly very different from a cogito, is the subject of science. Descartes’ punctual and vanishing subject. Two things should be distinguished in this respect. In the first place, this subject of science which emerges with Descartes is, at the same time that it emerges, rejected by the discourse of science. He is simultaneously one of its conditions; but it is a foreclosed condition, rejected to the exterior, which means that science presents itself as a discourse without subject, as an impersonal discourse, as the discourse of the supposed subject of knowing in person.

The academics, and I am one of them, always introduce themselves as the representatives of the supposed subject of knowing. This is particularly evident in the universities, in Caracas or in Brussels: the academics pretend to articulate statements (énoncés) as if these were without enunciation (énonciation). We know that when one says “I” too frequently, and when one puts oneself on the scale, there appears to be a transgression against the discourse of science and its impersonality. In the case of psychoanalysis, the teaching does not take place in the same way as in the other disciplines. In fact, it is in the discourse of science that one can truly find the subject of Chomsky, about whom I spoke in my previous lecture: the ideal speaker- hearer who knows perfectly well the detours of his language and who transmits (that is the hope) without equivocations. Chomsky’s formulation is the ideal of scientific language, not the language that we speak and the language that speaks to us. Indeed, in the history of science itself one can perceive what could be called returns of the subject. This is observable precisely when one believes in the possibility of identifying oneself with the supposed subject of knowing. We may think of Frege. who believed that he could malhematize classical logic completely, through the achievement of a perfect, unequivocal and total written language. What happened to Frege is one of the great dramas of the history of science. At the time when the second volume of his work was about to be published, he received a letter from Bertrand Russell in which Russell told him that there was a small paradox in his first volume which spoilt the whole work. It is a very short paradox of only one paragraph, it fits within a sheet of paper, and Prege spent the last twenty years of his life ruminating over that significant fact. There are those lapses within the discourse of science which put all certainties in question. There is still another example taken from the history of mathematical logic which is, par excellence, where the perfect certainty of the discourse of science should be established. I am referring to the famous proof of Gödel. When Gödel postulated his theorem, the guarantee provided by the Other for the manipulation of the small letters, which had commenced with Descartes, appeared to suddenly collapse. I quote these examples simply to evoke the discourse of science in so far as this rejects the subject; and in turn, the subject also fractures the consistency of that discourse.

In the second place, the subject of the unconscious, in Lacan’s sense, is nothing else but subject of the signifier, that is to say, the subject of science, but regained in a scientific field as the subject who speaks. He is a subject who serves in an integral form as the vehicle of the signifier. Psychoanalysis is different from all forms of initiation and contemplative asceticism known in Antiquity. It is also different from all the vague bodily manipulations which are again fashionable today – those exercises through which an attempt is made to help the subject to get rid of his pain, to encourage him. to influence him by suggestion and to stimulate him. The psychoanalytic exercise is different from all initiation precisely because, if psychoanalysis is to work, the subject is not to have any form of mental preparation, contemplation or asceticism. On the contrary, the subject of psychoanalysis must arrive without preparation and must offer himself for the exercise without any previous purification. He must attend his sessions regularly, in a manner that can be called bureaucratic, and tell everything that goes through his head. He must not prepare fine speeches. It is not a question of purification through language, but on the contrary of releasing the material in disorder. And which is the operation peculiar to the psychoanalyst? To guarantee that all this material released in disorder has a cause. In this respect the fundamental postulate of psychoanalysis is determinist. Everything has a cause. This is one of the two formulations of the principle of sufficient reason, which emerged only with Leibniz. Once again, this is a principle linked to the discourse of science and which, incidentally, Heidegger commented in his work The Essence of Reasons. This is why in the psychoanalytic operation the psychoanalyst plays the part of the supposed subject of knowing. The analyst occupies this place in order to render the analytic operation possible. It is a very dangerous place, because this can easily lead the psychoanalyst to identify himself with the good God. This is, in fact, what we can verify in the history of psychoanalysis. The analysts have gladly identified with the divinity. They even experience a very special infatuation: given that as a consequence of their function they are supposed to know, they do not feel obliged to know anything. I mean that they can well be swimming in ignorance, but this does not prevent that, as their position is that of the Other in the experience, they consider themselves to be perfect. Sometimes they regard themselves as the model for their patients, as their ideal; sometimes they confuse the psychoanalytic treatment with a form of education which would simply aim at leading the subject to identifying with the psychoanalyst. They believe themselves to be the sovereign good. Lacan has made remarks like these, and naturally he did not make many friends among the psychoanalysts through them. If he is occasionally critical of the practitioners of other disciplines, certainly he is less critical of them than of his colleagues.

Lacan has also stated that the analytic experience does not consist in the identification of the patient with the psychoanalyst, but on the contrary in the evacuation of the supposed subject of knowing. There is only one practice that could truly be called atheist, and that is psychoanalysis. This is why priests are so interested in psychoanalysis. One can also observe the opposite trend. One can see psychoanalysts, even of Lacan’s school, like Françoise Dolto, telling the masses that the first psychotherapist was Jesus Christ, which pleases neither the psychoanalysts nor the Church. This is what after thirty years of Lacan’s discourse one can again hear in Paris. We must be sceptical about the effects that can be achieved through the! production of theory.

It is already time to finish. I still have to discuss two points, which I shall only do briefly.

IX. This point was originally aimed at showing how Lacan has, in the analytic experience itself, structured those paradoxes of communication which I presented in my second lecture and which prompted Professor Cadenas to say that they rendered knowledge impossible. I would have liked to demonstrate how Lacan, in a domain which is undoubtedly very difficult, attempts to structure those paradoxes. It is true that generalized equivocation is a motive to lose one’s mind; and yet this generalized equivocation has a structure.

X. I would have like to acquaint you with that formula of Lacan’s which I presented rather abruptly: “The woman does not exist.” It is a very good example precisely because Lacan attempts to write this paradox in a logical form; by this I mean he borrows the tools of mathematical logic. One should not believe that logic is simply what is taught at the first classes of the University about the principle of contradiction, and that where the principle of contradiction is not valid, there is no logic. This is an error. On the contrary. There exists something like Russell’s paradox which requires elaboration. There are inconsistent mathematical logics, founded on the negation of the principle of contradiction. It is possible to make a mathematical logic work while negating the principle of contradiction. If there are logicians present here, I think they will not disqualify what I am saying, given the existence of inconsistent mathematical logics. Lacan’s logic of the signifier. that logic which suits the unconscious and which does not know of contradiction, as Freud^said, is an inconsistent logic. The whole algebra of Lacanian terms .is organized around inconsistency.

I hope that logicians from Venezuela, if they are present here, will not contradict me, since the development of inconsistent mathematical logics has taken place particularly in Latin America. The Brazilian, Argentinian and Chilean schools of mathematical logic, whose recent symposium has been published two years ago by the North Holland Collection of works on logic, have shown all the resources that from the mathematical point of view can be found in the inconsistent logics. This demonstrates that there are more things in science than one imagines.

Lacan developed an inconsistent logic .of the phallus. He thought, very faithful in this respect to his teacher. Little Hans, that the phallus could be considered as a predicate. Lacan was able to arrange the Freudian paradoxes of castration of the basis of an inconsistent logic of the predicate phallus.

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