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Introduction to Guy Le Gaufey's Article on Sexuation

The Letter, Issue 39, Autumn 2008, Pages 1 - 9


Cormac Gallagher

The author discusses his difficulties in translating Guy Le Gaufey’s article "Towards a Critical Reading of the Formulae of Sexuation”. He summarises this article as it first appeared and outlines the historical and clinical issues in Le Gaufey’s recent book, Lacan’s Notall.


Early in 2005 a senior French psychoanalyst who had been secretary of the old EFP for twelve years and who during the early 1970’s was spoken of as one of the ‘gang of four’, the ‘Bande de Moebius’ who were likely to succeed Lacan as its head, asked me if I had read Guy Le Gaufey’s article on Sexuation: “the best thing ever written on the subject.” Since this man rarely recommends any reading material - I should know since he has been my psychoanalyst for the guts of forty years - I set about reading the article and got Le Gaufey’s go-ahead to attempt a translation.

By September 2005 I had a letter from him welcoming the first draft and making a few suggestions regarding two particular expressions that form a Leitmotif of the article and of much of Lacan’s work from the late 60’s on: the il n'y a pas de rapport sexuel which I had rendered as ‘there is no sexual relationship’ and the pas tous and pastout which I had handled according to the context but generally as ‘not every’ and ‘notall.’ I will say more about this choice anon but the final decision about what would get across in English was left to me.

I continued to revise the translation for two years and worked through it with my final MSc class in St. Vincent’s University Hospital and with a working group of experienced psychoanalysts in 2007. In both cases the response confirmed that this was indeed a remarkable though difficult piece of work.

Meanwhile, Le Gaufey had published a book entitled The Pastout of Lacan: Logical Consistency, Clinical Consequences[1] which the author modestly called ‘un instrument de travail’ which contained the article on sexuation with numerous modifications, without however changing the general profile of the text which had originally appeared in the journal L’Unebévue[2] from which I had worked.

I had neither the time nor the inclination to revise my translation in function of these modifications. Other weighty writings of Lacan remained to be translated and worked through such as L’Etourdit which currently occupies our work group but I would encourage the ‘curious reader,’ as Freud calls him somewhere, to read the article as it appears in the Pastout book. Patricia McCarthy has in particular signalled the important clarifications of Lacan’s use of Jacques Brunschwig’s article on Aristotle[3] which add to what appears here towards the middle of the article and which in the book runs from the last paragraph of p. 78 to the last paragraph of p. 84. I have not inserted this nor have I looked for the other modifications mentioned by Le Gaufey. In retrospect it might have been better to have translated the later version but then the year of ‘06 would have been all the poorer.

What I propose to do in this introduction is to reverse the order of presentation in the book and first to discuss the sexuation article, then to outline the introductory historical chapter which deals with the attempts to answer the question of sexual identity and difference throughout the ages and finally to present the third chapter on some of the clinical consequences of the formulae of sexuation. All of this will be done as briefly as possible and to end I will offer a few words on why Le Gaufey thinks that Lacan’s excursion into the Borromean Knot ends with the conclusion that it is not an adequate metaphor for the relations between the Real, the Symbolic and the Imaginary.

Towards a Critical Reading of the Formulae of Sexuation

Some Lacanians have been put off by the very title of the article as if Le Gaufey was setting out to discuss one of the high points of Lacan’s achievements in a critical or censorious way. This is far from being the case. From the middle ages on, in both English and French, the critic is one who is seen as skilful in judging, as the drama or literary critic shows. Critics i decide whether a novel is worthy of a Man-Booker Prize or a play of a 1 Tony. Guy Le Gaufey was one of the very few to be accepted as an AE in Lacan’s last years and has been an unrelenting critic of Jacques-Alain Miller’s establishing of Lacan’s publications. No one who knows anything about Le Gaufey as an analyst, writer and teacher can have any doubt that for him Lacan’s work will withstand any amount of skilled judgment and not be found wanting in either its theoretical or clinical aspects. Carefully read, and no one to my knowledge has read him so carefully as Le Gaufey, Lacan can hold up against the criticism not only of psychoanalysts and clinicians but also of the other groups to whom he has addressed himself from time to time - philosophers, theologians, mathematicians, artists and indeed the general public who flocked to his weekly seminars especially from 1968 on.

Rather than working from a final-state Lacan, Le Gaufey points from The Family of 1938 to L’Etourdit of 1972 to “a progressive elaboration with its chaotic elements and its lightening flashes, its explorations and avoidances.” The path through this elaboration is not an easy one and explains why this text is best read in a group with different members charged with explicating Lacan’s progress and his use of other writers. The first stage is the superseding of the imaginary unity of the object in the mirror stage of The Family to the emergence of das Ding in the ‘Ethics’ and the unary trait in ‘The Commentary on the Purloined Letter’, as well as the discovery of a new type of object in the ‘Transference’, the agalma or part object which results in the splitting of the imaginary small other into a specular other, i(o), and the little o-object - the objetpetit a.

Part of Le Gaufey’s critical reading is to examine Lacan’s use of the agalma in the Symposium, and Kant’s ‘nihil negativum’ in his search for something ‘to sustain the paradoxical existence of a nothing cleansed of any essence.’ A third of the way through the article, therefore, we are beginning to sense the way in which Lacan is laying the foundations in psychoanalysis and philosophy for another of his well-known phrases ‘the Woman does not exist.’

The next step is to explore the notion of non-relationship. I have mentioned earlier Le Gaufey’s difficulty of my translation of il n ’y a pas de rapport as ‘there is no relationship.’ I have been in the habit of translating Lacan’s relation as relation and rapport as relationship. But in his letter Le Gaufey had urged the use of ratio to emphasise the mathematical and logical influences on Lacan’s thinking: ‘is there any possibility,’ he asks ‘of using something like there is no sexual ratio.' I don’t think so. But we can see where Lacan and Le Gaufey are coming from by, amongst other mathematical analogies, the use made of the Fibonacci Series for almost ten years between 1961 and 1969.

We must prepare here for a number of dazzling leaps if we are to follow Lacan’s use of this metaphor. The series proposed by the founder of European mathematics is well known:

1, 1, 2, 3, 5, 8, 13, 21, 34, and so on

where starting from 1 the next number of the series is expressed as Un = Un-1 + Un-2, e.g. 8=5+3. What is called the ratio of this series, Un-l\Un is equal to 0.61803989....which is the Golden Number discovered by Euclid and widely used in art and architecture. This number is characterized by astonishing properties such as 1\.61=1+.61 and is quite unexpectedly identified by Lacan to his objet a which means that its relationship to 1 is to say the least unique and bizarre.

To keep this introduction within reasonable limits I will say no more on this and be contented to refer the reader to my article on the ‘Logic of Phantasy’ which can be found in The Letter no. 17, and is based on a presentation at a 1999 meeting in Rome.

Instead, let us move on to the emergence of the formulae of sexuation on 17 February 1971 which began with Lacan’s explication of a proposition he had put forward in La Psychanalyse a I’envers (1969/70): ‘there is no sexual relationship in the speaking being’ which leads on to a reading of the myth of ‘Totem and Taboo’ and his conclusion that ‘there is no universal of the Woman.’

Much of what follows requires for the non-logician a study of the relevant chapters of Kneale and Kneale’s book[4] which was greatly admired by Lacan or some shorter volume which will explain the notations used in modem logic for ‘all’ - or ‘any’ as Le Gaufey suggests - ‘existence,’ ‘negation,’ etc., since Lacan’s seminars from March 1971 to March 1972 and beyond make extensive use of them. Jacques Brunschwig’s article on Aristotle’s maximal and minimal particular assumes a thorough familiarity with these notations. Very briefly, the particular in agreement with the universal is called minimal and the maximal particular excludes the universal of the same meaning. Very roughly, all men are minimal particulars and notall women are such since there is no universal of the Woman.

This then leads on to the construction by Le Gaufey of the logical square of the maximal particular which is implicit in Lacan and refutes Aristotle’s derivation of existence from essence which had guided philosophical thinking (including that on the relationship between the sexes) for millennia. All of this goes by way of a mind-wrenching mathematical and logical explanation to the conclusion that the idea of non-relationship can hold up to the most critical reading.

As published in L’Unebévue but not in the book, Le Gaufey concludes with an addendum on L’Etourdit in which he says that Lacan gathers together in it the elements that he (Le Gaufey) has assembled from the Seminars leading to the Formulae of Sexuation. Admitting that this text, which he describes as having ‘tone of the Last Will and Testament,’ is extremely dense, he nevertheless denounces its publications in Scilicet and in Autres écrits which seem to have been designed to mislead the careful reader. Both French versions contain a ‘procession of errors’ which he attributes to J-A Miller, but also allows him to spot the one error of Lacan’s which he does criticize: ‘why does he here name exponential what is a hyperbolic function?’ My reply, even though I don’t fully understand the objection - hands up everyone who does! - is that ‘even Homer nods.’

Logic of the Sexual Gap (Logique de la Faille Sexuelle)

This section and those that follow will be briefer, and simply attempt to give a glimpse of the way in which Lacan (and Freud) are in continuity with millennia of reflection on the identity and difference of the two sexes that make up our human species. Genre in French can be translated as either ‘race,’ species,’ or ‘gender’ but the important point is that the sexual difference between genders is always expressed logically, in terms of same, different, identical, contrary, etc. The Concise Oxford Dictionary defines gender as ‘the grammatical classification of objects corresponding to the two sexes and sexlessness, i.e. masculine and feminine.’

Le Gaufey begins, as Lacan frequently did, from the two accounts of the creation of man and woman in Genesis. In 1:27 man and woman are created together; in 2:18-24 the woman is constructed from a rib in man’s side thus justifying biblically the order of patriarchy which has subsisted for millennia. Porphyry’s Isagogue (introduction) to Aristotle’s ‘Categories’ as translated by Boethius into Latin circa 500 AD was, in the view of Étienne Gilson, an anodyne text that nevertheless was the foundation of metaphysics for 1000 years. The quarrel about Universals that dominated philosophy in that millennium - does the species horse exist or is it simply a pure concept - still continues to weigh heavily, according to Le Gaufey’s hypothesis, on the contemporary debate about the sexes.

The notion of there being one common trunk to both sexes continued even up to Freud. I quote:

Freud does not free himself from the figure of thought in which each and every writer finds himself caught up when it is a matter of going from the difference between the sexes to the existence of two clearly differentiated sexes. [5]

Lacan, after following the Freudian line for many years, finally in a little read text: Propos directifs pour un Congrès sur la sexualité feminine,[6] while stating that neither sex can be accorded a nature since they are not destined to evolve developmentally but in function of one another, e.g. in castration, nevertheless concludes at this stage that phallic jouissance is not unique. There are not, however, two jouissances, the male and the female and thereby hangs a tale.

To summarise this enigma of the failed passage from 1 to 2 which will be reestated in L’Etourdit, Le Gaufey quotes that most popular of contemporary English poets, Philip Larkin:[7]


Some Clinical Consequences of the Logical Difference between the Sexes

As already stated, in the ‘Notall’ book the historical survey precedes the article on the Formulae on Sexuation and so we now move to the third chapter on the clinical relevance of what has gone before.

Le Gaufey’s main criticism is the use of the case presentation in clinical practice to present the illness of a particular individual as an illustration of the theory in general, e.g. here is an example of hysteria, or anorexia nervosa, etc. This is the clinical vignette style which has become common only in the last thirty years and is also used in psychoanalytic practice as shown by the case, which he quotes, of Pauline which the author claims to be an illustration of Winnicott’s theory of phobia as a defense against a subjective collapse into melancholia. In saying this Le Gaufey is not challenging the case histories produced by Freud, Ferenczi, Klein and Lacan. He even lists a number of the cases the latter refers to: the fresh-brains man that he takes from the accounts of Kris and Schmideberg; Joyce; Aimée and others.

The key to the correct use of clinical material is the distinction highlighted by Brunschwig between maximal and minimal particulars. The majority of clinicians consider their cases as minimal particulars which agree with the universal and in Aristotle’s logical square are subaltemates or subordinates to the universal. Le Gaufey’s criticism of J. C. Milner for using this approach in order to arrive at his conclusion that according to Lacan there is a male essence which can be opposed to a female one drew down the ire of Miller and others in École de la Cause. But for Le Gaufey, Milner is simply prolonging the traditional Aristotelian theory which holds that there can be no existence without an essence and contradicts Lacan’s statement that although women exist, the Woman does not exist. In other words there is no essence or nature of Woman which can be applied to each particular woman. In an enigmatic follow-up to this Lacan will say that there is a domain of women, although there is no set or group of women.

Lacan has in fact inverted Aristotle’s logical square of universal affirmative, particular affirmative, universal negative and particular negative which had already been questioned in antiquity, because psychoanalysis demonstrates that it does not provide an adequate basis for the logical distinction and non-relationship between men and women. This subversion of the automatic passage from the particular to the universal is then seen to have a wide clinical application. If existence is not part of the concept then the existential feature found in a particular case is not the same feature as is supposed in the universal concept.

The pastout, the notall, which Le Gaufey would prefer to see translated as notany leads to the greater attention to the individual case which may contradict the general theory. This was already recognized by Freud in 1915 when he published his “A Case of Paranoia running counter to the Psychoanalytic Theory of the Disease” and perhaps even anticipated by William James, one of his heroes, when he distinguished in the The Will to Believe between two mindsets: the presumption of harmony as opposed to an openness to the brute facts of existence.

In summary, the male has for too long has been taken as the norm (nor­ mal) for human subjectivity and Lacan’s square of the maximal particular which privileges the notall and refuses to subject women to the dominance of the phallus opens up a whole area of enquiry for clinicians and theoreticians alike.


The Scholion is a term quite familiar to scholastic philosophers as an explanatory note added at the end of a particular thesis but it can also be defined as an observation or note added to a mathematical proposition. Le Gaufey’s use of this term as a heading for his discussion of the Borromean Knot emphasizes once again the importance he gives to logic and mathematics in Lacan’s work.

He highlights the importance of Lacan’s discussion with Soury on the Borromean knot especially on the conundrum of how Real, Symbolic and Imaginary circles are to be distinguished if they each have the same value. The initial solution is that they could be given different colours. Briefly, this results in the red circle representing the symbolic while the two sexes are represented as the imaginary and the real by two other colours. (Cf. Session of 9.3.1976). But, thorough reader of Lacan that he is, Le Gaufey can quote from one of the very last seminars: ‘The metaphor of the Borromean Knot in its simplest state is wrong....That there is no sexual relationship because there is a symbolic, an imaginary and a real, is what I never dared to say. All the same I said it. It is quite obvious that I was wrong... (Session of 9.1.79).

And on that sad note of the tireless old man who was never afraid to admit his errors we will leave this introduction.


[1] Guy Le Gaufey, Le Pastout de Lacan: consistence logique, conséquences cliniques, Paris: EPEL, 2006.

[2] L’Unebévue, Paris: L’unebévue ed. (2005), no. 22.

[3] Jacques Brunschwig, “La proposition particulière et les preuves de non-concluance chez Aristote”, Cahier pour l ’analyse, no 10, Travaux du Cercle d’épistémologie de l’ENS (Paris: Seuil, 1969) pp. 3-26.

[4] W. Kneale & M. Kneale, The Development o fLogic, Oxford: Clarendon Press, 1962.

[5] G. Le Gaufey, Le Pastout, p. 35.

[6] J. Lacan, “Guiding Remarks for a Congress on Feminine Sexuality” in Juliet Mitchell, Jacqueline Rose (eds.), Feminine Sexuality, Jacques Lacan and the Ecole freudienne (London: Macmillan, 1982) pp. 87-98.

[7] P. Larkin, Collected Poems (London: Faber & Faber, 1989) p. 108.

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