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Reading L’Etourdit: First Turn: Chapter 4. The Phallic Function and the Formulae of Sexuation

The Letter, Issue 53, Summer 2013, Pages 1 - 39




Christian Fierens

(111) Let us take phallic functioning up again starting from the Oedipus complex summarised in the first two formulae of the phallic function. What obliges us to go beyond the Freudian Oedipus complex formulated in that way?

Free association and the equally floating listening open up the path of ab-sense and of an saying freed from the search for a relationship between meanings. The experience of analysis demonstrates the ab-sense of sexual relationship: there is no relationship between the existences (‘masculine’ and ‘feminine’: nia and nya) and there is no relationship between the two universals (masculine and feminine). The masculine Oedipus complex cannot define ‘femininity’.

Psychoanalytic discourse gives the means to go beyond the Oedipus complex: it produces the phallic signifier which will mean something quite different than the phallus. The phallus is reputed to be the sexual copula between the man and a woman; further, its meaning is supposed to condense every meaning among speaking beings. In opposition and as a contrast to this conception proper to the phallus, the phallic signifier will not be a sexual copula, nor will it be the condensation of every meaning. But what will the phallic signifier mean positively? Starting from the ab-sense of the sexual relationship, the phallic function opens up a sexual bond between speakers which is based neither on an anatomical relationship, nor on a chromosomatic relationship, nor on a cultural relationship: the phallic function supplies for the ab-sense of the sexual relationship by its own functioning, which is unfolded in the four phallic formulae. These four formulae are called formulae of sexuation because they construct what is sexed in the speaking being (the first two formulae will be called ‘masculine’, the following two ‘feminine’). Contrary to (112) sexuality, which is valid as an already established given, sexuation is always under construction, in process, in function. How is that? The production of the phallic signifier in psychoanalytic discourse presupposes the putting in parenthesis of any meaning in order to keep only the grammar (S1 → S2) of the signifier and the logic that flows from it. Not being able to take on its sense in terms of meaning, the phallic function finds it in its journeying and its functioning: the four formulae are designed to be interconnected from the first to the fourth and beyond the fourth towards a second turn.

The phallus had its maximum weight in the domain of meaning. By passing to the signifier, the maximum of weight becomes the minimum of meaning: the phallic function is emptied of all meaning except for its grammar and its logic; it is the signifier from which there is cut away all semantics, it is the asemantic signifier which is only valid from its grammar.

Later, the phallic function as asemantic signifier, will be developed as a topology which does not produce meaning properly speaking, namely, as a topology which is not metaphorical. This topology will respond to the ab-sense proper to psychoanalysis. It alone allows access to structure. Then to interpretation.

1. The first two formulae and the Oedipus complex. (14e-17b; 458-460)

The Oedipus complex is summarised and developed as ‘the logical correlation between two formulae’:∀x.Φx and ∃x.Φx.

‘For all x, Φx is satisfied’. Since the phallic function Φx is not limited by any meaning, it is satisfied for all x, for any argument whatsoever. How can we say what it is and what it means? After putting meaning in parenthesis, there still remains saying, its grammar and its logic. To define the phallic function, it will be enough to (113) follow its logical journey and to see how it is satisfied by logical arguments (‘for all’, ‘there exists one’, ‘no’ [ne pas]); such is the development of the formulae of the phallic function or of sexuation. At the end of the journey the enigmatic Sphynx will be able to say: ‘You have satisfied me, littlecutman’ (25a).

First formula.

From a formal point of view, one could imagine ∀x.Φx as the equivalent of the universal ‘all x is phi’, the function (phi) replacing the verb and the argument (x) replacing the subject. Nevertheless between the two, the copula ‘is’ has disappeared. This ‘modification’ already indicates to us that our universal (∀x.Φx) does not function by relying on a ‘being’ which would establish a meaning-relationship between the subject and the attribute. On the contrary, it is by functioning that the function can set up secondarily the possibility of a being. The function is there first of all in non-being, in the gap of its ab-sense; it is from there that different arguments can take their place. A first argument, ‘all x’, will give the first formula ∀x.Φx. This formula admits two translations of this ‘for all x’, one at the level of the said, the other at the level of saying. The fact that there are two possible translations already announces a split which will generate the other formulae. The first, all meaning refers to another meaning, is the dit-mension of truth. We find there the meaning-relationships, which lead reason to pose the ego, the world and God vs. man, the unconscious and the Oedipus complex. At the level of this first, the subject is represented by a signifier for another signifier (the subject is the truth of the master discourse). The second translation implies saying: every subject is inscribed in the phallic function to ward off the ab-sense of the sexual relationship (15a; 458). As the Other of psychoanalytic discourse, the subject is the problematic stake in analysis; irreducible to a meaning-relationship, it will be grasped from the ab-sense and the impossibility proper to this discourse. ‘The practice of making sense’ begins not through the meaning-relationship (6-7), but through ab-sense – the nonsense of the witticism for (114) example – which suspends every said in order to make saying appear (‘the practice of making sense, is precisely to refer oneself to this ab-sense’ 15ab; 458). This ab-sense is not simply a suspension of sense, of the meaning-relationship; it is the ‘reference’ or the Bedeutung of the phallic signifier (in other words, the phallic function and its development). The practice of making sense from absense is not determined by a will, but comes from the function [the quotation marks of ‘veut dire’ ironises on the veut while pin-pointing the dire].

Second formula.

‘There is by exception the case…where there exists an x for which Φx, the function, is not satisfied…’ (15ab). The exception of the second formula operates from the first formula on, especially as saying. Saying ex-sists, poses itself as outside the all of the phallic function, in order to be able to pose the first formula (the all); in other words, its ex-sistence is inherent to phallic functioning. In that way saying as exception appears to be inherent (from Φx) and outside (not Φx), intimate and ‘extimate’ with respect to the phallic function. How explain this apparent contradiction? The ‘case’, what falls outside the phallic function starting from the phallic function, is first of all explained by mathematics. The fractional function[1] ‘1\x’ has no sense if x = 0; in effect, by definition, the divisor or the denominator of a fraction is not null (otherwise the fraction, not responding to its grammar, would have no sense). To say 1\x implies – among other things – that x is not equal to 0 or again that for x equals 0, the function does not function. This exception confirms the rule in that it goes outside the rule to mark the limit of its definition. It is ex-sistence.

These two formulae are going to be combined, amalgamated: one is the reason for the other. But this combination, in accordance with (115) what was said above, is brought about ‘by going back’ (10e); starting from the third person of midit (the first translation of the first formula: every meaning always has something of the moiety-said) it goes back towards the tu (second translation of the first formula: tu médites [you meditate] towed by the signifier), then towards theje (second formula: by posing myself as an exception, I speak ill of, je médis); it is only from the said that a saying appears. It is in this way that ‘for all x’ modifies ‘the all of the universal’ (15b; 459). ‘For all’ is submitted to the modes of saying (modi-fié), the discourse is no longer constructed from outside by an agent that is supposed to organise a subject, a predicate and a copula; but the phallic function makes the combining of different formulae appear by its very functioning. By introducing the mode (qu’on dise…), the ‘quantifier’ (‘forall’) modifies the classic universal and makes it appear as possible, depending on saying. The ‘all’ of the classical universal was composed from a sum of examples, of grains of sand, of innumerable ‘quanta’. But just like light that is both quantic or discontinuous (made up of particles, of quanta), and wave-like or continuous (made like a wave), the phallic theory articulates in its first formula a discontinuous said and a continuous saying. The topology of the second turn will show us this articulation in the opposition of the cut to the surface.

To the quantic universal saying is paired; onto the universal there is grafted ‘a particular saying’. In function of its particularity, this saying may only appear quantic (‘there exists one’) but it is quite different to Aristotle’s particular proposition. For Aristotle the particular affirmative is 10 contradictory to the universal negative proposition and 20implied by the universal affirmative proposition; it is encased in the universal, simply adding to it true and verified existence for the ‘some’ of which it speaks. On the contrary, in the practice of saying, the particular affirmative implies the particular (116) negative: if I say that some women are phallic, I also mean that some – and even the majority – are not so. The particular therefore is not something said which would be encased in a more universal ‘said’, but it presupposes a complex saying; it exceeds the universal. The exception at stake in the second formula (‘there exists one’) only exists moreover ‘by being formulated as an saying no’ (‘not phi of x’); it ‘does not belong to the dit-mension of truth’. While the first formula can be said to be true (15a), the second is correct [juste] (15e). This correctness of the existence of the exception is ‘to set a limit to the forall’ of the universal by constituting it or confirming it: ‘which a proverb already opposes to Aristotle’s contradictory’. For Aristotle, ∀x.Φx and ∃x.Φx are in effect two strictly contradictory propositions. Nevertheless, ‘the exception proves the rule’, says the proverb. The existence of a saying excepting itself poses and confirms the rule of the universal said. The Aristotelian construction centred on the contradiction of the said by the universal affirmative and the particular negative collapses in favour of the dynamic of saying.

We find the reason for this combination of saying and the said in the subject: ‘the analytic discourse concerns the subject, which as an meaning-effect is a response of the real’. How is this subject concerned by analytic discourse? As a meaning-effect, it represents a signifier for another signifier, it is the truth of the master discourse; but the discourse of the master is powerless to grasp this subject: the ‘response of the real’ prevents the subject from being apprehended outside the roundabout of discourses. The subject can only be defined by the different places that it may take: semblance (of the hysteric), truth (of the master), product (of the academic), Other concerned (by the analyst). This journey can only be begun after the putting in parenthesis of the meaning which riveted us to the master and academic discourses. We will start then from the grammar ‘of the asemantic signifier’ (15c; 459). The ‘quotation about the non-semantic signifier’ is drawn from the seminar of 11 April 1956 (Seminar III) and recalled later (40; 483): Ad usum autem orationis, (117)incredibile est, nisi diligenter attenderis, quanta opera macinata natura sit: ‘nature has contrived a great number of works for the use of the word; one cannot believe it unless one pays careful attention to them’. The sentence quoted – independent of any meaning – insists on the machinery proper to the signifier, on its syntax or on its grammar. By ab-sense, there is introduced a new subject: ‘The subjective is not on the side of the one who speaks, it is something that we encounter in the real’ (Seminar III, p.211), p. 207. Faced with the subject concerned in the psychoanalytic discourse as Other, the analyst is ‘called to a function of waste product’ (15c; 459): as o-object, as waste product, turd and reject, he takes the place of semblance.

The opening up of the subject (Du sujet enfin en question, E 229) is impossible to hear for anyone who situates himself in the ‘academic discourse’, ‘which, from its structure, has a horror of psychoanalysis’ (Radiophonie, p.64). The academic does indeed produce the subject; but it is a matter here of putting him in question inasmuch as he is in the position of the Other, which implies the putting in parenthesis of meaning (proper to the master and to the academic). The putting in question of the subject ought to be opposed to the inflation of meaning, ‘to this hermeneutic, indeed semiologising dripping … streaming as it now is from all sides’ (15d; 459). If the academic discourse is ‘now coming from every angle’, it is because analysis has not ‘fixed its deontology’. It is up to analysis to indicate how the academic discourse ought to be, namely, how it ought to separate itself out from being (l’être), in order that the phallic function may appear. The subject is in effect put in question when the product of the academic discourse comes up against its powerlessness. The academic discourse then switches into the psychoanalytic discourse not without involving a de-construction of being, ‘the de-ontology’ of that which, as being, prevented the question of the subject.

Beyond the ‘subject’ as meaning-effect, namely represented by (118) a signifier for another signifier, the existence of a subject is posed as ‘saying no to the propositional function Φx’. This saying, which is not a contradictory said of the universal, is posed outside the dit-mension of truth (true or false), it has ‘no value that can be noted as truth, which means none of error either’ (15e): at the precise point of existence (∃x.Φx), the phallic function is neither true nor false (the ex-sistence posed is in no way the recognition of a ‘truth’). The false just as much as the true implies saying. Instead of being the contrary of the true in the dit-mension of truth, the ‘false’ falls, it is the fall or the fallen, the Latin falsus (past participle of fallere, ‘to make fall’) that makes saying appear. Let us take up again the example of the fractional function 1/x: a ‘case’ (x = 0) fallen, collapsed outside the domain of the function makes saying of the function appear. The ‘case’ (from the Latin casus, the fall but also the past participle of cadere, to collapse) goes along with the false (falsus). In the putting in question of the subject, interpretation ought then to plead the false, as required passage of the phallic function, as the second formula necessary for the movement of saying, to make the position of the ‘ex-sistence of the truth’ (6c; 450) appear and the time required (‘la faux du tempsRadiophonie, p.81) to go over the different positions of the roundabout of the four discourses. One position (a first discourse, a first formula) brings about a new position that denies it and corrects it: the bud disappears when the flower comes out, the flower withers when the fruit matures, the fruit falls to the ground in order that the plant may be reborn; these figures (c.f. Hegel) or formulae incompatible with one another are supplanted in the functioning of the plant, which only exists by these necessary forms which are nevertheless contradictory among themselves.

‘It is therefore correct to write... ∃x.Φx’ (15e), the ‘case’ ‘falls’ just right to limit the universal. Saying is then sup-posed to the said and the ‘subject’ is ‘sup-posed from the fact that the phallic function is forfeited by it’ (from foris, outside): ‘the existence of the subject’ is sup-posed…outside the phallic function. The two formulae are (119) fundamentally disparate: the one (the universal) is said as ‘truth’, on condition of perceiving that this truth is only posed, is only possible; the other (the particular) is a saying that is ‘just right’, without any truth value, it belongs to the domain of the necessary, of saying necessary for there to be the said. From these two formulae, the universal is valid for all and cannot be used to specify one sex or the other. The particular would seem more adequate for the definition of the masculine subject: the masculine subject could then be defined by the transgression of the law, the daring to pose its existence, the opposition of ‘saying no’ (the nia) to the phallic function. Might this be a ‘mode of access’ ‘to the sexual relationship’? Might the woman be castrated, subject to the phallic function? And is the uncastrated man supposed to partially escape the phallic function? This mode of access is ‘hopeless’ (16a; 459), for the exception (∃x.Φx) or the affirmation of existence does not concern reality, but the appearance or the semblance, a pure construction made in haste or precipitation, in the ‘s’emblant’ (embler from classical Latin involare, to fly on, or to precipitate oneself onto; we rediscover the term in the adverbial locution d’emblée). ‘The syncope of the function’ (the ex-sistence) ‘is only supported…by pretending (sembler)’, only by precipitating oneself, while all the time remaining in phallic functioning; despite ‘saying no’, man does not escape from the phallic function. Far from inaugurating a sexual relationship, ex-sistence appears as ‘what does not cease to be written’, the necessary present in the phallic function. The exception ‘completes’ the consistency of the phallic function (for all x), ‘fixing the limit’, by restricting the universal as pure possible posed by saying. This saying s’emblant in precipitation is therefore nothing other than the necessary that is appropriate, the ‘décence’ limiting the universal; in convening the universal, it can only pose itself from the sense (of the universal): ‘the semblance is no longer anything but dé-sens’ (16ab) and already calls for the more radical ab-sense.

‘The ab-sense of the relationship would seem to be plugged at the suspension point of the function’ (16b, my italics), the position of (120) exception would deaden the shocks of the absence of the sexual relationship. In fact, this quite hypothetical and fictitious plug is a ‘trick’, a means elaborated to deceive the absence of sexual relationship. This deception is therefore a ‘signifying equivocation’ (16ab; 459) since it plays on sense in order to distance itself from it.

The dé-sens (the exception), far from being a means of escaping castration, limits its universality. This dé-sens, this exception of saying is in no way a reality; attributed to castration, it is denoted as ‘symbolic’ (16b). For there to be symbolic castration, there must be an exception that traces its limits (‘the agent’ of castration…)[2]. We can now better comprehend castration as symbolic lack of an imaginary object provoked by a ‘real’ agent. The imaginary object is the imaginary phallus taken from the imaginary body and put to death to become a signifier, the phallic function. The universality of the phallic function ought to be correlated to saying of the mother, of the father or of whoever might ex-sist. Castration (for the man as for the woman) is then reduced to the articulation of the two masculine formulae of sexuation. It presupposes the notion of subject inasmuch as the said is put into perspective by saying.

‘The subject – implied by symbolic castration – was already sup-posed’ in the very context of the psychoses (Seminar III). The articulation of the psychosis (of Schreber) presupposes this symbolic structure: not alone do the hallucinations have the structure of the said (the hallucinations are essentially verbal), but in addition the language of psychosis presupposes an saying, presupposes the Other and its four-termed structure (schema L): the schema I – a schema made up of multiple deformations – maintains absolutely the structure of schema (121) L on which it is constructed. There is no psychosis without this dimension of saying, without the dimension of castration, without at least the double dimension of the masculine formulae of sexuation. The reading of Schreber’s Memoirs of my nervous illness accompanied by the Freudian interpretation (President Schreber) furnishes Lacan with the opportunity for ‘the exhaustion of psychosis’. In what does this exhaustion consist? In the draining, indeed in the drying up of psychosis and in more and more precise approximations of the subject of the subject, as is explained in A question preliminary to any possible treatment of psychosis (E 531): 1) psychosis is first of all seen here from the hallucination as a voice, as signifier, 2) then it is situated with respect to the big Other and therefore to saying, 3) finally the subject supposedly specific to psychosis is defined in schema I which is only a distortion of schema L as condition of the subject whatever it may be. The preliminary question is the question of the subject: ‘the condition of the subject S (neurosis or psychosis) depends on what is happening in O’ (E 549).

There ‘where the subject found itself already sup-posed’, ‘there where the Name-of-the-Father showed itself responsible (in 1956) according to tradition’ (16c, my parenthesis), there opens up a beach-head (plage) of saying. How determine this beach-head? Or again how circumscribe this beach-head in such a way that it becomes a ‘locus’, that it becomes determined (as locus of rendezvous, geometrical locus or locus of work)? In 1956, Lacan responded to this question by making an appeal to tradition and to the ‘Name-of-theFather’. Now, in 1972, ‘the real of this beach-head…’ where ‘the semblance lands’ realises, demonstrates the passage from the beach-head to the locus by the four discourses. How is that? The powerlessness of a discourse expels the term which occupies the beach-head of the Other in this discourse and this term lands on the beach-head of the semblance in the following discourse. The real beach-head of saying is in that way occupied by the semblance which was the Other in the preceding discourse. The beach-head of saying becomes a real locus when it has been successively occupied by the o-object analyst who comes from the Other of the academic, by the barred hysterical subject which comes from the Other of the analyst, (122) by the master signifier which comes from the Other of the hysteric, by academic knowledge which comes from the Other of the master. This procession of terms to the locus of the semblance is conditioned by the absence of sexual relationship: it depends on the powerlessness of each discourse developed from the absence of the sexual relationship; this procession of terms is a supplement: it supplies for the absence of sexual relationship. In the apparition of the locus, the Name-of-the-Father is henceforth replaced by the succession of terms which come to occupy the locus of the semblance in the roundabout of discourses. In this fashion, the semblance ‘supports our reality’ from the roundabout of discourses, just like the phantasy[3]. The support of our reality by the phantasy is nothing other than the ‘realisation’ attributed to the phantastical scenario as a universal ‘said’ is limited by saying which excepts itself from it. This saying presupposed for Freud a series of phases (A child is being beaten, 1919) or the passage from one discourse to another.

In this journey of discourse, saying does not determine simply a locus (the semblance), but ‘loci’ [the foursome of loci being opposed to the foursome of terms (S1, S2, o and $)]. Thus we can differentiate ‘in each discourse’ the universal of the said (perceptible in the terms S1, and S2) and the loci of saying (the real). Through this distinction between the said and saying, ‘each discourse is connoted in terms of virility’ (16cd), each discourse is linked to the two masculine formulae (∀x.Φx and ∃x.Φx). These two formulae are valid for all men, whatever may be the discourse in which it is inscribed: forallmen (pourtouthomme) condenses the pourtout of the phallic function (∀x.Φx) and the thomme[4] of ‘saying no’ (∃x.Φx). Saying nevertheless cannot be said; the ‘thommage’ is what follows from (123) ‘saying no’ at the level of the said rather than saying itself. The thomme is a fragment of the said that has cut itself off from the phallic function, the ‘not phi of x’; it can henceforth be comprehended in two different existences, two different ‘thommages’ as we will later see (16e-17b; 460): ∃x.Φx and ∃x.Φx. If the articulation of saying and the said was attributed – according to tradition – to the Name- of-the-Father, castration relays now ‘that which in every discourse is connoted as virility’, especially by the first two phallic formulae. This connotation of virility will be rediscovered in each of the discourses: each discourse articulates the foursome of terms (saids) and the foursome of loci (saying).

The psychoanalytic discourse has a particularity: in proceeding from the second formula (∃x.Φx), from what is necessary in saying, it accepts right away the dwindling of sense. ‘It doesn’t matter whether it makes sense or not, just say it’. Like every discourse, the psychoanalytic discourse is connoted by virility; but it is the only one to proceed from the second formula straight away to be inspired by the fact of Freud’s saying, to put sense in suspense, to take its start from these semblances. Decency, respects for what touches on propriety, especially in sexual matters (there is no sexual relationship), ‘takes its start from these – ‘: decency is the respect of loci (without consideration of the term that will come to be lodged there). Let us note that the term ‘men’ or ‘beings’, that might come to occupy the place of the semblance, is not used. These ‘ – ‘ only realise the relationship as impossible: they are not therefore particular beings but logical loci, even if ‘the biological heritage bestows the largesse of the semblance’, of the phallus to some who seem to escape castration by being identified to the exception. ‘Chance does not seem to deserve to be reduced right away to this apportioning’: despite the apparent advantage procured by this biological largess, there are always grosso modo as many women as men; the two sexes are always divided (124) according to the proportion, the sex ratio ½, ½: moiety/moiety (18c; 462). Unluckily, ‘mâle heur for me’ (16e; 460), chance, luck, a random product, for the male (moiety) ego (indeed for the male named Lacan) is going to be turned into bad luck by remaining at these two masculine formulae.

‘The loci of this thommage ‘(16e), the loci determined as real by saying are located, se re-pèrent (re-père, a new formulation of the father) by what goes through this locus. In that way the locus of the semblance can only be located (repérer) by the succession of semblances which pursue one another, the locus of truth only by the reiteration of ‘there is no sexual relationship’, the locus of the Other by what supplies for this absence of relationship, likewise for the fourth locus, the locus of the ‘product of their complex’, which depends on the interweaving of the three other places (the semblance, the truth and enjoyment).

If the ‘privilege’ of the particular (of the exception) is to locate the loci (from which each discourse is situated), ‘these elegant pathways, allées.(17a) – which recall the vas of the Sphynx – have the elegance to gather together (legare) the whole from a position of exception (e-legare). Could not these elegant pathways redistribute what must be divided, the ‘dividend’, namely the ‘speakers’, in a more reasoned way, according to the ratio of the strongest? Would it not be appropriate then to divide these ‘—‘otherwise than according to the measure of the sex ratio: one man for one woman? The gain would be for the masculine exception who has the phallus. In agreement moreover with a sexual theory constructed on a masculine model, a naïve psychoanalysis might in that way believe that it would be appropriate to go as far as saying: ‘Be the exception’, ‘Authorise yourself’, etc. This position of exception nevertheless only exists in its articulation with the universal: ‘this thommageforalls itself (∃x.Φx is articulated with ∀x.Φx). The phallic function inasmuch as it is universal would aggravate the aspect of collapse, of failure and of the running aground of this falsus, of this ‘case’: the exception would be sanctioned by the universal law.

(125) The ‘semblance of luck’ for the masculine moiety, announced by the ex-sistence outside the phallic function (∃x.Φx) is reversed into bad luck in the phallic function (∀x.Φx). This reversal is readable in the articulation of the Oedipus complex: the obedience to the phallic law promises the male that he will become like the exceptional father (recompense); but to pose oneself as exception in order to find the semblance of luck promises nothing other than a return to the phallic law (punishment).

This reversal is proved ‘by the fact that the organ itself suffers from it’ (17b; 460): a male who wants to escape from the phallic function (from castration) falls into impotence (the organ detached from the phallic function no longer functions) and reciprocally, this male is healed of his impotence by the putting into function of the phallic function[5].

This ‘thommage’ (∃x.Φx), this position of exception makes a subject appear in saying of the parents (17b): in that way a priori, in the discourse of the parent, the child represents a signifier of the parents for another signifier. This thommage is a priori a prejudice for the child who finds himself enslaved by saying of his parents. The prejudice does not result from the imagining of the phallophore, but from the fixity of an a priori affirmation which believes it is announcing a truth, while it is only a modi-fication from the phallic function of the parents. For the daughter a similar prejudice is played out; but it could be worse, because her thommage, is that ∃x.Φx (third formula, more complex, as we shall see). These two thommages are explained a priori from saying of the parents, but this psychogenetic conception remains fixated on the past: ‘that is why (126) your daughter is mute’ (or again ‘that is why your map is mute’ 40e). The fact of remaining at the first two phallic formulae (namely at the Oedipus complex) is a prejudice not alone from the genetic point of view (‘a priori’, from the parents) but also from the structural point of view (‘a posteriori’, from the discourses).

2. The prejudice of the first two formulae (17b-18b; 461-462).

Escaping from the law, from the phallic function, being the exception entails a certain ‘prejudice’; a priori prejudice where the exception feeds the narcissism of parents, but especially a posteriori prejudice in the measure that this thommage is ‘caught up’ in a specific discourse and its promises of ‘happiness’ (‘happiness’ and its ‘American way’, E 591). ‘Caught up’ in this way, the phallic function is reduced to the phallic organ, which is asked ‘to carry out the business’ of a rigid discourse, dispensed from any switching towards another discourse.

Caught up in the hysterical discourse, ‘people put it down to it being emotional’ to reinforce the truth which ought to be the o-object; caught up in the master discourse, could it not have been better trained, the better to erect the product of this discourse; caught up in the academic discourse would it not have been better to ‘educate it’ to make of it the Other of the academic. ‘For that you will have another think coming’: for the phallic signifier continues nonetheless to run through the roundabout of discourses.

‘It is only because it is not pleased with what it is made say, that it comes up against an obstacle’. The Lacanian ‘Satyricon’ (sic)[6] carries the Dionysian phallic mystery; in order that the phallic function should not be reduced to the organ, Lacanian satire attacks the use of (127) the phallus in the three discourses that attempt – ‘to command’ the ‘emotional organ’ (hysterical discourse), - ‘to train’ it and to implore it (master discourse), - to educate and ‘to control’ it and ‘to put it in vitro’ (academic discourse). Why would the phallus not accept these roles? It is because the organ phallus has always already made room for the phallic signifier with the switches and the moods of the phallic function.

As opposed to these diverse discourses capturing the phallus in their fixedness, Lacan proposes ‘to tame it’ quite differently: the topology of the phallic function – namely, of the cross-cap or of the ‘mitre’[7] – ought to account for ‘its virtues’ and its power of movement.

This topology (Chapter 1 of the second turn) is characterised by its dismantling: its structure will only be noticed by showing how it can be untied, because this ‘surface’ does not separate two regions of space: it is what is untied by a ‘circular cut’ (17de; 461, see later 26a; 469).

The topology of the cross-cap is the structure of the phallic function:

‘It is a matter of structure, in other words of what is not learned from practice’. Practice situated from a discourse only confirms and repeats this discourse; in that way the ‘clinic’ can only confirm the discourse on which it depends. Far from playing this ‘forced card of the clinic’ (E 800), psychoanalytic practice is learned not from clinical experience, but from ab-sense, from the discourse of the analyst, from the structure, which will allow one or other practice to be situated and illuminated in the roundabout of discourses. For the psychoanalyst, ‘those who know’, it becomes explicable that we have only come to (128) know recently this discursive structure of the phallic function, which is only unveiled by the discourse of the analyst. ‘Yes, but how’ explain this structure otherwise than from the practice? We will see explicitly later that the experience of psychoanalytic discourse presupposes the topology of the cross-cap (29; 472). Before that: but how (mais comment) explain the structure if not as mécomment, as miscognition? The miscognition is double: a miscognition proper to the fixation of one discourse (where the structure is not illuminated by the practice) and a miscognition proper to ab-sense (in which the practice is illuminated from the structure). It is clearly a matter in L’étourdit of following the path of this second miscognition proper to ab-sense, to the structure determined by the absence of sexual relationship, to the phallic function on its discursive journey (which will be extended into the second turn: topology, discourse of the analyst, structure and interpretation).

The ‘organo-dynamics’ of Henry Ey, a classmate Lacan’s salle de garde, is a mixture of ‘the organic’ and ‘the dynamic’, of the phallus as organ and of the phallic function. The ‘bastardy’ of ‘organodynamics’ explodes precisely when it mixes up the use of the organ and use of the function. Lacan pointed it out ironically: ‘Can it be believed that it is by the organ itself that the Eternal feminine draws you on high’…that the phallic function must employ the tool to develop its feminine formulae? Inversely, do we believe ‘that it works better (or worse) because the marrow frees it from signifying’? Do we believe that an organ determined by medullar mechanisms alone, on a purely reflex model, would function better organically?

Ey allows himself to ‘get lost’ by his ‘organo-dynamics’; the salle de garde admits that its rowdiness is not of the order of an (organic) reality but of a (dynamic) reputation linked to the songs of medics, to the symbolic of their words perhaps, but especially to their ‘yelping’, puppy-like cries, to the oobject that is summoned there.

(129) A reputation made from the fiction and songs of medics: ‘fiction and song, fiction et champ’ (18a; 461) were already in Function and field of speech and language in psychoanalysis (1953 E 237). The dimension of fiction and of song given to speech in its functioning allows former to be freed from established discourses and to make its way right through the structure. From this dimension of speech, the junior psychiatrists (of Henry Ey), ‘boys and girls’, might have been able, against the Permissive Father Masters (Permaîtres), ‘permitted themselves’ to follow Lacan by situating themselves in the position of exception (∃x.Φx). In fact these juniors had already taken on the style of their Père Maître, of their father-master in the novitiate of religionpsychiatry; they were assigned to remain in another discourse than that of the analyst and none had gone to Saint-Anne to attend the teaching that the I.P.A. had ‘interdicted’.

‘After all who knows?’ (18a; 461). The structure of the phallic function and its knowledge are also at work in those who allow themselves to get lost. The ‘rabble’ (c.f. The knowledge of the psychoanalyst, 1 June 1972) – the faithful dogs of their master – who have not dared ‘to permit themselves against their Permaîtres’ can surely not become engaged in analysis except from the point of view of a different discourse. This stupidity, remaining nevertheless always in the phallic function, ‘has its impenetrable ways’ since it wants to know nothing about it. This stupid psychoanalysis still propagates the psychoanalytic discourse, even despite itself; ‘the result is more good than bad’.

‘Let us conclude that there is a misdeal (maldonne) somewhere’ (18c; 462) this mâle donne inherent to the phallic function is the deal of the male which is cantoned to the two masculine formulae. Do we believe that the Oedipus complex would be able to account for the integrality of phallic functioning? Nothing of the kind, ‘the Oedipus complex is not what is believed’, it is limited to the first two formulae of the phallic function, which is developed in four formulae.

Remark: the discourses, their racism. (18b-19d; 462-463).

(130) The phallus, inasmuch as it is comprehended indifferently as organ and/ or as function (‘organo-dynamism’), only grounds its universality on the position of exception (that the organ assures).

Comprehending the phallic function no longer from the absence of sexual relationship, but from the presence of the organ derives from a ‘slippage’ that Freud was not able to avoid: this slippage ‘implies’ the ‘significance’ of the phallus as ‘organ’ in all human sexuality (‘the universality of the intermingling in the species that speaks, où ça parle’), for instance, among others, in the ‘fruitful’ heterosexual relation, that reproduces life and maintains the ‘sex ratio’ (18c; 462). Such a slippage of the function towards the organ claims to explain the whole of sexuality in function of the ‘bearers’ of the organ.

Freud’s insistence on an exclusively masculine reference is all the more curious that, from the time of his emotional correspondence with W. Fliess, he had ‘strongly emphasised the bisexuality of somatic organs’ (18d), namely the presence of all the organs relating to the soma in the two sexes, even if only in the embryonic state. This remark alone might have led him to cover this fundamental bisexuality by a unique function, the phallic function. Why did Freud not arrive at this discovery of the phallic function (detached from the organ) when he was so close to it?

This slippage of Freud reducing human sexuality to the phallic organ ‘acknowledges its truth’ in Totem and taboo, where Freud creates a myth distinct from the Oedipal myth: the latter is dictated by the structure, while the myth of the Father of the primal horde is dictated by Freud’s own impasses, especially in relationship to his exceptional father (Seminar XVIII, On a discourse which might not be a semblance, 9 June 1971). This myth is ‘less sure than that of the Bible’, - where Eve is born from Adam’s phallic rib – not alone (131) because it results from Freud’s neurosis, but again because it does not include any trace ‘of the little boy, of the mother, of the tragic nature of the transition’ (ibid.), elements nevertheless essential for phallic functioning. This ‘truth’ of Freud, $ in a master discourse, his divided position with respect to his patriarchal father, highlights the barred subject implied in the Freudian myth (divided between obedience to the law and the sharing of enjoyment). Freud could not reach his truth by remaining in a master discourse; he had to borrow the twisted paths of a neurosis and more broadly the torsion of the phallic function in general, from which there ‘proceeds, where it speaks, où ça parle, the sexual act’ (18de; 462) inasmuch as the sexual act implies the different formulae of the phallic function. Freud’s ‘allmanity’ (touthommie) avows its truth: it is not of a biological order, it is not a function of the organ; it comes from the ex-sistence that has created it, ‘from the myth that Freud created in Totem and taboo’, of the ex-sistence of the father of the primal horde. Has this ex-sistence left a ‘biological heritage’ (16de), a ‘biological trace’, a purely organic t-race?

No! Every trace and every race comes from an existential position depending on a discourse. Every race is ‘d’race à se thommer’ (18e), in posing itself as an exception; it has nothing to do with the universal of the phallic function, ‘zilch with foralling itself’ (qu’dale à se pourtouter)’. The universality of the phallus (confusing the function and the organ) depends on ∃x.Φx, on the race and has no longer anything to do with the universal of the phallic function.

Racism articulated in this way (in the confusion of the organ and of the function) does not depend on organic characteristics and has nothing to do with the races of a physical anthropology (etymologically natural) which observe the human as a skin colour or as a skull. No racism is effectively constructed on these kinds of physical criteria: racism only takes support from ‘physical’ characteristics in order to justify a position of exception as a ‘Reich called third’ (19a; 462) shows us. Beyond the third Reich, the (132) confusion of the phallic function and the organ which is boasted about, is illustrated by another Reich: Wilhelm, the founder of ‘bioenergetics’.[8]

Race ‘is constituted by the mode in which symbolic places are transmitted by the order of a discourse’ (19a); each race derives directly from a symbolic place transmitted by a singular discourse, whether from the place of the semblance, or from the place of the Other. In that way in the order of the master discourse, the place of the semblance symbolically occupied by S1 will define the race of ‘masters’, while the place of the Other symbolically occupied by S2 will determine the race of ‘slaves’. In that way in the order of academic discourse the place of the semblance symbolically occupied by S2 (knowledge) will define the race of ‘pedants’ (pedagogues)[9] while the place of the Other occupied by the o-object will determine the race of pédés (fags). In that way in the order of the hysterical discourse, the place of semblance occupied by $ will define the race of ‘scients’, (shits, the agent of production of hysterical knowledge) while the place of the Other symbolically by S1 will determine the race of ‘sciés’ (bored). There will be essentially three times two types of races corresponding to the semblance and to the Other of each of the first three discourses.

Race is not deduced from the brain or from the brain-pan, as if the serf or the slave possessed a less evolved brain: ‘I will completely skip over then the time of cervage (brain/servitude)’ (19b). Servitude, the condition of the serf or the slave depends on the rope around the neck (from cervage, from the Latin cervix, poll, neck) which links him to the master in a single discourse. Race does not flow historically from the opposition of Greek civilisation to what was supposed to be outside (the Barbarians). Nor is it a more distant cultural heritage, a (133) survival of a tribal division inherent in the ‘Elementary structures’.[10] Without going back in time, as in archaeological anthropology, as in the history of civilisation (‘the Greeks and the Barbarians’), without either moving around in present day space on the side of ‘primitives’ or of elementary structures, every racism, seen from a general point of view, is justified by a discourse inasmuch as this discourse is rigid, without switching towards another discourse[11].

These six discursive positions that produce ‘racism’ are each exceptional: each race is an exception of, to and in the phallic function (∃x.Φx). Why not add to it the race of analysers and that of analysts (who would correspond to the discourse of the analyst)? The discourse of the analyst is precisely the one that makes the organ pass over to the phallic function: in psychoanalytic discourse, every exception to the phallic function finds itself immediately andautomatically reversed into the phallic function: ∀x.Φx ∃x.Φx. A pre- and anti- analytic slope draws its privilege from saying in order to definitively distribute the roles: in that way by an established master discourse, the race of masters could be opposed to the race of slaves; in that way in an established hysterical discourse, the race of hysterics could be opposed to the race of their victims; in that way in an established academic discourse, the race of pedagogues could be opposed to the race of students. Each time we see the constitution of a (134) race from the privilege of a discourse which is maintained at the same time as it refuses to switch towards another discourse.

The discourse of the analyst follows a completely different slope, a ‘counter-slope’ (19c; 463) which prevents any apparition of race, since it reverses the acquired position for new discourses, for new switches. While racism is constructed on the exception, ∃x.Φx, psychoanalysis goes through all the positions; the analytic discourse ‘closes the real’ by the roundabout of discourses. The ∀x.Φx appears as a complex position that implies going through the whole of the phallic function: in a first phase, the formula constituted a simple universal, in a second phase it implied saying, in a third phase it means that the phallic function operates at every point and at each point of the development of the phallic function.

This journeying of the phallic function in each one is expressed by the career, ‘in which the analyst must first of all be analysed’; the term analyser precisely describes this journey. The analyst’s discourse is only constituted from the roundabout of discourses and, in this way, it dislodges every race depending on the stagnation of a discourse (master, slave, pedants, fags, shits, bores). In that way the analyser can enter into analysis by way of the discourse of the hysteric, of the master, of the academic; as analyser, he can allow himself to go beyond each one of them. The ‘cervice’ (19d; 463) bowing the neck (cervix) under the yoke of an established discourse, must be straightened in order to go through the roundabout of discourses and enter into the discourse of the analyst.

3. Feminine sexuality. (19d – 21e; 463-465).

For Freud, ‘the sexual function is stated from a forall’: the two sexes seem to traverse in the same way the first stages of the libido, both are supposed to have the phallic organ. With the Oedipus complex (which can be articulated in two formulae ∀x.Φx and ∃x.Φx), Freud (135) remains at the male ‘moiety’ of speakers. He uses the same Oedipal scale to take the measure of the other moiety: ‘every human being sees the task of mastering the Oedipus complex imposed on him’ (Three essays on the theory of sexuality. SE VII, 226, n1). Serving in that way as a standard, the two masculine formulae are for all; henceforth, the difference between masculine sexuality and feminine sexuality is reduced to the ‘anatomical difference between the sexes’ (On some psychical consequences of the anatomical difference between the sexes, 1925).

‘This carryover’ of the two ‘masculine’ formulae onto the feminine moiety ‘sufficiently demonstrates what is involved in the ab-sense of the sexual relationship’ (19e; 463). Making a tabula rasa of femininity, this carryover is nevertheless operative: it gives rise to a response of the shepherdess to the shepherd, which is going to reproduce the question and in that way lead to a new development.

The acceptance of the Oedipus complex for all is a ‘scandal’, a stumbling stone which ought to re-launch psychoanalytic discourse. In the I.P.A., the Society preserving what Freud said, the scandal in question was ‘stifled, as one might say at birth’; the saying of the unconscious was strangled there in favour of a psychologising depending on the academic discourse.

The ab-sense, which allows saying to develop, was nevertheless at work in the ‘now defunct debate of the 30’s’ (20a; 463) where the phallic phase of the girl was the object of lively controversies especially on the part of women analysts. ‘Karen Horney, Helene Deutsch, indeed Ernest Jones and still others’ (20a) confronted Freud to contest the primary universality of the phallic phase: for Karen Horney, the little girl was supposed to have vaginal drives before any phallic phase; for Jones, the fear of aphanisis or the disappearance of desire was supposed to be the condition of the later apparition of the phallic phase (deutero-phallic).

The ‘lid’ (20a) stifling the phallic question in the 30’s ‘says a lot’ about the containment, the immobility imposed on Freud’s saying by (136) master and academic discourses. ‘In his pessimism’, Freud was uneasy ‘about the securing the maintenance of his thought in its completeness, when he himself would no longer be there to defend it’ (E 473); to perpetuate his work, he had put in place a ‘parasitic organism’ charged with faithfully transmitting what he said after his death. This organisation, I.P.A., comprehending nothing about it, did not take the risk of watering down what he said (13de). But the said is not saying. To entrust the transmission of the said analytically to other discourses was to ‘lose’ its saying. In order to rediscover it, it was necessary then to bring about ‘a return to Freud’, which allowed the debate to be reframed. Lacan’s symbolic, centred on saying, displaced the phallic question towards the signifier (1958: The meaning of the phallus, To the memory of Ernest Jones, Directive proposals for a congress on feminine sexuality); from then on the adjective phallic no longer qualified in the first place an organ, but a function, whose importance we are going to see.

Let us start again from the 1930’s.

Karen Horney, Helene Deutsch, ‘appealed’ (20b; 463) to ‘the voice of the body’ against the Freudian judgement promulgating the universality of the Oedipus complex. In this way, Karen Horney wants to give its voice again to the vagina. Now ‘precisely’, the body only takes on a ‘voice’ – the fourth oobject – from the unconscious which is the very dynamic of the switching of discourses, without which the voice cannot appear as such. To have recourse to the voice of the organic body as a superior agency to judge the unconscious is quite frivolous if the voice is not articulated with the dynamic of the unconscious which phallic functioning presupposes. The authority of these women ‘in the analytic discourse’, which is not unrelated to the third and the fourth formulae contrasts curiously with the triviality of the proposed solutions – the appeal to the organic is in effect quite frivolous to account for an affair dealing with ‘voice’ and ‘signifier’.

Their ‘charming finger-stall’ as it ‘contributes to dating’, to a rendezvous with the masculine sex, brings grist (de l’eau) to their mill (137) for sure; it waters ‘the flowers’ of their remarks. These are ‘rhetorical’ flowers (20c; 464): it is indeed from discourses and their rhetoric that we may expect a relationship between the sexes…, ‘even if it were only from the said’, even if saying is forgotten.

The theory of Jones, whose servility with regard to Freud was scarcely compatible with the discourse of the analyst, takes on the symptomatic form of compromise: he says ‘exactly the contrary of Freud…while at the same time giving the impression of saying the same thing’ (20d; 464). According to Jones, sexuality is supposed to be organised at first in terms of the fear of the abolition of sexuality (aphanisis) and would only be secondarily phallic (‘deuterophallicity’). In the girl, the fear of aphanisis would appear first of all as the fear of being abandoned, then secondarily there would appear the envy of a penis (especially the paternal one); from this secondary stage, the girl could then chose: either to remain faithful to her sex and re-state her (paternal) object or re-state her sex and enter into a phallic and paternal organisation. The first case (normal femininity) corresponds to the supposed primary nature of the fear of aphanisis (which says the contrary of Freud), while the second case (which links her pathologically to her father: the penis complex) corresponds to secondary phallicity.

To transmit his work, ‘Freud was sure of nothing’ with the Jews, because they would have worked over what he had said and would have distorted it. He chose ‘the best of the goyim’, Jones his future biographer. In that way Jones transmitted intact what Freud said, with the logical subtlety of putting it back to back with something that was exactly the contrary. Jones’ ‘logical subtlety’ does not rule out, nevertheless, his ‘mental debility’. This insulting remark with respect to the one who had interrupted Lacan during his account of the mirror stage at the Congress of Marienbad in 1936 is aimed at the lack of logical vigour in deuterophallicity. ‘A woman of my school’ (Françoise Dolto) clearly demonstrates that mental debility can be the consequence of the ‘parental saying’; in that way Jones debility is presented as a symptom of his neurosis.

(138) ‘There is no sexual relationship does not imply that there is no relationship to sex’ (20e; 464): the absence of sexual relationship affirms that there is no relationship between the two sexes, but implies on the contrary the relationship to the feminine sex precisely at stake in the ab-sense. ‘Here indeed is the very thing that castration demonstrates’: it initiates by the two formulae of sexuation a relationship to the feminine sex and to ab-sense, distinct for ‘each moiety’ (21; 464) - as we have presented it above in the nia/nya.

This distribution into two moieties is not done by the organ: the masculine moiety is not defined as that which would have the ‘organ’ and the feminine is determined neither as the one which is not supposed to have it, nor as the one which would have another organ. The organ is a ‘veil’ of the phallic function, which is where Karen Horney, Helene Deutsch, ‘went astray’. ‘May God receive their souls if He has not already done so.’ Their singular soul gathered up by God at their death is not important (Karen Horney died in 1952, Helene Deutsch in 1982 after Lacan). But may heaven grant that the structure (God) may take their souls, in the plural, as o-objects, as ‘abois’ (desperate straits), as ‘voices of the body’, to be put in the place of the semblance in the analyst’s discourse. May God, in as much as he determines the structure, restore the o-object to its correct place in the structure. Now, in this structure, ‘what is important is that this does not start from the tickling’, that the ‘ignored’ vagina or the ‘little darlings (mignons)’[12] feel, titillations that should be referred to the moi-haut (high-ego), to consciousness, in lifting a supposed repression relative to the vagina. A woman is lifted above the first Oedipal formulae not from the ‘lower’ moiety of organs, but from the ‘upper’ moiety of the signifier which should ‘make its entrance as an empress’ (21b; 464). She enters it through the master discourse in which she is inscribed in the position of semblance as signifiant-m’être: a woman ‘is not without being it’. But what being if not the one that is eager, as (139) an ‘empress’, right away (s’empresse, en emperesse, en s’emblant) in the precipitation that animates the phallic function and which is only a phase in the journey. The phallic function is organised ‘in a quite unified way’ (‘there in effect Freud was right’): for the man and for the woman, it supplements the absence of sexual relationship in supplying for it. This single function for the two sexes (∀x.Φx) draws its signifying material no doubt from ‘a single phanere’ (21b and 12-13); in subverting the ‘organ’, it is nevertheless ‘organised’ as a ‘logic’ which ‘revises’, which examines anew Aristotle’s ‘Organon’ in order to revise and modify it.

For men, Freud was inscribed in an Aristotelian logic by articulating the Oedipus complex from a universal and a particular; but ‘for women nothing guided him’, especially not ‘the hysterics who play the man’ (21b; 464); to play the man and to support his desire as unsatisfied, the hysterics again take their side in the opposition of an exception to the universality of desire. The Studies in hysteria could not then lead Freud onto the path of ‘a woman’. Over against Freud, Lacan does not remain with these two formulae: ‘I will not impose on women the obligation of measuring by the yardstick of castration the charming sheath that they do not even raise to the level of the signifier’, (21c; 465). ‘The obligation to measure’, the obligation stated by Freud to measure feminine sexuality by the ‘yardstick’ of castration, must be gone beyond: ‘the charming sheath’ like the ‘charming fingerstall’ cannot measure the heritage, measure the heir of masculine sexuality. The ‘charming sheath’ remains an organ, it is not raised to the level of signifier (despite the metaphor), and it, contrary to the phallus with a ‘yardstick’ that passes to the signifier (to the phallic function); this does not prevent the feminine organ from finding its joy (pied). ‘That a shoehorn is recommended here, subsequently follows’ (21cd).

Women participate in this shoe-fitting (chaussure), a sure thing (chose sûr), which consists in finding one’s footing (pied) especially in the universality proper to the masculine. But a woman is not (140) reduced to this universality; Lacan ‘repudiates’ the generality, ‘the woman’, or the universal ‘the women’: a woman worthy of the name is a singular woman. ‘Men are hard of hearing on this subject; (21cd; 465): like Freud, they are ready to reduce her to the first two formulae. ‘On occasion’, feminine enjoyment passes by way of coitus, but it is foreseeable that a feminine enjoyment may be able to do without it. This forecast does not depend on a contingent and momentary testimony like that of the Movement for the liberation of women (M.L.F.). Feminine enjoyment outside the masculine type of enjoyment depends on the contrary on the structure, on the absence of sexual relationship and on the phallic function that supplies for it.

‘The Freudian lucubration of the Oedipus complex’ (21de; 455) presupposes that the woman is by nature ‘castrated’: she is supposed to be in castration like a ‘fish in water’, she would then be all in function of the phallus, which could be written ∀x.Φx. This so-called co-naturality of the woman and castration ‘woefully contrasts with the fact of the devastation in women, for the most part, in their relationship to their mother’. The devastating effect of a mother on her daughter could no doubt be explained by the disappointment of not having received from the mother the phallic organ that is so desired; but she expects from her mother ‘more subsistence’ than from her father. What is this subsistence that makes her woman?

Lacan then lays on the table his ‘cards’, which unveil this feminine subsistence; he poses the ‘quantic mode’ of the third and fourth formulae: ∃x.Φx and ∀x.Φx (22a; 465). Why speak here about ‘quantic’? The phallic function – far from any specified meaning – is essentially developed by these logical operators: negation and quantifiers (for all, there exists). What is more, these operators imply a discontinuity (metaphorised by Planck’s quantum theory). In other words each ‘feminine’ formula responds to a masculine formula by a break in continuity, by a discontinuity, by a modal leap. In these leaps (141) of the phallic function, the subject is always divided and never appears except as a moiety: for one ‘moiety’ it is man (the first two formulae) and for the other moiety ‘woman’ (third and fourth formulae). It thus always pre-supposes the four formulae of sexuation.

4. The third and fourth formulae of sexuation (22a; 465)

The four formulae of sexuation could be naively ascribed to the four propositions of the logical square: the first two formulae would correspond to the universal affirmative and to the particular negative; the third and fourth formulae would correspond to the universal negative and to the particular affirmative. Such a comprehension – which is quite false – only leads to a caricature of feminine sexuality opposed to a masculine sexuality. The formulae of sexuation are not scientific formulae of two distinct sexual entities in a relationship of similarity or opposition.

Let us rather say that these formulae are ‘modes’. In the first two formulae, the subject can ‘be expressed (dit)’ according to an Oedipal mode. Here (22a; 465), it can be expressed in accordance with the third and fourth formulae whose quantifiers deny the quantifiers of the second and first formulae. The third and the fourth formulae are therefore identically the first two modulo the mode of saying explained by the denying: ∃x.Φx and ∀x.Φx. ‘Their inscription is not used in mathematics.’ ‘To deny that there exists one is not done’ (the exception denied is equivalent to the universal affirmative); nor does one say either ‘that forall is fornotalled, que pourtout se pourpastoute’, (the universal affirmative denied is equivalent to the particular negative).

‘It is there nevertheless that the sense of saying is delivered’: in the passage from one formula to another (as we have already seen in connection with ‘nia/nya’ 11bc or the ‘combination’ (10e). This transition, which is the phallic function in practice, ‘supplies for the (142) absence of sexual relationship’: the nya is primordial there (there is no sexual relationship). Therefore ‘nyania’ combines the negation perceptible at the level of the said (‘nia’) in the perspective that ‘there was not a sexual relationship (nyait)’. This ‘nyania’ – or the two ex-sistential modes of the woman and the man – produces soundeffects when the sexes are ‘in company’: the one affirms itself as exception because of his past in order that the other should respond that there is no trace in the present.

If two negations suppressed one another, the third formula would be reduced to the first formula and the fourth formula to the second: ∀x.Φx would bear witness to the existence ‘of a subject to say no to the phallic function’. This would be to suppose the subject starting from ‘the contrariety expressed in the two particulars’ (22bc): the subject would be supposed sometimes to be Φx, sometimes not to be so (there are some that…, there are some that are not….). This ‘reading in terms of Aristotle’ leaves no place for the sense of saying, for the dynamic of reversals of one formula into another. In this ‘Aristotelian’ reading, there is no place for either the third formula of sexuation, nor for the fourth (the ‘notall’[13]). But the first two formulae already went beyond ‘the reading according to Aristotle’: ‘the all of the universal is modified in the forall of the quantifier’ (15b) and the second formula is reversed into and ∃x.Φx, in the ‘sense of saying’ or of the journeying of the phallic function that is ‘inscribed from these quantifiers’.

‘To introduce as moiety those to be called (à dire) women’ (22c; 466), the subject reverses the necessary ex-sistence (second formula which restricted the possible universal (first formula): ‘The subject is determined by the fact that not existing from the suspension of the phallic function, all can be said about it…’; this ‘all’ is this time no longer restricted, limited or contained in the ex-sistence that gave it its ‘reason’ (7-15); thus this ‘all’ is an ‘all outsideuniverse’, a ‘notall’. Far from being restrained with respect to the all, the notall is at the (143) same time the limited all and the beyond of limits; it goes beyond the limit of reason (22c; 466). This ‘without reason’ alleviates the law (7d) and inaugurates the ab-sense proper to psychoanalysis and to the feminine sex.

The feminine ‘moiety’ is determined by the third and the fourth formulae whose quantifiers are denied: ‘from the fact that nothing existent creates a limit to the function’ (third formula: ∃x.Φx), ‘would not be able to guarantee anything at all about a universe’ (fourth formula: ∀x.Φx). These last two formulae can be rendered respectively by ‘none makes up the all’ (there does not exist an x which makes the all) and ‘they’ are notall, elles sont pastoutes‘ (‘not for all x phi of x’). Why these quotation marks “they, elles”? The two feminine formulae concern not only women, but the second moiety of every subject, of every speaking being (him or her), provided it is not reduced to the Oedipal articulation. This is what we are going to see in connection with Schreber.

The introduction of feminine sexuality can be developed from the angle of Schreber’s psychosis (22d; 466). In the Question preliminary to any treatment of psychosis, Lacan schematised Schreber’s psychosis by a double gulf: - the field of the Other does not have the support of the signifier of the Name- ofthe-Father, - as a result of which, the field of the subject loses phallic support. These two holes are fundamental for our remarks: the absence of the Name-of-the-father is the absence of the position of exception (∃x.Φx is denied) and the absence of the phallus makes the universality of the phallic function disappear (∀x.Φx is denied). These two gulfs, which announce the two formulae with denied quantifiers, involve schema L (see my Logique de l’inconscient): schema R is in that way transformed into schema I, which is ‘the inscription that I made by a hyperbolic function’ (22d; 466). This schema I is a new inscription of (144) the phallic function: when the Name-of-the-Father (∃x.Φx) no longer comes to limit the possible (∀x.Φx), that is the Other, then the Other heads off towards the unlimited, to the infinite, drawing along with it into the hyperbola the two other primordial signifiers: I, the ego ideal and M, the signifier of the primordial object. On the other hand, when the phallus is missing, the unsupported subject also heads off to infinity, drawing with it into the hyperbola the ego and the ego ideal:

The Phallic Function And The Formulae Of Sexuation

The Phallic Function And The Formulae Of Sexuation

From which there flows schema I properly so called (E 571).

The two gulfs (phi = 0 and P = 0) deny the quantifiers proper to the two masculine formulae: now (in 1972) the lack of the Name-of-the- Father can be written: ∃x.Φx, and the default of the phallus: ∀x.Φx. Read in this way, the third and fourth formulae demonstrate the (145) double ‘effect of the push-tothe-woman, pousse-à-la-femme’ proper to psychosis[14] (22d; 466). This double effect is first of all specified from the first quantifier (namely, starting from the third formula). How is that? It is ‘the irruption of A-father (Un-père) as without reason’ which unleashes the psychosis and its ‘effect of push-towardthe-woman’. Ordinarily a father arises with reason, this reason is precisely to create a limit to the forall (15c). For Lacan the unleashing of the psychosis depends on the contingent and dateable irruption of a father insofar as it appears as without reason (7d-22c), namely, without posing or limiting an all of the universe, a forall. This A-father is real not in the sense of a factual reality, but in the sense initiated by ab-sense, as without reason. It is from this A-Father provoking the third formula that there is precipitated here the effect experienced as ‘forcing’, the effect of ab-sense and of non-sense. This effect experienced as forcing operates in the field of an Other which henceforth is not limited and ‘thinks itself most foreign to all sense’. In that way is posed the question of ab-sense which is referred back to notall.

‘To carry the function to its extreme logical power would lead away from the right path’ (22e); for this function pushed to extremes, pushed as far as the hyperbolic would be the equivalent of radically and definitively rejecting (to foreclose) the phase of existence which sets the limit to the universality of the phallic function. Now, psychosis is the response (given by the perceived in psychosis 14c) and the response takes up the question again. To the extreme logical power (proper to the hyperbolic function) there is opposed the logical power of the notall (23a; 466) already readable in the without reason (7d-22c-22e): the logical power of the notall, far from confusing us about the functioning indicates its path to us. Laplanche in his Hölderlin ou la question du Père (1961) attempted to apply the theory (146) of foreclosure with an extreme logic; a waste of effort (22a) responding to the effort of the philosopher seeking sense in meaning (7e). This goodwill – entrenched in the first two formulae – causes the thread of the other formulae to be lost.

The third formula introduces and determines the feminine moiety not without a certain malaise, since it contradicts the second formula. How much more easy is it not (22e; 466) to remain with the third formula but to already look towards the fourth formula ∀x.Φx and to attribute to the other quantifier, the singularity of a confine (23a; 466). This is only possible if the extreme logical power (which was the radical foreclosure of the second formula) is replaced by the logical power of the notall (fourth formula); the singular of a confine is not the simple negation of the second formula, it denies the ex-sistence that poses the limit which because it carries with it the narrow minded (borné) beyond the boundaries and the boundary (borne) itself (confine: cum fine, with the boundary); the singular of a confine (confins is a noun that is always plural) does not need moreover to do away with all the boundaries, it is enough that a single one should be swept away for the enclosure of the universal to be opened up to the beyond of the universal, onto the notall. By this confine, the logical power of notall begins to be inhabited (s’habiter), to be furnished with the other formula, with the retreat of enjoyment that femininity conceals; from the third formula on, femininity conceals, steals the enjoyment of ∃x.Φx and is provided by retreating (recés[15]), by withdrawing itself from this position that plays ‘thomme’. A veritable Aufhebung, which suppresses and preserves at the same time, the third formula denies and raises up again the existence of the second. Femininity in that way allows the combination of two existential formulae: the second (masculine) and the third (feminine), in other words the conjugation of nyania. (147) This confine, enunciated here in terms of the logic of the notall which comprises the all and the beyond of the limit is depicted by Ovid in the myth of Tiresias (Métamorphoses, III, 320ff). Ovid ‘shelters’ behind the figure of the ‘myth’: it is the myth that is going to speak and not the author Ovid. The very story of Tiresias explains by its content the transition from one moiety to another: seeing two serpents in the process of coupling, Tiresias separated them (vs wounded them, vs, killed the female); following this intervention, he was transformed into a woman. Seven years later, by the repetition of the same intervention, Tiresias becomes a man again. His passage through the two sexes made of him an impartial judge of relationships to sex. In that way Zeus and Hera appealed to his arbitration: does the man or the woman have the greatest enjoyment? Tiresias is supposed to have responded by a sexual ‘ratio’ (‘rapport’): the two enjoyments would be in the proportion of one for the masculine enjoyment and nine for feminine enjoyment. ‘To say that a woman is notall’ (23ab; 466) is to say that her enjoyment starts from masculine enjoyment and overtakes it.

A woman wants to be recognised: in the theory of 1953, a woman is recognised by her own message which comes back to her in an inverted form through the mouth of her partner: ‘You are my woman’. She is in that way recognised as one person of the couple and by the meaning-relationship (‘You are my woman – You are my man’). ‘We only know it too well’ (it is the scandal that situates her in function of the first two formulae). But ‘it is as the only one that she wants to be recognised by the other part’: a woman remains alone beyond the masculine enjoyment that she shares with her man (if her partner does not have access to a feminine jouissance). ‘She wants to be recognised as the only one’: her solitude, which is not the absence of a rival, concerns her properly feminine enjoyment. Which deserves to be recognised.

‘That a woman should want to be recognised as the only one’ teaches us that ‘the enjoyment that one has of a woman divides her’ (23b; 466) between on the one hand the masculine enjoyment shared with her partner and on the other hand the properly feminine (148) enjoyment inaccessible to the man of the first two formulae. For this other moiety of enjoyment ‘there is no partner’: ‘union remains on the threshold’.

The man would do well to serve this feminine enjoyment which goes beyond and extends his own in the sense of saying and of the sequence of the formulae of the phallic function. ‘To what would a man avow himself to serve better’ than ‘to recreate’ (23c; 466), than to raise up anew, than to inflame again this feminine enjoyment that goes beyond him. The enjoyment ‘that is got from coitus’ is then no more than an eventual means to fan ‘feminine enjoyment’.

5. The notall or the Heteros (23c-24c; 467-468)

‘Sex’ in the singular, ‘the singular of a confine’, includes solitude. ‘What one calls sex…is…the Heteros’ (23c; 467). The feminine sex ‘is the Other’, but not the Other of the Lacan of 1953; it is not in a meaning-relationships, it is not the one from which one receives one’s own message in an inverted form (‘You are my woman’ – ‘You are my man’); not situating itself from the first two formula, it ‘cannot be staunched by the universe’. ‘An all outside universe’ (22c), it is defined by the absence of border, of limit, of ‘definition’; it does not accept the articulation of the definite article that sets a limit to a universal and makes it impervious: ‘the’ woman does not exist. The other sex is supported by the fourth formula ‘∀x.Φx’ and falls outside the reckoning of ‘forall’; it is foolish to count it as the second sex (The second sex, 1949, Simone de Beauvoir) because it does not enter into the reckoning that is proper to the ‘first’.

‘Let us call heterosexual by definition, one who loves women, whatever may be his/her own sex’ (23c; 467). To love ‘women’, is to be turned towards femininity (explained in the two feminine formulae). The usual homosexual-heterosexual classification would presuppose the relationship between the partners (‘You are my woman – You are my man’). The heterosexual, defined as turned towards the (149) Heteros, presupposes ‘ab-sense’ (which designates ‘sex’).

‘To love’ women does not signify ‘being engaged’ (passive) to them starting ‘from a relationship that is not there’ (23d; 467), starting from ‘You are my woman - You are my man’; it is on the contrary ‘to engage oneself’ (active) (22e) to arouse properly feminine enjoyment. This overflowing of feminine enjoyment as compared to the masculine, this non-relationship ‘implies the insatiability of love’: love will never have done enough to fill up this absense. Love is explained by this premise of non-relationship and not from a sexual relationship.

‘It is not in every discourse that a saying comes to ex-sist’ (23d; 467): saying only comes about as ex-sistence by ‘saying no’, by the switching of discourses. It is especially in the discourse of the analyst that an saying comes to ex-sist, for this discourse always presupposes the roundabout of discourses. Its proper structure is not being able to be ‘established’. The question of saying ex-sisting with respect to the said ‘was tossed around’ throughout centuries of philosophy up to the Cartesian ‘intuition of the subject’: Cogito ergo sum The subject is ‘very capable of seeing it’ (23de; 467), to see this saying ‘without it ever having been taken seriously’. In what does this lack of ‘seriousness’ consist? The subject of the Cogito only exists through the moment of doubt: the Cogito must start from doubt for the sum to appear with clarity and conspicuousness. Now ‘there where I am, I do not think’ and ‘there where I think I am not’. The subject is separated from its thoughts, this sum is separated from the Cogito (like the second formula ∃x.Φx is separated from the first, ∀x.Φx). The subject therefore (ergo) follows thought. This subject consecutive to thought can become in its turn an object of second thought, I can doubt it and this second doubt implies a new subject, which itself will be able to be the object of new thoughts and of a third doubt and so on in series (Seminar IX, Identification, 10 January 1962). To take the Cogito seriously, is to enter into a series which goes from one thought to a new subject and from a thought subject to a new thought always (150) unfathomed. In a parallel way, the intuition in the second formula – ∃x.Φx – does not suffice to guarantee the existence of the subject of saying: it only appears in the series of formulae between the first that makes it necessary and the third that says it is impossible. From where should this series start?

‘It is the logic of the Heteros that must be got going’ (23e; 467); we must ‘understand’ that the logic should start from the Heteros. The question posed by the notall is that of an ‘all outside universe’ or of an all ‘that cannot be staunched by a universe’. Can all be one, a ‘universe’? ‘Yes’ said Parmenides ‘both thought and being is a same’ (French translation by Barbara Cassin). But the question, taken up again in Plato’s Parmenides, opens out onto another response on ‘the incompatibility of the One with Being’ and on the question of notall. This dialogue, an enigmatic text commented on a thousand and one times in the history of philosophy, had been abundantly quoted in the seminar ...ou pire (1971-1972). Lacan acknowledges here the insufficiency of his commentary: “how give a commentary on this text in front of seven hundred people?”

How situate this dialogue?

Returning from his second voyage to Sicily, Plato finds an open rebellion at the heart of his Academy: Aristotle had in effect published his Peri Philosophias, a well-ordered attack against his master’s theory of Ideas and Platonism in general (Kojève, Essai d’une histoire raisonnée de la philosophie païenne II, p.353-369). Plato responds with a set of seven dialogues (to which no doubt the ‘seven hundred people’ make an illusion to, 23e). Parmenides is the first of these seven dialogues.

The first part of Parmenides converges on a dialogue between the old Parmenides and the very young Socrates; the latter affirms the identity of ideas to themselves: the similar is similar, one is one, etc. Old Parmenides criticises Socrates scholastic presentation; in addition, some objects can manifestly not correspond to an Idea: hair, mud, filth. All these very human waste products, in which the psychoanalyst will hear the o-object, do not enter into the topology of (151) Ideas identical to themselves. The world of Ideas (the One) and the human world here below are radically separated: one knows nothing about the other, the One knows nothing about men and men know nothing about the One. Still the One is nonetheless thinkable. How? Old Parmenides suggests the dyadic method: let us suppose that the One is (and let us see the logical consequences of this), then let us suppose that the One is not (and let us see the logical consequences of that). To think the One is to successively make the first then the second supposition: 10 if the One is, a) what is the result for itself ? b) what is the result for the others, for what is not one?; 20 if the One is not, a) what is the result for itself? b) what is the result for the others? Which gives us four questions: (1) if the One is, what is the result for itself? (2) if the One is, what is the result for the others? (3) if the One is not, what is the result for itself? (4) if the One is not, what is the result for the others? Each of these four questions is nevertheless reduplicated in two different formulations or hypotheses and the first question is even presented in three different hypotheses: which makes nine hypotheses.

We will content ourselves here with showing how the ‘incompatibility’ of the One with Being appears starting from this first question (if the One is, what is the result for itself?) sub-divided in three hypotheses following the three ways of conceiving the One: 1) the One which is truly one (if the One is one), 2) the One which is and contains heterogeneity in itself (if the One is), 3) the One which goes from the One which is one to the One which is. [Plotinus and the Neo-Platonists in general retained these three hypotheses to define their three ‘hypostases’: the one, being and the soul.]

First hypothesis of the first question: ‘If the One is truly one, what can we conclude about it for itself?’. We conclude that such a one is not. In effect a ‘One’ which is truly one does not admit of any alterity and will not be able to be inscribed in any dichotomy; if it were the case, opposed to the other term of the dichotomy, it would no longer be the One: thus it is neither limited or unlimited, neither moved nor (152) immobile, neither identical nor different, neither similar nor dissimilar, neither equal nor unequal, neither past nor present nor future; now all that shares in being is inscribed in the past, present or future tense; therefore the One which is one is not. The One which is one is incompatible with Being.

The ‘One’ – which constitutes a universe - nevertheless appears and leads us to pose the first question differently:

Second hypothesis of the first question. ‘ If the One is (without always being one) what is the result for itself?’ To be one, it must be inscribed in the two terms of dichotomies; if this were not the case, it would only be a part of the dichotomy and would therefore not be the One: thus it is limited and unlimited, moved and immobile, identical and different, similar and dissimilar, equal and unequal, past and present and future. The One which is can only be by including in itself the heterogeneous, the Other, the Heteros.

This Heteros presupposes a transition between the two terms of each dichotomy.

Third hypothesis of the first question. The transition between the two terms of each dichotomy (second hypothesis) pre-supposes a point which is neither of the two terms, neither limited nor unlimited, neither moved nor immobile, neither identical nor different, etc. Thus the change (inherent in the second hypothesis) presupposes a transition point between the two opposites of each dichotomy, an instantaneous (exaiphnes), which is neither the one nor the other of the two opposites and which, as neither- nor, returns to the first hypothesis. Being and the One are incompatible and must nevertheless be articulated.

The articulation of Being and of the fundamentally heterogeneous One, Heteros, ‘Other’, presupposes therefore the transition from one saying (first hypothesis) to another (second hypothesis) and their articulation (third hypothesis). This circuit is expanded again by the other hypotheses of Parmenides that we will not deal with here.

The point of departure of the notall – the Heteros or the incompatibility of the One and of Being – was available for centuries, (153) since Plato’s Parmenides. Why did the question of saying and of the notall have to wait for the analytic discourse to be developed? Response in the form of a question: “how give a commentary on such an enigmatic text in front of such a numerous audience at my seminar?” The paronomasis indicates to us the ritornelle of the commentary, which is plunged into the ‘mécomment’ and miscognition (méconnaissance) (17e): the -commentaries of centuries of the history of philosophy were not able to open out into ‘proper logic’ starting from Heteros because they lacked the ‘arena’, the free rein of the roundabout of discourses which is only constructed by the analytic discourse. The putting into parenthesis of the whole history of philosophy (starting with the Parmenides) introduces the absence of the philosophical page, which is the everyday resource of the analyst (7e -8a).

With psychoanalysis, we leave the philosophical commentaries of the Parmenides to follow the ‘practice’ of ‘absence’, “the arena always open to the equivocation of the signifier’ (23e; 467). The signifier is going to take up again the question of the Heteros. The equivocation of the signifier is illustrated by three examples where a homophone (same sound) corresponds to two different writings and words (different grammar and logic): 10 the equivocation of the Heteros(‘the Heteros being declined into the Hetera, is etherised, indeed hetaerised...’, 23e): 20 the equivocation of the deux (‘The prop of the deux to make d’eux...’, 24a): 30 the equivocation of semble (s’emble,..., s’emblave, and le semblable). These three equivocations do not remain at simply homophony but are analysed in terms of ‘writing’ or of ‘grammar’, then of logic.

The first of these three equivocations – ‘the Heteros, by being declined as the Hetera, is etherised and hetaerised...’ – is a grammatical declension: the Hetera (feminine which will pose the enigmatic question of the notall as ‘pastoute’); the sequence of the equivocation ‘is etherised, indeed hetaerised …’ confirms it: ‘ether’ the purest air and the celestial space animating the entire world, is ‘hetaerised’, is feminised into ‘hetaera’, companion, mistress, (154) courtesan of the highest rank in ancient Greece. The equivocation of the Heteros remains here at grammar (without yet going on to the logic that Lacan keeps in suspense).

The second of the three equivocations: the equivocation of deux/d’eux is articulated like the equivocation of the Heteros. ‘Eux’ are ungraspable and inaccessible. The Heteros, ‘this notall’ lends us a support to reduce these eux to deux. Let us see how: it is on the Heteros that there is constructed the Greek comparative suffix (makros, big: makroteros, bigger, or makro-heteros, big other) which allows the elements of a set (d’eux) to be compared two by two. Thus ‘bigger’ (particularly big) will allow us to rank them by order of sise. The Heteros or notall (or the beyond of a boundary) is thus a deux (bigger, smaller or on this side of or beyond a boundary) on which eux will be supported to be ordered and counted. ‘This support of the deux’ nevertheless ‘creates an illusion’ (24a; 467), for the multiplicity of the notall is inaccessible and is not enumerable like the ordered whole numbers (ordinals). Why can ‘eux’ not be ordered by the deux of the comparison? Why can we not order speaking beings according to some sexual criterion? Because there is no sexual relationship between two speaking beings; in other words, because they will always keep an irreducible hetero-geneity between one another. If the Heteros provides a (‘particularly big’) trick to order the individuals, it is also installed as irreducibility between them. Repetition - Beyond the pleasure principle – is not reduced to a temporarily ordered sequence of symptoms, but reveals itself as a new dimension which goes beyond the numerable. It is ‘transfinite’. ‘It is a matter of an (155) inaccessible starting from which’ one could enumerate or count the repeated events, but at the price of a reduction ‘of them’. If one can order the events of a sexual life it is because it is already reduced. Repetition testifies to the infinite research of a fundamental inaccessible, which can be restrained to an enumerable multiplicity. In that way Don Juan, to escape from the inaccessible ‘notall’ (‘the solitude’ of a woman), orients his search towards the enumeration of women (the preceding one then the next one). By this method of taking them one after the other, the enumerable is ‘sure’, but the ‘reduction also becomes so’. [In this equivocation, homophony was pursued in its grammar and in its logic].

The third of the equivocations treated here, the equivocation of the ‘semblance’ is articulated on the illusion of the enumerable. ‘They’ cannot enter into the things to be counted [16] unless they are similar among themselves. Thanks to this levelling off, they can resemble (156) one another and gather themselves together (first formula) on condition that there is one which ‘s’emble’ (24a), which precipitates itself to limit (second formula) this sequence of semblables [like the prisoner of logical time who ‘precipitates himself to affirm himself as man for fear of being convinced by the others that he is not a man’. (E 213)]. Thanks to this operation the semblance ‘is sown’, is seeded with wheat (blé), in that way creating for itself its own semblables (on the model of the ‘mirror stage’). ‘L’hommosexué’ (23ab) sexed in the mode of the man or of the same, of the semblable, precipitates itself into these first two formulae, articulated according to the ‘all semblable’ and the precipitation of the ‘semblance’.

Having gone through the ordered sequence of these three homophonic equivocations, Lacan takes up again the first (the question of the Heteros) which had not yet been articulated in its logical dimension: to complete the universal and to limit it, the semblable only precipitates itself (s’emble) by excepting itself, ‘by discord’ (24b; 467) with the universal. ‘It is the Heteros…that raises up man in his status which is that of the hommosexuel’: ‘all semblable’ (hommo-) only holds up because there is the affirmation of discord. Now this discord shows that the Other, the ‘notall’ is already at work in the passage from the first to the second formula. The ‘status... of the hommosexuel, ‘the erection’ of the man, namely, the articulation of the first two formulae depends on the Other, on the ‘notall’. Freud himself showed it, the Oedipus complex implies that the phallic ‘appendix’ is rendered to man, not simply as an erectile ‘appendix’, but above all as an appendix becoming a phallic function thanks to the discourse of the analyst.

This precipitation where man ‘plunges’ into the second formula is only produced if saying is already well advanced, thanks to the ‘notall’. Before this, ‘what is striking at first’ is the masculine statement (dit), the hommodit, the said of ‘allmanity’ (18d), the ‘run-of the-mill of the unconscious’ (24c; 467), namely, the unconscious inasmuch as it comes first of all in the mode of ‘all’ (first formula) and of themanofthesaid (‘l’hommodit). Now Lacan correctly states the (157) unconscious otherwise than in the mode of all: it is ‘structured like a language’, in which the particularising ‘a’ contradicts the all and the said. As compared to the (particular) saying, the said ‘is not weighty’: ‘it causes/speaks [cause]... but that is all it knows how to do’. ‘I have been so little comprehended, so much the better’: the incomprehension will induce the reversal of positions or discourses and in that way it will serve the purpose ‘that one day people will make objections to me’ (24c; 468) no doubt for a new reversal.

‘In short, we float from the islet phallus’: in a masculine mode, ‘the islet phallus’ emerges from the sea of saids. But the phallic function implies the development of the third and fourth formulae. If this ‘feminine’ side ‘is cut back from it’, there remain only the first two formulae. But why withdraw oneself in this way from the ‘feminine’ side? It is a matter of a defence, a protection, a retrenching before the enigma of the ‘notall’: ‘one’, namely, ‘the hommosexuel’, ‘the man’ ‘entrenches himself’ in the fortress of the first two phallic formulae.

The congruence of the phallic function.

‘Thus history’ (24d; 468) concerns the semblances which correspond to the first and second formulae, the semblances that float from ‘the islet phallus’. These ‘boats form a ballet’ of ‘naval manoeuvres’ with ‘a limited number of figures’. This limitation depends on the first two formulae in which the notall has been reduced in order to become enumerable and sure.

But when ‘women do not disdain to take up the running in it’ in these masculine naval manoeuvres – think of Jeanne d’Arc, Catherine de Médicis or Madame de Maintenon – then there flourishes dance whose steps are enumerable (one step and then another step), the dance of history which is a masculine affair. But what is contributed by these women who engage themselves, notall (pastoutes), in the dance of history? This dance ‘flourishes when the discourses hold sway…for the congruent signifier’; the discourses only hold sway by (158) the phallic signifier. Each discourse supposes in effect the articulation of the phallic function starting from the first two formulae; each discourse presupposes a said and a saying that is excepted from it. By phallic functioning, there is established then a ‘congruence’, namely, a relation of equivalence, of reflexivity, of symmetry and of transitiveness between the different discourses in the roundabout of the discourses. Congruence is nevertheless only assured thanks to the fourth formula: the logic of discourses starts from the Heteros, from the notall which implies their switches (such is the ‘plus’ that ‘women’ can contribute). In this history, ‘those who know the steps’, those who lead the dance, those who direct the enumerable sequence of actions, are those ‘who have it in them’ to pass to the phallic signifier.


[1] The text says ‘exponential function’ (15b). The exponential function with a base of a (positive real) is written and is read ‘a exponent x’; in its place Lacan writes 1/khi which is of course a fractional function and not an exponential (moreover it does not matter whether one writes x or khi)

[2] Castration as symbolic lack was distinguished from frustration as imaginary lack and from privation as real lack, as is indicated at the start of the academic year of 1956, at the start of Seminar IV, Object relations, p.36-39. In 1972, the date of L’étourdit, this seminar was only published in the form of a report by J.B. Pontalis.

[3] Already in the Ecrits (1966) it is the structure of the phantasy which supports the field of reality (as the note of page 526 shows in connection with schema R).

[4]thomme‘ (16d) refers to ‘man’, but also to the Greek: tome cut, tomos cutting, etc.

[5] See the case of the obsessional in Ecrits woken from his impotence and replaced into the phallic function by the dream his mistress recounts to him (The direction of the treatment, E 631)

[6] The title of the novel Satiricon, attributed to Petronius, signifies pot-pourri (satura), ‘a medley of stories’; with the variant Satyricon, Lacan draws it into the phallic roundabout of Dionysian satyrs. As a realistic epicurean novel, the Satiricon describes especially the wanderings of the young libertine Encolpe under Nero. He has offended the god Priapus, the phallic god, and suffers his malediction. The satire of L’étourdit is directed at the human activity that offends the phallic function by capturing it to the advantage of a particular discourse.

[7] The mitre, the ‘texture’(trame), the ‘stuff’ constructed during his Seminar IX, Identification (196162), shows how identification is only woven from the phantasy ($ Δ o). ‘The conspiracy (trame) designed to make Lacan shut up’ in his dealings with the I.P.A. has same structure. In that way there is nothing astonishing in the fact that the ‘bishops’ of the I.P.A. s’en chappotent: are capped by it, quibble over it, and are capsized by it (s’en coiffent, s’en chipotent and s’en capotent) [Since capote is a condom, ‘capsized’ though accurate acquires a new nuance.]

[8] The strange condensation between the third Reich and W. Reich whose writings were burned by the Nazis is justified from the functioning of an ‘allmanity’ centred on the organ. Reich’s The function of the orgasm (1942) tries to demonstrate that psychical health depends on the orgasmic power or on the organ.

[9] In that way the pedantry of psychological objectification (E 418-419). The pedant is indeed a

pedant from his academic knowledge.

[10] Levi Strauss’ The elementary structures of kinship, 1947, describes the positive laws of preferential marriage: these structures require the individual to choose his partner within a precise class different from his own. It presupposes then a difference of classes. Races are not explained by this class difference.

[11] The races created and maintained in the vegetable and animal world, as phenomena of man’s discourse, highlight the properly discursive dimension of racism in general; these variations within a botanical or zoological species depend in effect on culture (horticulture), ‘on art, therefore on discourse’: these races of men, created in the house of man, are then d’hommestique (domestic) and live from our domesticity (19bc; 463)

[12] A name for the chat (pussy) which designates the sex of the woman (Pierre Guiraud, Dictionnaire érotique).

[13] Tracking down his pastout Lacan is supposed to have encountered it in Aristotle (mè pantes) c.f. The sinthome, 18 November 1975. This quotation could not be located by Pierre-Christophe Cathelineau (Lacan lecteur d’Aristote, p.198).

[14] The double effect is sardonic: it is both laughter and madness; the herba sardonia, the ranunculus from Sardina was supposed to provoke laughter; it is unleashed here by the perturbation of the phallic function.

[15] From the Latin recessus, the action of distancing oneself, retreat, of folding back which supposes that the place to which one withdraws is preserved. [16] Cantor introduced the ‘transfinites’ as infinites not reducible to the infinite sequence of integers or to the denumerable (D). This latter infinite is the ‘cardinal’ or the ‘number’ of integers, but also the number of even numbers, of algebraic integers, or of fractional numbers: these sets can be ranked in strict biunivocal correspondence with the series of integers (1 2 3 4 5...). But there exist transfinite sets which can not be put into biunivocal correspondence with the denumerable (D). Thus the ‘power of the continuous’ (C) equivalent to the set of real numbers of a segment of a straight line included between 0 to 1. It can be proved (par absurdum) that C is irreducible to D. Let us suppose that C is reducible to D and that all its real numbers A1 A2 A3...An...are ranked according to the order of integers (the decimals of A1...An...are written with the lower case a, b, etc.): A1 = 0, a1 b1 c1... = for example 0.439…(a1=4, b1=3, c1=9, etc. A2=0, a2 b2 c2… ……………………. An=0, an bn cn dn …………… ……..…………………….. One can construct a number X (0, x1 x2 x3 x4 …) contained between 0 and 1 such that its first decimal (x1) is not the first decimal a1 of the first number A1, its second decimal (x2) is not the second decimal b2 of the second number (A2) and so on… This number X is not a number An of the ordered series since by definition its nth decimal ought to be different to the nth decimal An. We have therefore demonstrated that X is not ranked in the denumerable transfinite. The power of the continuous (the cardinal of all the real points included between 0 and 1) is therefore denumerable.

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