🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

You know it, here I say what I think. This is a feminine position, because in the end, thinking is very particular.

So, as I write to you from time to time, I have… like this, during a little trip I just took …written down a certain number of propositions, the first of which is that we must recognize that the psychoanalyst is placed, by discourse… it’s a term of my own …by the discourse that conditions him… which, since me, is called the discourse of the psychoanalyst …in a position, let’s say, difficult, Freud said impossible: unmöglich, maybe that’s a bit much, he was speaking for himself.

Well! On the other hand—second proposition: he knows… this from experience, which means that even if he has practiced psychoanalysis only a little, he knows enough of it for what I’m going to say …in any case, he knows how to have a common measure with what I say.

This is entirely independent of whether he is—in terms of what I say—informed, since what I say leads to… as I have, it seems to me, demonstrated this year …locating his knowledge[S2].

That’s the story of knowledge about the truth: – that’s the place of truth—for those coming for the first time. – that, the place of semblance, – that, the place of jouissance [of speaking], – and that, of surplus-jouissance, which I write in abbreviated form as: “+ de jouir”. For jouissance, we’ll use a J.

It’s his relation to knowledge that is difficult, not—of course—not to what I say, since in the whole of the no man’s land of psychoanalysis people do not know that I say it. That doesn’t mean that nothing is known of what I say, since it comes from experience [i.e. analytic].

But what is known of it is abhorred! Which I can say, just like that, quite simply, that I understand them… “I can say,” that is: “I can say, if one insists…” …but I understand them… I put myself in their place, all the more easily because I am there.

But I understand it all the more easily because, like everyone else, I hear what I say. Still, it doesn’t happen to me every day, because it’s not every day that I speak. In fact, I understand it—that is, I hear what I say—on the few days, let’s say one or two, immediately preceding my seminar, because at that moment I start writing to you.

On other days, the thoughts of those I’ve had to deal with overwhelm me. I have to admit this to you, because at that moment, the impatience of what I’ve already called… and so I can call again, because it’s rare, like this, for me to come back …of what I called “my failure” in Scilicet, dominates me. There you go…

Yes… they know! I remind you of this because the title of what I have to deal with here is The Knowledge of the Psychoanalyst. “Of” in this case evokes the “the,” the definite article in French, well, it’s what is called definite. Yes! Why not “of psychoanalysts,” after what I’ve just told you? That would be more in keeping with my theme this year, that is to say “ya d’l’un” [there is some One]. “There are some” who call themselves such.

I am all the less inclined to discuss what they say since there are no others. I say “of”, why? It’s because it is to them that I speak, despite the presence here of a very large number of people who are not psychoanalysts.

So the psychoanalyst knows what I say. They know it—I told you—from experience, however little they have of it, even if it is reduced to the didactic, which is the minimal requirement for them to call themselves “psychoanalysts”.

For even if what I have called “the pass” fails, well, it will be reduced to this: they will have had a “didactic analysis”, but in the end, that is enough for them to know what I say.

The pass… all of that drags along in Scilicet, that is rather the right place for it [Scilicet: “namely”] …when I say that “the pass” fails, it does not mean that they did not offer themselves to the experience of the pass.

As I have often pointed out, this experience of “the pass” is simply what I propose to those who are devoted enough to expose themselves to it, solely for informational purposes, on a very delicate point, and which consists in… in short, what is asserted in the surest way is that: it is entirely (a)normal—object (a) normal—that someone who undergoes a psychoanalysis should want to become a psychoanalyst.

It really requires a kind of aberration that was worth being exposed to all the testimonies one could collect. That is truly why I have provisionally instituted this attempt to collect them, in order to know why someone who knows what psychoanalysis is through their didactic analysis could still want to become an analyst.

So I will not say any more about what their position is, simply because this year I chose The Knowledge of the Psychoanalyst as the topic I was offering for my return to Sainte-Anne. It is not at all to spare the psychoanalysts; they do not need me to have vertigo about their position, but I will not increase it by telling them so.

What could be done… and perhaps I will do it at another time …what could be done in a piquant manner in a certain reference I will call “historical” only in quotation marks… anyway, you will see when the time comes, if I am still here …for those who are clever, I will talk to them about the word “temptation”.

Here I speak only of knowledge and I note that it is not about the “truth about knowledge”, but about “knowledge about the truth”, and that this “knowledge about the truth” is articulated from the point I am advancing this year on “Y a d’l’un!” [there is some One], “Y a d’l’un” and nothing more: it is a very particular One, the one that separates One from Two, and it is an abyss.

I repeat: the truth—I have already said it—can only be half-said. When the time of alternation has passed, which will allow me to respect the alternation, I will speak of the other side: of the “half-true”. One must always separate the wheat from the “half-true”!

As I may have told you earlier, I am back from Italy where I have only ever had reason to praise the welcome, even from my psychoanalyst colleagues! Thanks to one of them, I met a third who is absolutely “up to date”, at least to my page, of course. [Laughter]

He works with Dedekind, and he found this entirely without me. I cannot say, at the date he began to get into it, that I was not already there, but in any case, it is a fact that I spoke about it later than he did, since I am only speaking about it now and he had already written a whole little book on it. He realized, in sum, the value of mathematical elements for making something emerge that really concerns our experience as analysts.

Well, as he is very well regarded, he did everything for this, he managed to get himself heard in very well-placed places in what is called the I.P.A.—the Institution Psychanalytique Avouée, I would translate—so he managed to be heard. But what is very curious is that he is not published!

He is not published, with the explanation: “You understand, no one will understand!” I must say I am surprised because, after all, “Lacan”, in quotation marks of course, in short, things of the kind I am supposed to represent to the incompetents of a certain linguistics, there is rather a rush to stuff the International Journal with them.

The more stuff there is in the trash, naturally, the less it can be discerned! So why on earth, in this case, did they think they had to put up an obstacle, since for me, it seems to be an obstacle and the fact that it is said readers will not understand is secondary: it is not necessary that all the articles in the International journal be understood. So there is something in there that does not please.

But it is obvious that, like the one I have just—not named… because you are profoundly unaware of his name, he still hasn’t managed to publish anything …is perfectly recognizable, I do not despair that, following what will filter through from what I say today… and especially if it is known that I have not named him …he will be published [Laughter]. Really, it seems important enough to him that I would gladly help him with that. If it doesn’t happen, I will tell you a little more about it!

Let’s return to time. The psychoanalyst thus has a complex relationship to what he knows. He denies it, he “represses” it… to use the term which, in English, translates as repression, Verdrängung …and sometimes he doesn’t want to know anything about it.

And why not? Who could that impress? Psychoanalysis—you might say—so what?

I can already hear the bla-bla-bla of anyone who hasn’t the slightest idea about psychoanalysis. I answer what might come from this floor—as they say—I answer: is it knowledge that heals… whether it be that of the subject or that supposed in the transference …or is it the transference itself, as it occurs in a given analysis?

Why knowledge… the one which, I say, every psychoanalyst has as a dimension …why should knowledge be, as I said earlier, “avowed”? It’s from this question that Freud, in sum, derived Verwerfung, he calls it: “a judgment which in the choice rejects.” He adds “which condemns,” but I condense it.

It is not because Verwerfung drives a subject mad, when it happens in the unconscious, that it does not reign… the same and under the same name from which Freud borrows it …that it does not reign over the world as a rationally justified power.

“Psychoanalysts”… you will see, in contrast with “the” …“psychoanalysts” prefer themselves, you see! They’re not the only ones, there is a tradition about this: the medical tradition.

To prefer oneself, no one has ever done better, except the saints—the saints (s.a.i.n.t.s) [wordplay: “saint” and “saint” as “healthy”]… Yes, you are told so much about the others [Laughter] that I specify, because the others… well, let’s move on …the saints (s.a.i.n.t.s) also prefer themselves, that’s all they think about, they consume themselves in finding the best way to prefer themselves, when there are such simple ways, as the “med-saints” [wordplay: “médecins” (doctors) and “saints”], also show [Laughter]. Anyway, those are not saints. That goes without saying…

There are few things as abject to leaf through as the history of medicine: it could be recommended as an emetic [Laughter] or as a purgative, it does both. To know that knowledge has nothing to do with truth, there really is nothing more convincing. One cannot even say that it goes so far as to make the doctor a kind of provocateur.

That does not prevent doctors from having managed… and for reasons that had to do with their platform with the discourse of science becoming narrower …from having managed to bring psychoanalysis in step with them.

And in that, they know what they’re doing! This naturally all the more since the psychoanalyst, being quite embarrassed… as I started out saying …quite embarrassed about his position, he was all the more ready to receive the advice of experience.

I care a great deal about marking this historical point which is in my affair… insofar as it matters …quite a key point: thanks to this conjuring… against which an express article of Freud’s on Lay Analysis was directed …thanks to this conjuring that took place shortly after the war, I had already lost the game before I had even begun it.

I simply want to be believed on this, because—why, shall I say it?—if tonight I bear witness… and I do not do it by chance at Sainte Anne since I tell you that it is there that I say what I think …if I declare that it is precisely in the capacity of having known very well, at the time, that the game was lost, that I engaged in this game.

There is nothing heroic about it, you know! There are plenty of games that are taken up under these conditions. It is even one of the foundations of the “human condition,” as the other says, and it succeeds no less than any other enterprise. Proof, right!

The only trouble—but it is only for me—is that it does not leave you very free, I say this in passing for the person who… I don’t know what, two seminars ago …who questioned me about whether I believed in freedom or not.

Another declaration I want to make… and which is indeed important, since after all, I don’t know, that’s my mood tonight …another declaration, which this time is completely proven—here I ask you to believe me— is that I was well aware that the game was lost… after all, I wasn’t so clever, maybe I thought I had to push ahead and that I would wreck the International Psychanalytic Avowed …and here, no one can say the contrary of what I am about to say: it is that I never let go of any person whom I knew would have to leave me, before they went off themselves.

And this is also true of the moment when the game was—at least for France—lost, which is the one I referred to earlier: that little commotion in a medical-psychoanalyst conjuring from which emerged in 1953 the beginning of my teaching.

On the days when the idea of having to continue said teaching does not inhabit me—that is to say, a certain number— it is obvious that I, like all fools, have the idea of what it could have been for French Psychoanalysis (!) if I had been able to teach where, for the reason I have just mentioned, I was in no way prepared to let go of anyone.

I mean that however scandalous my propositions on Function and Field may have been…and so on and so forth… of speech and of language, I was prepared to cover the furrow for years even for the most stubborn of the lot and—as things stand—no one among the psychoanalysts would have lost anything.

I told you I had made a little trip to Italy. In those cases, I also go—why not?—because there are a lot of people who like me… By the way: there is someone who sent me a tumbler! I would like to know who it is, so I can thank that person. There is a person who sent me a tumbler! I say this for those who were at the Panthéon last time. It’s a person I thank all the more as it’s not a tumbler. It’s a marvelous little red glass, long and curved, in which I will put a rose, whoever it is who sent it to me. But I only received one, I must say that. Anyway, let’s move on… there are people who like me a little everywhere, even in the corridors of the Vatican. Why not, right? There are some very fine people.

It’s only there… this is for the person who questions me about freedom …it’s only at the Vatican that I know any free-thinkers. I am not a free-thinker, I am forced to stick to what I say, but there: what ease! [Laughter] Ah, one can understand that the French Revolution was carried by abbots. If you only knew what their freedom is, my good friends, it would give you chills. I try to bring them back down to the hard ground, there’s nothing to be done, they overflow: for them, psychoanalysis is outdated! You see what free-thinking is good for: they see clearly… Yet it was a good profession, eh [Laughter]? It had its good sides. When they say it’s outdated, they know what they are saying, they say: “it’s finished, because surely we must do a bit better!”

I say this all the same to warn people… people who are “in the loop,” and particularly, of course, those who follow me …that you should think twice before involving your descendants, because it is very possible that, at the rate things are going, it could collapse all at once, just like that. Anyway, it is only for those who have to involve their descendants, I advise them to be cautious.

I have already spoken, in this way, about what is happening in psychoanalysis… certain points I have already touched upon must nonetheless be specified, and so I believe I can address them briefly at this stage …it is that this is the only discourse… and let us give it its due …it is the only discourse… in the sense in which I have catalogued four discourses, …it is the only discourse in which scoundrelism necessarily leads to stupidity.

If one immediately knew that someone who comes to request a didactic analysis is a scoundrel, one would say: “No psychoanalysis for you, my dear! You will become as dumb as a post.” But one does not know!

It is precisely carefully concealed. Still, after a certain time in psychoanalysis, it becomes known, since scoundrelism is always, not hereditary—it is not heredity at stake, it is desire, the desire of the Other from which the person has arisen. I speak of desire: it is not always the desire of the parents, it may be that of the grandparents, but if the desire from which one is born is the desire of a scoundrel, he is inescapably a scoundrel.

I have never seen an exception, and that is even why I have always been so tender toward those whom I knew would have to leave me, at least in cases where I had psychoanalyzed them, because I knew very well that they had become completely “duuuumb.” I cannot say I did it on purpose: as I told you, it is necessary. It is necessary when an analysis is taken all the way, which is the least that can be expected for didactic analysis.

If the analysis is not didactic, then it is a question of tact: you must leave the person enough scoundrelism so that he can manage reasonably well thereafter. That is truly therapeutic, you must let him stay afloat. But for didactic analysis, you cannot do that, because God knows what would come of it.

Suppose a psychoanalyst who remains a scoundrel: that haunts everyone’s mind! Rest assured, psychoanalysis—contrary to what people believe—is always truly didactic, even when it is someone stupid who practices it, and I would even say: all the more so!

In the end, all you risk is ending up with stupid psychoanalysts. But this, as I have just told you, is ultimately harmless, because after all, the object (a) in the place of semblance is a position that can hold. There you go! One can also be dumb by origin. That is very important to distinguish.

Well! So I have found nothing better, as far as I am concerned, nothing better than what I call “the matheme” to approach something concerning knowledge about truth, since it is there, in sum, that one has managed to give it a functional scope.

It is much better when it is Peirce who deals with it; he puts in the functions 0 and 1 which are the two truth values. He does not imagine, on the other hand, that one can write T or F to designate truth and falsehood. I have already indicated this, just in a few sentences, I have already pointed this out at the Panthéon; it is that, around the Y’a d’l’un [there is some One], there are two stages: – “Parmenides,” – and then after that, one had to get to set theory, …so that the question of such a knowledge, which takes truth as a simple function and is far from being satisfied with it, which involves a real that has nothing to do with truth—it’s mathematics—nevertheless for centuries it seems that mathematics did without any question there, since it was only later and through a logical questioning that it advanced a step in this question which is central for what concerns truth, namely: how and why “Y’a d’l’un”—you will excuse me, I am not the only one!—“Y’a d’l’un”: around this One turns the question of existence.

I have already made remarks on this, namely – that existence was never approached as such before a certain era – and that it took a long time to extract it from essence. I spoke about the fact that in Greek, there is not, strictly speaking, a common word that means “to exist,” not that I was unaware of ἐξίστημι [existémi], ἐξίσταμαι [existamai], but rather that I noticed that no philosopher ever used it.

Yet it is here that something begins which might interest us: it is a matter of knowing what exists. There exists only the One… with everything pressing in around us, I am also forced to hurry …set theory is the question: why “there is some One”?

The One is not common in the streets, whatever you may think, including that utterly illusory certainty, and illusory for a very long time—it does not stop us from clinging to it—that you are One as well. You are One, it suffices for you to even try to lift a finger to notice that not only are you not One, but you are, alas, countless, countless each for yourself.

Countless until you are taught… which may be one of the good results of the psychoanalytic current …that you are, depending on the case, quite finite— this, I tell you quickly because I do not know how much longer I will be able to continue …quite finite: – as for men, that is clear: finite, finite, finite! – as for women: countable!

I will try to briefly explain something that begins to open the way for you on this point, since of course, these are not things that jump out at you, especially when you do not know what “finite” and “countable” mean! But if you follow my hints a little, you will read anything you want, because books now abound on set theory, even to go against it.

There is a very nice person whom I hope to see in a little while to apologize for not having brought tonight a book that I did everything to find and that is out of print, which he lent me last time, and which is called “Cantor is Wrong.” It is a very good book.

It is obvious that Cantor is wrong from a certain point of view, but he is incontestably right for the simple fact that what he put forward has had a countless progeny in mathematics, and that all that matters is this, that what makes mathematics advance is enough to defend it.

Even if Cantor is wrong from the point of view of those who decree—one does not know why—that number they know what it is: the whole history of mathematics long before Cantor showed that there is no place where it can be demonstrated, that there is no place where it is more true than “the impossible is the real.”

It started with the Pythagoreans, to whom one day this obvious fact was stated… which they surely knew, because we must not take them for babies …that √2 is not commensurable.

This was taken up by philosophers, and it is not because it has come down to us through the “Theaetetus” that we should believe that the mathematicians of the time were not up to it and incapable of responding, that precisely realizing that the incommensurable existed, they began to ask themselves what number was. I will not give you the whole story!

There is a certain matter of √-1, which has since been called, for reasons unknown, “imaginary.” There is nothing less imaginary than √-1 as subsequent developments have proved, since it is from there that what we can call “the complex number” emerged, that is, one of the most useful and most fertile things ever created in mathematics.

In short, the more objections are raised about this entry through the One, that is, through the whole number, the more it is demonstrated that it is precisely from the impossible that, in mathematics, the Real is engendered. It is precisely because, through Cantor, something could be engendered… which is nothing less than the whole work of Russell, and indeed countless other points which have been extremely fertile in the theory of functions …it is certain that, with regard to the Real, it is Cantor who is directly in line with what is at stake.

If I suggest to you—I am speaking to psychoanalysts—to bring yourselves a little up to speed with this, it is precisely for the reason that there is something to draw from it in what is, of course, your favorite sin. I say this because you are dealing with beings who think… who of course think, because they can do nothing else …who think like Telemachus, or at least like the Telemachus described by Paul-Jean Toulet: “they think about the expense” [wordplay: “penser”/“dépense”]. Well, what is at stake is knowing whether you, analysts, and those you lead, spend your time in vain or not.

It is clear that in this regard, the pathos of thought that may result for you from a short initiation—though it should not be too brief either —to set theory, is quite something to make you reflect on notions such as existence, for example.

It is clear that it is only from a certain reflection on mathematics that existence has taken on its meaning. Everything that could be said before, through a kind of presentiment… religious, in particular, namely: that God exists …strictly has meaning only in this: that by putting the accent… I must stress this because there are people who take me for a “master thinker” …on this: whether you believe it or not… keep that tucked away in your ear: I do not believe it but it doesn’t matter, those who believe it, it’s the same …whether you believe in God or not, make sure you know that with God, in any case, whether you believe or not, you have to count.

It is absolutely inevitable. That is why I am rewriting on the board what I have tried to make turn around something about what is at stake in the so-called sexual relation.

I’ll start again: there exists an x such that what there is of the subject determinable by a function which dominates the sexual relation… namely the phallic function—that’s why I write it! …there exists an x which is determined by this: that he has said no to the function [:§].

You see that from where I speak, you can already see the question of existence linked to something we cannot fail to recognize as a saying. It is a saying no, I would even say more: it is a saying that no.

This is crucial. This is precisely what indicates to us the exact point where, for our training—training as analysts— what set theory states must be grasped: there is One, “at least One,” who “says no.”

It is a reference point! It is a reference point, of course, that does not hold for even an instant, that is in no way didactic nor teachable, if we do not join it to this quantificational inscription of the four other terms, namely: the quantifier called universal: ; !, that is, the point from which it can be said, as is stated in Freudian doctrine, that there is desire, libido—it is the same thing—only masculine. This is, in truth, a mistake.

Nonetheless, it remains that it is an error that has its full value as a reference point. That the three other formulas, namely:

— there does not exist this X [/ §], to say that it is not true that the phallic function is what dominates the sexual relation, — and on the other hand, we must—I do not say we can write—that at a complementary level to these three terms, we must write the function of the “not-all” [.] as being essential to a certain type of relation to the phallic function insofar as it founds the sexual relation, that is obviously what makes these four inscriptions a set.

Without this set, it is impossible to orient oneself correctly in what is at stake in the practice of analysis insofar as it deals with something that is commonly defined as being – “man” on the one hand, – and on the other hand, that corresponding entity generally called “woman,” who leaves him alone.

If she leaves him alone, it is not the fault of the corresponding entity, it is the fault of “man.” But fault or not fault… this is a matter we do not have to settle immediately, I note this in passing …what matters for now is to question the meaning of what these four functions have to do… which are only two: – one, negation of the function, – the other: opposing function …these four functions, insofar as their “quantized” coupling diversifies them.

It is clear that what : § means, that is, negation of !, is something that for a long time… and from early enough on that one can say that it is absolutely astounding that Freud ignored it …: negation of ! namely this at-least-One, this One all alone who determines himself by being the effect of the saying no to the phallic function, that is precisely the point under which we must place everything that has been said up to now about the Oedipus, so that Oedipus is something other than a myth.

And this is all the more interesting in that it is not about genesis, nor history, nor anything that resembles it, as at certain moments in Freud it seems he may have stated, namely, an event. It cannot be a question of event in what is represented to us as prior to all history. There is an event only in what is connoted in something that is said.

It is a matter of structure. That one can speak of “All-man” as being subject to castration [; !], this is precisely why, in the most obvious way, the myth of Oedipus is made.

Is it necessary to go back to “myth-ematic” functions to state a logical fact which is this: if it is true that the unconscious is structured like a language, the function of castration is necessitated in it, it is exactly in fact what implies something that escapes it.

And whatever it is that escapes it, even if it is not… why not, since it is in the myth …something human: after all, why not see the father of the primal murder as an orangutan, many things coincide in the tradition… the tradition from which, all the same, one must say psychoanalysis emerges: from the Judaic tradition …in the Judaic tradition, as I was able to state the year I did not want to do more than my first seminar on The Names of the Father, I nevertheless had time to emphasize there that in the sacrifice of Abraham, what is sacrificed is indeed the father, who is none other than a ram.

As in every self-respecting human lineage, its mythical descent is animal. So in the end, what I told you the other day about the function of hunting in man, that is what it is about. I did not say much about it, of course.

I could have told you more about the fact that the hunter loves his prey. Just like the sons, in the so-called “primal” event in Freudian mythology: they killed the father… like those whose traces you see in the caves of Lascaux …they killed him—my God—because they loved him of course, as the rest has proved, the rest is sad.

What follows is precisely that all men, ;, that is, the universality of men, is subject to castration. That there is “an exception,” we will not call it, from the point where we speak, “mythical.” This exception is the inclusive function: what can be said of the universal [; !], if not that the universal is enclosed, enclosed precisely by the negative possibility [: §]. Very exactly, existence here plays the role of the complement, or to speak more mathematically, the boundary.

This includes the following: that there is somewhere a “for all x”: ;, a “for all x” that becomes a “for all a,” I mean a (a), each time it is incarnated, incarnated in what one can call “a being,” at least “a being” who posits himself as being, and as a man specifically.

It is precisely this that means that it is in the other column… and with a type of relation that is fundamental, that something can be articulated… in which can be placed, can be placed for anyone who knows how to think with these symbols …under the title of woman.

Just to articulate it thus, this lets us feel that there is something remarkable, remarkable for you, that what is stated is that there is not a single one who in the statement… in the statement that it is not true that the phallic function dominates what is at stake in the sexual relation …registers as false [/ §].

And to help you find your way by means of references a bit more familiar to you, I will say—my God, since I spoke earlier of the father—I will say that what this concerns is: “There does not exist an x who is determined as subject in the statement of ‘saying no’ to the phallic function,” this is, strictly speaking, “the virgin.”

You know that Freud addresses it: the taboo of virginity, etc., and other wildly folkloric stories around this affair, and the fact that in former times virgins were not deflowered by just anyone, it had to be at least a high priest or a petty lord, well, never mind, the important thing is not that.

The important thing, in fact, is that one can speak around this function of the “vir,” this function of the “vir” so striking in that it is only ever of a woman, after all, that one says she is virile. If you have ever heard, at least nowadays, of a man who is, show him to me, I would be interested!

There, on the other hand, if man is everything you want in the genre: virtuoso, tacks to port, ready to tack, tacks as you like, the virile is on the side of the woman, she is the only one who believes in it! She thinks! That is even what characterizes her.

I will explain to you in a moment… I must tell you right away …that it is for this reason… I will explain to you in detail why …that the virgo is not countable, because she is located… contrary to the One which is on the side of the father …she is located between the One and Zero.

What is between One and Zero, is very well known and can be demonstrated, even when one is wrong, it is demonstrated in Cantor’s theory, it is demonstrated in a way that I find absolutely marvelous.

There are at least a few here who know what I am talking about, so I will indicate it briefly. It is absolutely demonstrable that what is between One and Zero… this is demonstrated thanks to decimals, decimals are used in the system of the same name: decimal …it is very easy to show that: “suppose” …it must be supposed …“suppose” it is countable, the so-called “diagonal method” can always be used to forge a new decimal sequence such that it is certainly not included in what has been counted.

It is strictly impossible to construct this countable, to give even a way—no matter how slim—of arranging it, which is really the least of things, since the countable is defined as corresponding to the sequence of whole numbers.

It is therefore purely and simply a matter of a “suppose…” and on this point Cantor will very readily be accused—as is done in that book, “Cantor is Wrong”—of having simply forged a vicious circle.

A vicious circle, my good friends, but why not! The more vicious a circle is, the funnier it is, especially if you can get something out of it like that little bird called the uncountable, which is surely one of the most eminent, most ingenious, most closely attached to the Real of number, that has ever been invented. Well, let’s leave it at that!

The “eleven thousand Virgins,” as it’s said in the Golden Legend, is the way to express the uncountable. Because eleven thousand, you see, is an enormous figure, it’s especially an enormous figure for Virgins, and not only in these times! So, we have pointed out these facts.

Let’s now try to understand what happens with this “not-all” [.] which is really the sharp point, the original point of what I have written on the board. For nowhere up to now in logic has the function of the “Not-All” as such been placed, promoted, put forward.

The mode of thought… insofar as it is, if I may say, “subverted” by the lack of the sexual relation …thinks and thinks only by means of the One.

The Universal is the something that results from the enveloping of a certain field by something that is of the order of the One, with this exception, which is the true meaning of the notion of set, it is very precisely this: it is that the set is the mathematical notation of that something—where alas, I am not for nothing—which is a certain definition, the one I note as S, namely the subject, the subject insofar as he is nothing other than the effect of the signifier, in other words: “what a signifier represents for another signifier.”

The set is the way in which, at a turning point in history, the people least made for bringing to light what is at stake for the subject, found themselves, so to speak, compelled to do so. “The set” is nothing other than the subject. That is why it cannot even be handled without the addition of the empty set.

Up to a certain point, I would say that the empty set is distinguished in its necessity by this: that it can be taken for an element of the set, namely that the inscription of the parenthesis which designates the set with the empty set as its element: {Ø}, is something without which any handling of this function is absolutely unthinkable, which… I repeat, I think I have sufficiently indicated to you …was made very precisely at a certain turning point in order to question… to question at the level of common language, I emphasize common, because here it is absolutely not any—of whatever kind—metalanguage that reigns …to question from the logical point of view, to question with the language of everyone, what is the incidence in language itself of number, that is – of something that has nothing to do with language, – of something that is more real than anything else, as scientific discourse has sufficiently shown.

“Not-All” [.] is precisely what results from this: not that nothing limits it, but that the limit is otherwise situated.

What makes the “Not-All” [.], if I may say and I’ll say it to be quick, is this: it is that… contrary to the inclusion in :§ “there exists the Father whose saying-no situates him in relation to the phallic function” …conversely, it is inasmuch as there is emptiness, lack, the absence of anything that denies the phallic function at the level of woman, that conversely there is nothing other than that something which the “Not-All” formulates in the position of woman with regard to the phallic function. She is, for herself, “Not-All.”

Which does not mean that, in any way, she denies it. I will not say she is other, because very precisely the mode in which she does not exist in this function—in denying it—which is precisely that mode, is that she is what in my graph is inscribed from the signifier of this: that the Other is barred: S(A). The woman is not the place of the Other, and more than that, she is inscribed very precisely as not being the Other in the function I give to the big A, namely as being the place of truth.

And what is inscribed in “the non-existence of what could deny the phallic function”… just as here I translated by the function of the empty set, the existence of the “saying no,” likewise it is by absenting oneself and even by being this “jouiscentre” [wordplay: jouissance + centre], this “jouiscentre” which is joined to what I will not call an absence, but a “de-sense”: s.e.n.c.e. …that the woman is posited for this signifying fact, not only that the big Other is not there—it is not she—but that he is altogether elsewhere: in the place where he situates speech.

I have left—since after all, you have the patience at an hour which is already eleven, to continue listening to me—to point out this, which is crucial… in what, after all, here—for you—I am forcing at the end of the year, a certain number of themes which are crystallizing themes …it is to denote the gaping split which separates each of these terms as they are stated.

It is clear that between :: “there exists,” and / : “there does not exist,” there is no babbling, it is existence.

It is clear that between: §: “there exists one who does not…” and ;!: “there is not One who is not…”, there is the contradiction:

When Aristotle speaks of particular propositions in order to oppose them to universals, it is between a positive particular and a negative universal that he institutes the contradiction. Here, it is the opposite: it is the particular that is negative and the universal that is positive.

Here, what we have between this / §, which is the negation of any universality, and this . ! what we have, I am only indicating it to you here, I will justify it later, is the undecidable:

Between the two… of which all our experience shows us, I think, quite enough that the situation is not simple …what is at stake? – We will call it lack, – we will call it the gap, – we will call it, if you wish, desire, – and to be more rigorous we will call it the object (a).

So it is a matter of knowing how, in the midst of all this… I hope at least some have noted it …how, in the midst of all this, something that could resemble a circulation functions.

For that, one must question the way in which these four terms are posited:

The : at the top left, is literally the necessary. Nothing is thinkable, and above all not our function of thinking as men. After all, a woman does think, she even sometimes thinks “therefore I am,” in which, of course, she is mistaken.

But anyway, as for the necessary, it is absolutely necessary… and this is what Freud tells us with that cock-and-bull story of “Totem and… Stand Up” …it is absolutely necessary to think anything at all about the relations… which are called human, no one knows why …in the experience that is established by this analytic discourse, it is absolutely necessary to posit that there exists One for whom castration: at the station!

Castration, what does it mean? It means that “everything leaves something to be desired,” it means nothing else. Well, there you have it! To think that, that is, starting from woman, there must be one for whom nothing is left to be desired.

That’s the story of the myth of Oedipus, but it is absolutely necessary, it is absolutely necessary. If you lose that, I absolutely do not see what could allow you to find your way at all. It is very important to find your way.

So, there you have it, this : I already told you it is the necessary. The necessary from what? From precisely what, as it happens, I wrote down for you earlier: the undecidable. In the end, one could say absolutely nothing resembling anything that could serve as truth, if this necessary [:§] is not admitted: there is “at least One” who says no…

I insist a bit. I insist because I could not tonight—we were interrupted—tell you all the nice things I would have liked to tell you about it. But I had a really good one and since I am being teased, I will bring it out anyway: it’s the function of the é-Pater [wordplay: épater (to impress, to astonish) / pater].

Much has been made of the function of the “pater familias.” We should better focus on what we can demand of the function of the father: this whole business of paternal deficiency, how people love to harp on that! There is a crisis, it’s a fact, it’s not entirely false: the é-Pater no longer amazes us. It’s the only truly decisive function of the father.

I have already pointed out that it was not Oedipus, that it was done for, that if the father is a legislator, you get President Schreber as a child. Nothing more. On any level, the father is the one who must impress the family.

If the father no longer impresses the family, naturally… well, we’ll find something better! It doesn’t have to be the biological father, there will always be someone to astonish the family, of whom everyone knows it’s a herd of slaves. There will be others to astonish them.

You see how the French language can serve many things. I already explained that to you last time, I had started with a trick: to melt or to found of them a One, in the subjunctive it’s the same trick, to found you must melt. There are things that can only be expressed in the French language, that’s precisely why there is the unconscious. Because it is the ambiguities that found, in both senses of the word, and that’s all there is…

If you ask yourself about “All” by looking for how it is expressed in each language, you will find lots of things, absolutely sensational things. Personally, I have inquired a lot about Chinese because I cannot make a catalogue of all the languages in the world.

I also asked someone, thanks to the charming treasurer of our School [Nicole Sels], who had her father write how “All” is said in Yoruba. But it’s crazy, you see! I do this for the love of art, but I know well that in any case I will find that in all languages, there is a way to say “All.”

What interests me is the signifier “as One,” it’s what is used in each language. And the only interest of the signifier is the ambiguities that can come from it… that is, something of the order of “found of them a One” and other nonsense of that kind …that is the only interesting thing, because for us, what is of “All,” you will always find it expressed, “All” is necessarily semantic.

The mere fact that I say I would like to question “All” languages solves the question, since languages, precisely, are “not all,” that’s their definition, whereas if I ask you about “All,” you see. There you go! Yeah, in the end, semantics comes down to translatability.

What other definition could I give? Semantics is that thanks to which a man and a woman understand each other only if they do not speak the same language. Anyway, I tell you all this to give you exercises, and because I am here for that, and also maybe to open your understander a bit about how I use linguistics.

Yeah… I want to finish, right?

So as for what necessitates existence, we start precisely from the point I inscribed earlier: from the gaping split of the undecidable, that is, between the “not-all” and the “not-one.” And after that, it goes there, to existence. Then after that, it goes there. To what? To the fact that all men are in potency of castration, it goes to the possible, for the universal is never anything but that. When you say that “All men are mammals,” it means that “all possible men” can be.

And after that, where does it go? It goes there: to the object (a). It is with this that we are in relation.

And after that, where does it go? It goes there, where woman is distinguished by not being unifying. There you go! All that remains is to complete here in order to go toward the contradiction, and to return from the “Not-All,” which is ultimately nothing other than the expression of contingency.

You see here… as I have already pointed out at the time …the alternation of necessity, contingency, the possible, and the impossible are not in the order Aristotle gives. For here it is the impossible that is at stake, that is to say, in the end, the real.

So follow this little path closely, because it will serve us later, you will see something of it. There you have it! It would be necessary to indicate the four triangles in the corners like this, the direction of the arrows is also indicated. Are you with me? There!

I think I have done enough for tonight. I do not wish to end on a sensational peroration, but the question that… yes, it’s quite well written. Necessary, impossible…

X – We can’t hear!

Lacan – Huh? Necessary, impossible, possible, and contingent.

X – We can’t hear anything!

Lacan

I don’t care! There you go! It’s a pathway.

You’ll hear the rest in almost fifteen days, since it’s on the 14th that I will give my next seminar at the Panthéon.

I am not sure that it won’t be the last.