🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

I apologize, this is the first time I am late. I am warning you: I am ill.
You are here, so am I, that’s good for you.
What I mean is that I feel abnormally well under the influence of a mild fever and a few drugs, so if suddenly, all at once, this situation were to change, I hope those who have been hearing me for a long time would explain to the newcomers that this is the first time this has happened to me.

So, I will try tonight, therefore, to be at the level of what you expect, what you expect here where I said that I am having fun.
It is not certain that it will always remain in the same tone.
You will have to excuse me; it certainly will not be due to my abnormal state.
It will indeed be in line with what I, this evening, intend to tell you.

Elsewhere, obviously I do not spare my audience much.
If some who are here – I see a few – remember what I spoke about last time:
I spoke, in sum, of this thing that I summarized in the Borromean knot, I mean a chain of 3,
and such that, if you detach one of the rings of this chain, the other two can no longer for even an instant hold together.
What does this concern?

I am indeed forced to explain it to you, since after all I am not sure that given all raw,
all simple, like that, it is enough for everyone.
It means a question concerning what is the condition of the unconscious.
It means a question posed to what language is.
Indeed, it is a question that is not settled.
Should language be approached in its grammar, in which case – it is certain – it concerns a topology…

X – What is a topology?

Lacan

Ah, what is a topology? How kind this person is!
A topology is something that has a mathematical definition.
Topology is this which is first approached by non-metric relations…

X – What does that mean?

…by deformable relations. It is, strictly speaking, the case of those kinds of flexible circles that made up my:

‘I ask you – to refuse me – what I am offering you’

Each was a closed thing, flexible and only holds by being linked to the others. Nothing supports itself alone.
This topology, because of its mathematical insertion, is linked to relations…
precisely that’s what my last seminar was intended to demonstrate
…is linked to relations of pure signifiance, that is to say, it is inasmuch as these three terms are three,
that we see that from the presence of the third a relation is established between the other two.
That is what the Borromean knot means.

There is another way to approach language, and of course, the matter is current.
It is current due to the fact that someone whom I have named…
it happens that I named him after Jakobson did,
but as it happens, I had known him already before, that is to say, someone named René Thom
…and this person is in sum attempting…
certainly not without having already blazed certain trails
…to approach the question of language through the semantic angle, that is, not through the combination of signifiers…
insofar as pure mathematics can help us conceive it as such
…but through the semantic angle, that is, not without also resorting to mathematics, to find in certain curves, I would say, certain forms, I would add, that are deduced from these curves, something that would allow us to conceive of language as – shall I say – something like the echo of physical phenomena.

It is based, for example, on what is purely and simply communication of resonance phenomena that curves would be developed, which, to have value in a certain number of fundamental relations, would then come together, become homogenized, so to speak, be placed within the same parenthesis from which the various grammatical functions would result. It seems to me that there is already an obstacle to conceiving things in this way: one is forced to include under the same term “verb” types of action that are very different.

Why would language have – in a way – gathered into a single category functions that can only be conceived as originally emerging in very different modes? Nevertheless, the question remains unresolved.

It is certain that there would be something infinitely satisfying in considering that language is, in a way, modeled on the functions supposed to belong to physical reality, even if this reality can only be approached by way of a mathematical functionalization.

What I am – for myself – currently putting forward for you is something fundamentally attached to the purely topological origin of language. This topological origin, I believe I can account for it based on this: that it is essentially linked to something that occurs – in the speaking being – through the angle of sexuality. Is the speaking being a speaking being because of something that happened to sexuality, or did this something happen to sexuality because he is a speaking being? That is a matter on which I refrain from deciding, leaving it to you to judge.

The fundamental schema of what is at stake, and which this evening I will attempt to push a little further before you, is this: the function called “sexuality” is defined… insofar as we know something about it, we do know at least a bit, if only by experience …by this: that the sexes are two.

Whatever a certain famous author may think, who, I must say, in her time… before she produced that book called ‘The Second Sex’ …had believed, for reasons of I don’t know what orientation, since in truth I had not yet begun to teach anything …had believed she should consult me before bringing out ‘The Second Sex’. She called me on the phone to tell me that certainly she needed my advice to clarify what the psychoanalytic contribution to her work should be.

As I pointed out to her that it would take at least… that’s the minimum since I have been speaking of it for 20 years and not by chance …that it would take at least 5 or 6 months for me to untangle the question for her, she observed that it was out of the question, of course, for a book already in progress to wait so long. The laws of literary production being such, it seemed to her excluded to have more than 3 or 4 meetings with me. As a result, I declined this honor.

The basis of what I have been putting forward for you for some time now, precisely since last year, is precisely this: that there is no second sex! There is no second sex from the moment language comes into operation.

Or to put things differently regarding what is called heterosexuality, it is precisely this: the word ετερος[étéros][in Greek, means ‘other’, wordplay] which is the term used to say “other” in Greek, is precisely in this position, for the relation that in the speaking being is called sexual, of emptying itself as being, and it is precisely from this void that it offers to speech what I call “the place of the Other”, namely, that place where the effects of the said speech are inscribed.

I am not going to elaborate on this, because after all, that would delay us, with a few etymological references:

– how ετερος[eteros] is said, in a certain Greek dialect, which I will spare you naming – ἅτερος[àteros],

– how this ετερος[eteros] is linked to δεύτερος[dèfteros] and very precisely marks that this δεύτερος[dèfteros], in this instance, is, so to speak, elided.

It is clear that this may seem surprising, as it is evident that for some time such a formula… the truth is that I do not know of any reference to a time when it would have been formulated …such a formula is very precisely what is ignored. Nevertheless, I claim it, and I support it with what you see on the board, that this is what psychoanalytic experience brings:

For this, let us recall what underlies what we may have as a conception, – not of heterosexuality, since it is after all quite well named, if you follow what I have just advanced a moment ago, – but of bisexuality. At the point where we are in our statements concerning the said sexuality, what do we have?

What we refer to… and do not believe that this goes without saying …what we refer to is the model, so to speak, supposedly animal.

There is thus a relationship between the sexes and the animal image of copulation, which seems to us to provide a sufficient model of what the relationship is, and at the same time that what is sexual is considered as need. That is not at all – far from it, believe me – what has always been the case. I do not need to recall what “to know” means in the biblical sense of the word.

Since always the relationship of the νοῦς[nouss] to something that would undergo its passive imprint, which is called variously, but certainly whose most common Greek denomination is ὕλη[ýli: substance], since always the mode of relation engendered by the spirit has been considered as shaping, not at all simply the animal relation, but the fundamental mode of being of what was held to be the world.

The Chinese on this occasion have called upon something that is written as follows:

yīn: 陰
yáng: 陽

The Chinese have long referred to two fundamental essences which are respectively the feminine essence, which they call Yin to oppose it to Yang, which it so happens that I have written – no doubt not by chance – below.

If there were an articulable relation on the sexual plane, if there were an articulable relation in the speaking being, should it – that is the question – be stated – of “all those” of one same sex, – to “all those” of the other.

It is obviously the idea suggested to us, at the point where we are, by the reference to what I have called the animal model: – the aptitude, so to speak, of each, on one side, – to stand for all the others, on the other.

You can thus see that the statement is promulgated according to the form, the significant semantic form, of the Universal. To replace, in what I have said, “each” with “whoever” or with “anyone” – anyone of one of these sides – we would be entirely in the order of what would be suggested by what would be called… recognize in this conditional something to which my Discourse that would not be semblance echoes …well, to replace “each” by “whoever” we would indeed be in that indeterminacy of what is chosen in each “all” to respond to “all the others”.

The “each” that I used at first still has the effect of reminding you that, after all, if I may say so, the actual relationship is not without evoking the horizon of the “one to one,” of “to each his own.” This, a biunivocal correspondence, echoes what we know is essential for presenting number.

Let us note this: we cannot from the outset eliminate the existence of these two dimensions, and one may even say that the animal model is precisely what suggests the “animic” fantasy. If we did not have this animal model… even if the choice is by encounter, the bi-univocal coupling is what appears to us, namely, that there are only two animals copulating together …well, we would not have this essential dimension which is very precisely that the encounter is unique.

It is no accident if I say that it is from there – from there alone – that the animic model is fomented: let’s call it “the soul-to-soul encounter”!

One who knows the condition of the speaking being in any case has no reason to be surprised that the encounter, based on this foundation, will precisely have to be repeated as unique. There is no need to bring any dimension of virtue into play here. It is the very necessity of what, in the speaking being, occurs as unique: it is that it repeats.

That is why it is only from the animal model that the fantasy I have called “animic” is supported and fomented. There are childish things[29’] under this, the claim that “language does not exist,” but that is obviously not what interests us in the analytic field. What gives us the illusion of the sexual relationship in the speaking being is everything that materializes the Universal in a behavior that is, effectively, one of the “herd” in relations between the sexes.

I have already emphasized that in the sexual quest – or hunt, as you wish: – the boys encourage each other, – and as for the girls, they like to double up as long as it is to their advantage, of course! This is an ethological remark I have made, on occasion, but it settles nothing, for it is enough to reflect to see in it a miracle quite equivocal, so that it cannot be sustained for long.

To be more insistent here and stick to the level of the most basic experience – I mean down-to-earth – the analytic experience, I remind you that the imaginary, which is what we reconstruct in the animal model… which we reconstruct according to our own idea, of course, since it is clear that we can only reconstruct it by observation …but the imaginary, on the other hand, we have an experience of it, an experience which is not easy but which psychoanalysis has enabled us to extend.

And to put it bluntly, it will not be difficult, it seems to me, to make myself understood if I put forward… I called it “bluntly,” it is not so much “blunt” as “cruel” that should be said …well, my God, in every sexual encounter, if there is something psychoanalysis allows us to put forward, it is indeed some profile of another presence for which the vulgar term “orgy” is not absolutely excluded.

This reference in itself is not at all decisive, since, after all, one could put on a serious face and say that it is precisely “the stigma of anomaly,” as if the normal – in two words – could be located somewhere.

It is certain that by advancing this term, the one I have just pinned down with this vulgar name, I certainly did not seek to strike an erotic chord in you, and if it simply has a small value of awakening, may it at least give you this dimension, not one that here could echo Eros, but simply the pure dimension of awakening. I am certainly not here to amuse you with that string!

Let us now try to forge what the kinship of “the Universal” is with our matter, namely, the statement by which objects should be divided into two “alls” of opposed equivalence. I have just pointed out to you that there is no need at all to require equinumerosity of individuals, and I have stuck – as best I could – to supporting what I had to put forward simply about the bi-univocity of coupling.

These are… these would be if it were possible, two “Universals,” defined by nothing but the establishment of the possibility of a relationship of “one to the other” or “the other to the one.”

The said relation has absolutely nothing to do with what is commonly called “sexual relations.” We have heaps of relationships to those relations, and on those relations we also have a few little relations: that occupies our earthly life. But at the level at which I place it, it is a matter of grounding this relation in Universals: how does the Universal “Man” relate to the Universal “Woman”? That is the question.

And this is the question that imposes itself on us from the fact that language very precisely demands that it be grounded in this way. If there were no language, there would also be no question; we would not have to bring the Universal into play.

This relation… to be precise: to render the Other absolutely foreign to what here could be purely and simply auxiliary …is what perhaps tonight forces me to accentuate the “A” with which I mark this Other as empty, with something additional: an “H,” the Hautre, which would not be such a bad way to make the dimension of “Hun” audible here, that can come into play, meaning to notice, for example, that all our philosophical concoctions perhaps did not emerge by chance from a certain Socrates, manifestly hysterical, I mean clinically: after all, we have the record of his cataleptic manifestations. The said Socrates, if he was able to sustain a discourse that is at the origin of the discourse of science, it is very precisely for having brought forth, as I define it, in the place of semblance: the subject.

And this he was able to do, very precisely because of this dimension which, for him, made present the “Hautre” as such, namely that hatred of his wife, to call her by name [Xanthippe], that person who was his wife, to the point that she “womaned” herself so much that at the moment of his death he had to politely ask her to withdraw in order to leave to that death all its political significance. This is simply an indicative dimension regarding the point where lies the question we are in the process of raising.

I have said that if we can say there is no sexual relation, it is certainly not in all innocence; it is because the experience, namely a mode of discourse that is not absolutely that of the hysteric, but the one I have inscribed under a quadripodic division as being the analytic discourse:

And what emerges from this discourse is the dimension never before evoked of the phallic function, namely that something by which it is not from the sexual relation that at least one of the two terms is characterized… and very precisely the one to which this word is attached here: the Hun, it is not from his position as Hun, which would be reducible to that something called either “the male,” or in Chinese terminology the essence of Yang …it is very precisely, on the contrary, due to what, after all, deserves to be recalled to accentuate the meaning… the veiled meaning because it comes to us from afar …of the term organ, it is precisely what is not organ – to stress the matter – except as a “utensil.”

It is around the “utensil” that analytic experience incites us to see everything that is stated of the sexual relation revolve. This is a novelty, I mean this corresponds to the emergence of a discourse that certainly had never before come to light, and which cannot be conceived without the prior emergence of the discourse of science as it is the insertion of language on mathematical reality.

I said that what stigmatizes this relation, of being in language profoundly subverted, is very precisely this: that there is no longer any way… as it used to be done, but in a dimension that seems to me to be a mirage …it can no longer be written in terms of male and female essences.

What does this “cannot be written” mean, since after all it has already been written?

If I reject this ancient writing in the name of analytic discourse, you could raise a much more valid objection: that I also write it, since after all… this is what I have once more put up on the board …it is something that claims to be supported by a writing – what? – the network of the sexual affair.

Nevertheless, this writing is authorized and takes its form only from a very specific writing, namely what was made possible to introduce into logic by the irruption precisely of what was asked of me earlier, that is, a mathematical topology. It is only from the existence of the formulation of this topology that we have been able, from any proposition, to imagine that we make a propositional function, that is to say, something specified by the empty place that is left in it, and according to which the argument is determined.

Here I want to point out to you that very precisely what I borrow, on occasion, from mathematical inscription, insofar as it substitutes itself for the first forms—I do not say formalisations—the forms sketched out by Aristotle in his syllogistics, that thus this inscription under the term function argument might, it seems, offer us a term easy to specify sexual opposition.

What would be required? It would suffice that the respective functions of male and female were distinguished very precisely like Yin and Yang. It is very precisely from the fact that the function is unique, it is always a matter of !, that difficulty and complication arise, as you know… as it is not possible, simply by your being here, that you do not at least have a little idea of it …that difficulty and complication arise.

! affirms that it is true… that is the meaning of the term function …that it is true that what relates to the exercise, to the register of the sexual act, comes under the phallic function.

It is very precisely insofar as it is a question of the phallic function, from whichever side we look, I mean: from one side or the other, that something compels us to ask then how the two partners differ. And it is very precisely this that is inscribed in the formulas that I have put on the board.

If it turns out that, due to the phallic function dominating both partners equally, it does not make them different, it nevertheless remains that it is elsewhere that we must seek their difference. This is why these formulas—the ones written on the board—deserve to be interrogated on two sides: – the left side as opposed to the right side, – the upper level as opposed to the lower level.

What does this mean?

What this means deserves to be examined, if I may say so, that is to say, to be questioned, I would say first on how they may show a certain abuse. It is clear that it is not because I have used a formulation arising from the irruption of mathematics into logic, that I use it in exactly the same way.

And my first remarks will consist in showing that, in fact, the way I use it is such that it is not at all translatable into the terms of propositional logic.

I mean that the mode in which the variable… what is called the variable, that is, what provides a place for the argument …is something here quite specifically determined by the fourfold form under which the relation of the argument to the function is posed.

To simply introduce what is at stake, I remind you that in propositional logic, we have in the foreground – there are others – the four fundamental relations that are, so to speak, the foundation of propositional logic, which are respectively: negation, conjunction, disjunction, and implication.

There are others, but these are the first, and all the others are reducible to them. I assert that the way our positions of argument and function are written is such that the so-called relation of negation, by which everything that is posited as truth could only negate itself by passing to “false,” is very precisely what here is unsustainable.

For you can see that at whatever level… I mean the lower level and the upper level …where the statement of the function—that is, that it is phallic—where the statement of the function is posited: – either as a truth, – or precisely as to be set aside, since after all the true truth would be precisely what cannot be written, what here can only be written in the form that contests the phallic function, namely: “It is not true that the phallic function is what founds the sexual relation.”

That in both cases, at these two levels that are as such independent, where it is not at all a question of making one the negation of the other, but on the contrary of one being the obstacle to the other, what you see distributed is precisely:

– an “there exists” [: §], and a “there does not exist” [/ §]

– it is a “All” on one side: “All x” [; !], namely the domain of what is defined there by the phallic function, and the difference in the position of the argument in the phallic function is very precisely that it is “Not all” woman who is inscribed there [; §].

You can see well that, far from one being opposed to the other as its negation, it is on the contrary from their subsistence, here very precisely as negated: – there is an x that can be sustained in this beyond of the phallic function [: §], – and on the other side there is not [/ §], for the simple reason that a woman could not be castrated for the best of reasons.

This is a certain level, it is the level of what is precisely barred from us in the sexual relation, while at the level of the phallic function, it is very precisely in that to the “All” is opposed the “Not All” that there is a chance for a distribution from left to right of what will be founded as male and as female.

Far from the relation of negation forcing us to choose, it is on the contrary insofar as far from having to choose we have to distribute, that the two sides legitimately oppose one another.

I spoke—after negation—of conjunction. For conjunction, I will only need, to deal with it, to make the remark, the remark for which I hope there are enough people here who have, just like that, vaguely browsed a book of logic so that I do not have to insist, namely that conjunction is founded very precisely on the fact that it only takes value from the fact that two propositions can both be true.

And this is precisely what in no way is permitted by what is written on the board, since you can see clearly that from right to left, there is no identity and that very precisely where what is posited as true is at stake, namely it is precisely at this level that the Universals cannot be conjoined: the Universal on the left side being opposed—on the other side, the right side—only by the fact that there is no articulable Universal, that is to say that the woman, in regard to the phallic function, is situated only as “not all” being subject to it.

The strange thing is that for all that, disjunction does not hold any better. If you recall that disjunction only takes value from the fact that two propositions cannot… it is impossible for both to be false at the same time.

It is assuredly the relation—shall we say the strongest or the weakest?—it is assuredly the strongest in that it is the hardest to crack, since it takes a minimum for there to be disjunction – that disjunction validates that one proposition is true, the other false, – that of course both can be true, – in addition to what I called “one true, the other false,” it could be “one false, the other true.” There are thus at least three combinatory cases where disjunction is sustained.

The only thing it cannot admit is that both are false. Now here we have two functions that are posited as not being—I said it earlier—the true truth, namely those that are on top. Here we seem to have something that gives hope, namely that at least we would have articulated a real disjunction.

Now notice what is written, which is something I will of course have the opportunity to articulate in a way that brings it to life: it is that there is, very precisely, on one side of this § with the sign of negation above, namely that it is inasmuch as the phallic function does not operate that there is a chance for sexual relation, that we have posited that there must exist an x for this [: §]. Now on the other side what do we have? That there does not exist any! [/ §]

So one can say that the fate of what would be a mode by which the differentiation of male and female, of man and woman in the speaking being, would be sustained, this chance we have that this exists, is that if at one level there is discord… and we shall see what I mean by that in a moment, I mean at the level of the Universals which are not sustained due to the inconsistency of one of them …what happens when we set aside the function itself, is that: – if on one side it is supposed that there exists an x that satisfies ! negated [: §], – on the other we have the express formulation that there is no x [/ §].

This is what I illustrated by saying that woman, for the best of reasons, cannot be castrated, but there is only the statement “no x.” That is to say, at the level where disjunction would have a chance to occur, we find: – on one side only 1, or at least what I have called the “at-least-one,” – and on the other very precisely non-existence, that is, the relation of 1 to 0.

Very precisely at the level where the sexual relation would have a chance, not at all to be realized, but simply to be hoped for beyond the abolition by the deviation of the phallic function, we no longer find, as presence, I dare say, but one of the two sexes.

It is very precisely this that is, obviously, what we must relate to the experience as you are used to seeing it stated in this form: that woman arouses, from the Universal, for her, it cannot arise from the phallic function, in which she participates, as you know… this is the experience, alas too everyday not to obscure the structure …in which she participates only by wanting it, – either to take it away from the man, – or, my God, to impose its service on him, in the case of “…or worse,” it is the case to say, that she gives it back to him.

But very precisely, this does not universalize her, if only because of this, which is the root of the “not all,” that she harbors another jouissance than phallic jouissance: the jouissance properly called feminine which in no way depends on it.

If woman is “not all,” it is because her jouissance is dual. And this is exactly what Tiresias revealed when he returned from having been, by the grace of Zeus, Thérèse for a time, with, naturally, the consequence that is known, and which was there at last as displayed, so to speak, visible—it is the case to say for Oedipus, to show him what awaited him for having existed precisely, himself, as a man of that supreme possession which resulted from the deception in which his partner maintained him, of the true nature of what she offered to his jouissance, or, let us say it otherwise: for lack of his partner asking him to refuse what she was offering him.

This obviously manifests, but at the level of myth, this: that to exist as a man at a level that escapes the phallic function, he had no other woman than the one who, for him, ought precisely not to have existed. There you go!

Why this “ought not to have,” why the theory of incest, that would require me to engage on this path of the Names of the Father, where I have precisely said that I will never again engage? That’s how it is!

Because it so happened that I reread… because someone asked me …that first lecture of the year 1963, right here – huh! – at Sainte Anne.

That’s exactly why I came back to it, because I liked to recall it, I reread it, it reads well, it even has a certain dignity, so I will publish it if I ever publish again, which does not depend on me! Others would have to publish a little with me, that would encourage me.

And if I publish it, you will see with what care I then pointed out… but I have already said it for five years on a certain number of occasions …the paternal metaphor especially, the proper name, everything was there for, together with the Bible, one to give meaning to this mythical concoction of my sayings.

But I will never do that again, I will never do it again because after all I can be content to formulate things at the level of the logical structure which, after all, has its own rights. That’s it!

What I want to say to you is that this /, namely “that there does not exist,” nothing else that at a certain level, the level where there would be a chance that there be a sexual relation, that this ετερος[eteros] as absent [/ §], is not at all necessarily the privilege of the feminine sex.

It is simply the indication of what is in my graph… I say this because it had its little fate …of what I inscribe of the signifier of Abarré[A], that means: the Other, however one takes it, the Other is absent from the moment the sexual relation is at stake.

Naturally at the level of what functions… that is, the phallic function …there is simply this discord that I have just recalled, namely that on one side and the other, in that case we are not in the same position, namely that: – on one side we have the Universal founded on a necessary relation to the phallic function, – and on the other side a contingent relation because the woman is “not all.”

So I emphasize that at the higher level the relation founded on the disappearance, the vanishing of the existence of one of the partners, which leaves the empty place for the inscription of speech, is not at this level the privilege of any one side. Only, for there to be a foundation of sex, as they say, they must be two: 0 and 1 certainly make 2, that makes two on the symbolic plane, inasmuch as we agree that existence is rooted in the symbol. That is what defines the speaking being.

Certainly, it is something. Perhaps, who is not what he is? Only this “being,” it is absolutely elusive. And it is all the more elusive in that, to sustain itself, it is forced to pass through the symbol. It is clear that a being, which comes to be only from the symbol, is precisely this being without being, in which – from the sole fact that you speak – you all participate.

But on the other hand, it is quite certain that what is sustained is existence, and insofar as to exist is not to be, that is to say, it is to depend on the Other.

You are all there, each in some way, existing, but as for your being, you are not so calm! Otherwise, you would not come seeking assurance in so many psychoanalytic efforts.

This is obviously something that is quite original in the first emergence of logic. In the first emergence of logic there is something quite striking, it is the difficulty, the difficulty and wavering, that Aristotle manifests regarding the status of the particular proposition.

These are difficulties that have been pointed out elsewhere, that I did not discover, and for those who want to refer to it, I recommend notebook no. 10 of the “Cahiers pour l’analyse” where a first article by someone named Jacques Brunswig is excellent on this subject. There they will see perfectly highlighted the difficulty Aristotle has with the Particular.

It is that he clearly perceives that existence in no way could be established except outside the Universal, and that is precisely why he situates existence at the level of the Particular, which Particular is in no way sufficient to sustain it, although he gives the illusion of it by the use of the word “some.”

It is clear that, on the contrary, what results from the so-called formalization of quantifiers, called quantifiers because of a trace left in the history of philosophy, by the fact that a certain Apuleius, who was a novelist of not very good taste and certainly a frenzied mystic, and who was called—I have told you—Apuleius. He wrote “The Golden Ass.” It is this Apuleius who one day introduced the idea that in Aristotle, what concerned “all” and “some” was a matter of quantity.

It is nothing of the sort, it is rather simply two different modes of what I could call, if you allow me this slightly improvised term, the incarnation of the symbol, namely that the passage into everyday life, that there are “all” and “some” in every language, is truly what forces us to posit that language must after all have a common root, and that… as languages are profoundly different in their structure, …it must be in relation to something that is not language.

Of course, it is understandable here that people slip, and that under the pretext that what one senses to be this beyond language can only be mathematical, it is imagined, because it is number, that it is a matter of quantity.

But perhaps precisely it is not strictly speaking number in its entire reality to which language gives access, but only to being able to hook onto 0 and 1. It would be in this way that the entry of this real would have taken place, this real alone able to be the beyond of language, namely the only domain where a symbolic impossibility can be formulated.

This fact that, from the relation, itself accessible to language, accessible to language if it is very precisely founded on the nonsexual relation, it can therefore only confront 0 and 1, this would easily find its reflection in the elaboration by Frege of his logical genesis of numbers.

I have told you—at least indicated—what makes difficulty in this logical genesis, namely precisely the gap… the gap I have highlighted for you of the mathematical triangle …between this 0 and this 1, a gap that is doubled by their opposition in confrontation.

That already what can intervene, is there only because it is the essence of the first couple, that it can only be a third and that the gap as such is always left of the 2, this is something essential to recall, because of something much more dangerous to allow to persist in the analysis, than the mythical adventures of Oedipus, which in themselves have no inconvenience so long as they admirably structure the necessity that there be somewhere “at least One” that transcends what is at stake in the grasp of the phallic function.

The myth of the “Primal Father” means nothing else. This is sufficiently expressed for us to be able to make easy use of it, in addition to finding it confirmed by the logical structuring which is what I remind you of what is written on the board.

On the other hand, assuredly, nothing is more dangerous than the confusions over what the One is. The One, as you know, is frequently evoked by Freud as signifying what would be an essence of Eros which would be that of fusion, namely that libido would be of that sort of essence that would tend to make Two into One, and which—my God—according to an old myth… which is certainly not at all good mysticism …would be what one of the fundamental tensions of the world would tend toward, namely to make but One. This myth is truly something that can only function on a horizon of delirium and which has strictly nothing to do with anything we encounter in experience.

If there is something that is very clear in relations between the sexes… and that analysis not only articulates but is made to play out in every sense …if there is indeed something that in relations causes difficulty, it is very precisely the relations between women and men and nothing in it could resemble I do not know what spontaneity, except precisely that horizon I mentioned earlier as being ultimately founded on some animal myth and in no way is Eros a tendency toward the One. Far from it!

It is in this measure, it is in this function, that any precise articulation of what is at stake at the two levels… of what is only in discord that the opposition between the sexes is founded, insofar as they could in no way be instituted by a Universal …that at the level of existence—on the contrary—it is very precisely in an opposition that consists in the annulment, the emptying out, of one of the functions as being that of the other, that the possibility of the articulation of language is contained, and this seems to me essentially what must be highlighted.

Notice that just now, having spoken to you successively about negation, conjunction, and disjunction, I did not go as far as to finish what was at stake with implication.

It is clear that here again implication can only function between the two levels: – that of the phallic function, – and that which sets it aside.

Now, nothing in disjunction, at the lower level, at the level of the insufficiency of universal specification, nothing for that matter, nothing requires that it is only if and only if the break of existence… which occurs at the upper level …effectively occurs, for the discord of the lower level to be necessary, and very precisely, reciprocally.

On the other hand, what we see is, once again, the relation of the upper level to the lower level functioning… in a way, but distinct, but separate.

The requirement that there exist “at-least-one-man”… which is the one that seems to be expressed at the level of the feminine which specifies itself as “not-all,” a duality …the only point where duality has a chance to be represented, there is nothing there but a gratuitous requirement, so to speak.

This “at-least-one,” nothing imposes it except the unique chance—provided it is played—of something functioning on the other side, but as an ideal point, as a possibility for all men to reach it. By what? By identification! There is only a logical necessity here that applies only at the level of the wager.

But notice, on the other hand, what results concerning the barred Universal… and this is where this at-least-one on which the Name of the Father, the mythical Name of the Father, is supported is indispensable …it is here that I advance an insight that is the one missing from the function, from the notion of the species or the class. In this sense, it is not by chance that all this dialectic in Aristotelian forms has been missed.

Where, then, does this : function, this “there exists at-least-one” who is not a serf of the phallic function? It is only a requirement, I would say of a desperate kind, from the point of view of something that does not even rely on a universal definition.

But, on the other hand, notice that with respect to the Universal marked ; !, every male is a serf of the phallic function. This at-least-one as functioning to escape it, what does that mean? I would say it is the exception.

This is indeed the time when what the proverb says—without knowing what it says—that “the exception proves the rule,” is found, for us, to be supported. It is remarkable that it is only with analytic discourse that this, that a Universal, can find in the existence of the exception its true foundation. This means that certainly we can, in any case, distinguish the Universal thus founded from any use made common by the philosophical tradition of the so-called Universal.

But there is a peculiar thing that I have found by way of inquiry… and because from an old training I do not entirely ignore Chinese …I asked one of my dear friends to remind me of what, obviously, I had kept more or less only as a trace and what I had to have confirmed by someone whose mother tongue it is, it is certainly very strange that in Chinese the denomination of “all men,” – whether it is the articulation of dōu, which I am not writing on the board because I am tired, – or the older articulation which is said as quán…

Well, if it amuses you, I will write it for you anyway: dōu: 都, quán: 全

Do you imagine that one can say, for example, “All men eat,” well, it is said: měi gèrén dōu chī : 每个人都吃

“Měi” insists on the fact that he is indeed there, and if you doubted it, the numeral “gè” clearly shows that they are counted. But that does not make them “all,” one adds “dōu,” which means “without exception.” I could, of course, cite other examples, I can tell you that “All the soldiers perished,” they are all dead, in Chinese it is said: “Soldiers without exception kaput.”

The “all” that we see for ourselves expanding from within and finding its limit only in inclusion, being taken into larger and larger sets. In Chinese, one never says “měi” nor “dōu” except by thinking of the totality in question as contained. You may say to me: “without exception,” but of course what we discover in what I am articulating to you here as the relation of unique existence in relation to the status of the universal, takes the figure of an exception. But this idea is only the correlate of what I earlier called “the void of the Other.”

Where we have advanced in the logic of classes is that we have created the logic of sets. The difference between the class and the set is that: – when the class is emptied, there is no more class, – but when the set is emptied, there is still this element of the empty set [Ø]. That is indeed why, once again, mathematics makes logic progress.

And it is here that we can… since we continue to discuss, but it will soon end, I assure you …it is to see then where to take up the unilaterality of the existential function for what concerns the other, the other partner inasmuch as he is “without exception.”

This “without exception,” which the non-existence of X [/ §] on the right side of the board implies, namely that there is no exception and that this is something that here no longer has any parallelism, no symmetry with the requirement I earlier called “desperate” of the at-least-one, it is another requirement and it is based on this: in the end, the masculine Universal can take its support from the assurance that there is no woman who needs to be castrated, and this for reasons that seem obvious to him.

Only this, as you know, in fact has no more effect for the reason that it is a completely gratuitous assurance, namely that what I recalled earlier about the woman’s behavior shows quite clearly that her relation to the phallic function is completely active.

Only here as before, if the supposition based, in a sense, on the assurance that it really is a matter of an impossible… which is the height of the real …this does not for all that shake the fragility, so to speak, of the conjecture, because in any case the woman is no more assured of it in her universal essence, for the simple reason of this: it is that the contrary of the limit, namely that there is none, that here there is no exception, the fact that there is no exception does not more guarantee the Universal… already so poorly established because of its discordance …does not more guarantee the Universal of the woman.

The “without exception,” far from giving any “All” a consistency, naturally gives even less to what is defined as “not-all,” as essentially dual. There it is! I hope that this remains with you as the necessary anchor for what we may later attempt as a climb, if indeed we are set on the path where the irruption of this strangest thing, namely the function of the One, must be rigorously interrogated.

There are many questions as to what the animal mentality is, which here serves us only as a mirror reference, a mirror in front of which—as in front of all mirrors—one purely and simply denies.

There is something one could wonder: for the animal, is there such a thing as the One? The exorbitant aspect of the emergence of this One, it is what elsewhere we will be led to try to trace, and it is precisely for this reason that for a long time I have invited you to reread, before I approach it, Plato’s “Parmenides.”