🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

If we were to find, within logic, a way to articulate what the unconscious demonstrates as sexual value, we would not be surprised. We would not be surprised—I mean here, right here in my seminar, that is, at the level of this experience, analysis, instituted by Freud, from which emerges a structure of discourse that I have defined.

Let us take up again what I said in the density of my first sentence. I spoke of “sexual value.” I will point out that these values are received values, received in every language—man, woman—that is what is called “sexual value.”

From the outset, that there be man and woman… this is the thesis from which I start today …it is first and foremost a matter of language.

Language is such that for every speaking subject: – either it is he, – or it is she. This exists in all the languages of the world. It is the principle of the functioning of gender: feminine or masculine.

That there be the hermaphrodite will only be an opportunity to play with more or less wit at slipping both the he and the she into the same sentence. One will not call it “it” under any circumstances. Except perhaps to manifest through that a kind of “sacred” horror, one will not render it neuter.

That said, man and woman—we do not know what that is. For a time, this bipolarity of values was taken as sufficiently able to sustain, to suture what is at stake in sex.

It is from there itself that resulted this muted metaphor which, for centuries, underpinned the theory of knowledge. As I have remarked elsewhere, the world was what was perceived, even glimpsed, as taking the place of the other sexual value. What was at stake in νοῦς [nous]—the power of knowing—was placed on the positive side, the active side of what I will question today by asking what its relation to the One is.

I said that if the step analysis made us take shows us, reveals to us, in every close approach to the sexual, the detour, the barrier, the progression, the quibble, the narrow passage of castration, it is precisely this that can only occur through the articulation I have provided of analytic discourse.

This is what leads us to think that castration can in no way be reduced to anecdote, to accident, to the clumsy intervention of a threat or even of censorship. The structure is logical. What is the object of logic?

You know, you know from experience, from having merely opened a book titled “Treatise on Logic,” how fragile, uncertain, elusive the first stage of any treatise of that kind can be: “the art of rightly conducting one’s thought”… conducting it where, and holding it by which end? …or again such a recourse to a normativity from which the rational would be defined, independently of the real. It is clear that after such an attempt to define it [the real] as the object of logic, what presents itself is of another order and of an altogether different consistency.

I would propose—if necessary, if I could not simply leave a blank there—but I will not leave it blank—I propose: “what arises from the necessity of a discourse.” It is ambiguous, no doubt, but it is not idiotic, since it implies that logic can completely change in meaning depending on where any discourse takes its meaning from.

So, since this is where all discourse takes its meaning from—namely, from another—I propose quite clearly, and for long enough that it suffices to recall it here: the real… the category in the triad from which my teaching began: the symbolic, the imaginary, and the real …the real asserts itself, through an effect that is not the least of its assertions, in the impasses of logic.

Let me explain. What logic originally set out to do, in its conquering ambition, was nothing less than to establish the network of discourse insofar as it articulates itself, and that in articulating itself, this network should close in upon a universe supposed to enclose and cover, like a net, whatever could be presented to knowledge.

Experience, the experience of logicians, has shown that it is otherwise. And without going into more detail today—when, by accident, I must strain my voice—this audience is nevertheless sufficiently informed as to where the logical effort has resumed in our time to know that, in approaching something as simplified in principle as the real of arithmetic… it has been demonstrated that in arithmetic, something can always be stated, whether offered or not offered to logical deduction, which articulates itself as ahead of what the premises, the axioms, the founding terms on which said arithmetic can rest, allow one to presume as demonstrable or refutable [cf. Gödel’s two incompleteness theorems].

Here we are touching with our finger, in a domain that appears the most secure [arithmetic]: – what resists the total grasp of discourse, to logical exhaustion, – what introduces into it an irreducible gap, this is where we designate the Real.

Of course, before arriving at this testing ground which may seem distant on the horizon, even uncertain to those who have not closely examined its latest developments, it will suffice to recall what “naive discourse” is. “Naive discourse” presents itself from the outset, inscribes itself as such, as truth.

It has always appeared easy to demonstrate to this naive discourse “that it does not know what it is saying”—I am not speaking of the subject, I am speaking of the discourse. This is the threshold—why not say it—of critique, that the sophist… to anyone who utters what is always posited as truth …that the sophist demonstrates to him that “he does not know what he is saying.” This is even the origin of all dialectic.

And it is always ready to be reborn: let someone come to testify at the bar of a court, it is the ABC of the lawyer’s art to show him that he does not know what he is saying. But there we fall to the level of the subject, the witness, whom it is a matter of confusing.

What I said at the level of sophistic action is that the sophist attacks the discourse itself. We may have occasion this year—since I have announced that I will address the “Parmenides”—to show what sophistic action is about.

What is remarkable in the development to which I referred earlier, in the logician’s enunciation—where perhaps some will have noticed that it concerns nothing other than the “Gödel theorem” regarding arithmetic—is that Gödel does not proceed in his demonstration from truth values… that there will always be, in the field of arithmetic, something that can be stated in the proper terms that it comprises, which will not be within the reach of what it posits for itself as the mode to be held as proper to demonstration …it is not from truth that he proceeds, it is from the notion of derivation.

It is by suspending the value of true or false as such that the theorem is demonstrable. What accentuates what I say about the logical gap at this point, a sharp point… a sharp point in that it illustrates what I intend to advance …is that if the Real… assuredly easily accessible …can be defined as the impossible… this impossible insofar as it proves to stem from the very grasp of discourse, of logical discourse …this impossible, this Real, must be privileged by us.

“By us”: by whom? By analysts. For it exemplarily shows that it is the paradigm of what puts into question what can emerge from language. From it emerge certain types—which I have defined—of discourse, as constituting what establishes a defined type of social bond.

But language interrogates what it founds as discourse. It is striking that it can only do so by fomenting the shadow of a language that would go beyond itself, that would be a metalanguage. I have often remarked that it can only do so by reducing itself in its function, that is to say, by already engendering a particularized discourse.

I propose… by focusing on this Real insofar as it asserts itself from the logician’s interrogation of language …I propose to find in it the model of what matters to us, namely what the exploration of the unconscious reveals, which—far from being… as Jung thought he could reinterpret it, by returning to the oldest rut …far from being a universal sexual symbolism, is very precisely what I earlier recalled about castration, with only the emphasis that it is essential that it not be reduced to the anecdote of a spoken word heard.

Otherwise, why isolate it, why grant it the privilege of I don’t know what kind of trauma, or even the efficacy of a rupture? When it is all too clear that it is nothing anecdotal, that it is rigorously fundamental in what—not establishes but—renders impossible the statement of sexual bipolarity as such, namely as—as curious as it may be—we continue to imagine it at the animal level.

As if every illustration of what, in each species, constitutes the tropism of one sex toward the other were not as variable for each species as their bodily constitution is.

As if, moreover, we had not learned—learned already for some time—that sex… not at the level of what I have just defined as the Real, but at the level of what is articulated within each science, once its object is defined …that sex involves at least two or three layers of what constitutes it, from genotype to phenotype, and that after all, after the latest advances in biology—do I need to specify which?—it is certain that sex merely takes its place as one particular mode within what makes possible the reproduction of what is called a living body.

Far from being the standard instrument of reproduction, sex is only one of its forms, and what is too often confused… although Freud, on this point, did offer an indication, albeit an approximate one …what is too often confused is very precisely the function of sex and that of reproduction.

Far from things being such that on one side there is the track of the gonad, what Weismann called the germ plasm, and on the other the wiring of the body, it is clear that the body, through its genotype, carries something that determines sex and that this is not sufficient: from its bodily production, from its corporeal statics, it emits hormones which, in that determination, can interfere.

So there is not, on the one hand, – on the one hand, sex, irresistibly associated—because it is in the body—with life, sex imagined as the image of what, in the reproduction of life, would be love, not that on one side – and on the other, the body, the body insofar as it has to defend itself against death.

The reproduction of life, as we are able to question it, at the level of the emergence of its first forms, arises from something that is neither life nor death, which is this: that very independently of sex… and even in connection with something already living …something intervenes that we will call the program, or codon again, as they say regarding certain identified points on chromosomes.

And then the dialogue “life and death,” it occurs at the level of what is reproduced, and it only takes on, to our knowledge, a dramatic character from the moment when, in the balance of life and death, jouissance intervenes.

The sharp point, the point of emergence of something which is that in which we all here more or less believe ourselves to take part—the speaking being, to put it that way—is this disordered relation to its own body which is called jouissance.

And this has at its center, has as its point of departure… this is what analytic discourse demonstrates to us …has as its point of departure a privileged relation to sexual jouissance.

This is why the value of the other partner, the one I began designating respectively as man and woman, is unapproachable by language, precisely for the following reasons: – that language functions, from its origin, as a substitute for sexual jouissance, – that it is in this way that it orders this intrusion, into bodily repetition, of jouissance.

This is why today I will begin to show you how, by employing logical functions, it is possible to give a different articulation—other than anecdotal—of what castration is. In the line of the logical exploration of the Real, the logician began with propositions. Logic only began when it succeeded, in language, in isolating the function of what are called quantifiers, which are nothing other than the “One,” the “some,” the “all” and the negation of these propositions.

You know this: Aristotle defines, in order to contrast them,
– “the Universals,”
– and “the Particulars,”
and within each:
– “affirmative,”
– and “negative.”

What I can point out is the difference that exists between this usage of quantifiers and what… for logical needs, namely for an approach that was none other than of that Real which is called number …what took place was something completely different.

The logical analysis of what is called a propositional function is articulated from the isolation within the proposition, or more exactly from the lack, the void, the hole, the gap that is made, of what must function as the argument. Namely, it will be said that every argument from a domain… which we will call however you wish, X or a Gothic A[;]— every argument from this domain, placed into the position left empty in a proposition, will satisfy it, that is, will give it truth value[; !].

This is what is written in the notation found at the lower left, the upside-down A X: ; !… no matter what the proposition is …the function takes a true value for every X in the domain.

What is this X? I said it is defined as being from a domain. Does that mean, for all that, that we know what it is?

Do we know what a man is, in saying that “every man is mortal”? We learn something from saying that he is mortal and precisely from knowing that for every man, it is true. But before introducing the “every man,” we only know the most approximate traits, which can be defined in the most variable ways.

That, I suppose you’ve known for a long time, it’s the story that Plato recounts, isn’t it, of the plucked chicken.

So that is to say clearly that we must question ourselves on the temporalities of logical articulation, namely this: that what the quantifier holds has, before functioning as an argument, no meaning; it only takes on one by entering into the function. It takes the meaning of true or false.

It seems to me that this is meant to make us feel the gap that exists from the signifier to its denotation,
– since meaning, if it is anywhere, it is within the function,
– but that denotation only begins from the moment the argument comes to be inscribed in it.

This at the same time calls into question something else, which is different: the use of the reversed letter E: , “there exists.”
“There exists” something that may serve in the function as an argument and may or may not yield a truth value.
I would like you to grasp the difference introduced by this “there exists” as a problematic:

– namely, that it questions the very function of existence in relation to what the usage of the particulars in Aristotle implied,

– namely, that the use of “some” seemed to entail existence with it, so that, since the “every” was supposed to include this “some,” the “every” itself took on the value of what it is not, namely an affirmation of existence.
We will not be able—given the time—to examine this until next time:
the status of the “every,” that is, of the Universal, exists only at the level of the possible.
It is possible to say—among other things—that “all humans are mortal.”
But far from resolving the question of the existence of the human being, it is necessary first, curiously enough, to be assured that he exists.

What I want to indicate is the path we will enter next time.
I would like to say that from the articulation of these four argument-function conjunctions under the sign of the quantifiers:

It is from there and only from there that the domain from which each of these X takes value can be defined.
It is possible to propose the truth function that is this one, namely that “every man” is defined by the phallic function,
and the phallic function is precisely what seals off the sexual relation.

It is otherwise that this letter will be defined:
the “inverted A,” called the universal quantifier, furnished, as I do, with the bar that negates it: ..
I have introduced the essential feature of the “not all”: . !, as being what can articulate a fundamental statement concerning the possibility of denotation that a variable takes in the function of an argument.

Woman is situated from this:
that not all can be said in truth to function as argument in what is stated by the phallic function. What is this “not all”?

It is very precisely what deserves to be questioned as structure, because contrary… and this is a very important point …to the function of the “negative particular,” namely that there are “some” who are not, it is impossible to extract from “not all” such an assertion.

It is the “not all” which alone is reserved to indicate that somewhere, and nothing more, she has a relation to the phallic function.
Now it is from there that the values to be given to my other symbols begin.

Namely, that nothing can appropriate this “all” to this “not all,” that there remains… between what symbolically grounds the argumentative function of the terms: man and woman …that there remains this gap of an indeterminacy in their shared relation to jouissance.
They are not defined in relation to it by the same order.

What must be… as I have already said of a term that will play a major role in what we will have to say afterward …what must be is that despite this “all” of the phallic function in which the denotation of man holds, despite this “all,” there exists… and “there exists” here means exactly as in the solution to a mathematical equation …there exists “at least one,” there exists at least one for whom the truth of his denotation does not reside in the phallic function.

Is it necessary to spell it out and say that the myth of Oedipus is what was devised to convey the idea of this logical condition, which is that of the approach—the indirect approach—that woman can take toward man?

If the myth was necessary, that myth of which it can be said that it is already extraordinary in itself that the statement does not appear absurd—namely that of the original man who would enjoy precisely what does not exist, namely “all women,” which is not possible, not simply because it is clear that… that one has limits [Laughter], but because there is no “all” of women.

So what is at issue is of course something else, namely that at the level of “at least one,” it is possible for the prevalence of the phallic function to be subverted, for it no longer to be true.
And it is not because I have said that sexual jouissance is the pivot of all jouissance that I have for all that sufficiently defined what the phallic function is.
Provisionally, let us admit that it is the same thing.

What is introduced at the level of the “at least one” of the father, is this at least one which means that it can function without it.
It means, as the myth demonstrates—since it is made solely to ensure this—that sexual jouissance will be possible, but that it will be limited.

This implies for each man, in his relation to woman, some degree of mastery, at the very least, of this jouissance.
Woman must have at least this: that castration be possible; it is her way of approaching man.
As for bringing it into action, this so-called castration, she takes care of it.

And so as not to leave you before articulating what concerns the fourth term, we will say what every analyst knows well: this is what the / § means.

I will have to return to it, of course, since today we have been somewhat delayed. I had intended to cover, as always, a much broader field, but since you are patient, you will come back next time.

What does it mean [the / §]?
The “there exists,” as we said, is problematic.
It will be an opportunity this year to interrogate what existence is.

What exists, after all?
Has it ever even been noticed that beside the fragile, the futile, the inessential that “there exists” constitutes, the “there does not exist” actually means something?

What does it mean to affirm that “there does not exist” an X such that it could satisfy the function ΦX, provided with the bar that establishes it as not being true: /§?
For this is very precisely what I questioned a moment ago: if “not all” women are involved with the phallic function, does that imply that there are some who are involved with castration?
Well, that is very precisely the point through which man gains access to woman.

I mean—this I say for all analysts, those who dawdle, those who circle around, entangled in Oedipal relations on the side of the father. When they cannot move beyond what happens on the side of the father, it has a very precise cause: it is that the subject would have to admit that the essence of woman is not castration, and to say it plainly, that it is from the Real—namely, apart from a little insignificant nothing—I do not say this randomly—well, they are not castratable. Because the phallus—which I underline I have not yet said what it is—well, they do not have it.

It is from the moment that it is the impossible as cause that woman is not essentially tied to castration, that access to woman becomes possible in her indeterminacy. Does this not suggest to you—I plant this so that it may resonate here next time—that what is above and to the left:

:§, the “at least one” in question, results from a necessity? And it is very precisely in this that it is a matter of discourse. There is no necessity except that which is spoken, and this necessity is what makes possible the existence of man as a sexual value. The possible—contrary to what Aristotle puts forward—is the opposite of the necessary.

It is in this—that : is opposed to ;—that lies the mechanism of the possible. I told you, the “there does not exist” [/] is affirmed by a statement, a statement of man. The impossible, that is to say, is that it is from the Real that woman takes her relation to castration.

And this is what gives us the meaning of ., that is, of “not all.” The “not all” means… as was just now the case in the left column [“what is above and to the left”] …means the not impossible: it is not impossible that woman should know the phallic function.

The not impossible, what is it? It has a name suggested by the Aristotelian tetrad, but laid out differently here:
– just as the possible was opposed to the necessary,
– to the impossible, it is the contingent.

It is insofar as woman presents herself to the phallic function in the manner of an argument in contingency, that what is at stake in the sexual value “woman” can be articulated.

It is 2:16, I will not go further today. The cut is made at a point not entirely ideally chosen. I think I have advanced enough with this introduction of the functioning of these terms to have made you feel that the use of logic is not without relation to the content of the unconscious.

It is not because Freud said that the unconscious does not know contradiction that it would not be the “promised land” for the conquest of logic. Have we arrived at this century without knowing that a logic can perfectly well do without the principle of contradiction?

As for saying that in everything Freud wrote about the unconscious, logic does not exist, one would have to have never read the use he made of this or that term… “I love her, I don’t love him,” all the ways there are to negate “I love him,” for example—that is, by grammatical routes …to say that the unconscious is not explorable by the paths of a logic.