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(All parts in English)

I wrote “I don’t know” and “I am ignorant.” This “I don’t know” and this “I am ignorant,” I confront them with something that will serve me as a base: poetry. To be more rigorous, I say that I assert that “I don’t know” is equivalent to “I am ignorant.” I admit, I take it that the negation is included in the term “I am ignorant.”

Of course, I could later return to ignosco and to what it very precisely indicates in the Latin language from which it comes to us, but logically, today I assert that the two terms are equivalent. It is from this supposition that what follows will derive its value. I write the word “everything” twice. These are indeed equivalent. What results from this?

That by the twice-repeated introduction, on these two levels, of this identical term, I obtain two propositions of essentially different value. It is not the same thing to say “I don’t know everything about poetry” or “I don’t know anything about poetry.”

Between one and the other, there is the distance — I say it straight away to clarify, since it is necessary — of where I want to go: to the significant distinction… I mean insofar as it can be determined by significant processes… between what is called a universal proposition, to speak with ARISTOTLE, and just as well with all that has since extended from logic, and a particular proposition. Where then is the mystery if these signifiers are equivalent term by term?

Let’s say that here we have posited it by convention — I repeat — it is only a scruple around the etymology of “I am ignorant.” “I am ignorant” means quite simply what it means in this instance: I do not know, I am not acquainted. How does this lead to two propositions, one of which clearly presents itself as referring to a particular of the field of poetry:

“There are some things in it that I don’t know, I don’t know everything about poetry.”

And this proposition, clearly universal, even though negative:

“Of everything that belongs to the field of poetry, I know nothing, I don’t get a thing.”

Which is the general case. Are we going to stop at this, which immediately introduces us into the specificity of a positive language, into the particular existence of French, which, as was explained in their time by very learned people, presents a duplicity — duplicity of the terms upon which negation relies — namely, that the “ne,” which seems to be the sufficient support — the affonctif as it’s called — necessary and sufficient for the negative function, is, apparently, reinforced, but perhaps after all complicated, by the addition of a term whose use in the language alone allows us to see what it is for.

On this point, someone whom I can only cite in passing, namely a fellow psychoanalyst and eminent grammarian by the name of PICHON, in the work he devised with his uncle DAMOURETTE on French grammar, introduced some very lovely considerations, in line with what was his method and procedure, concerning what he calls — the rather “discordantial” function of “ne,” — and the rather “forclusive” one of “pas.”

He said some very subtle and richly illustrated things about this, with all sorts of examples drawn from all levels and very well chosen, without — I think — being aligned, at least for us, with what may be of real importance. How this importance is determined for us is what I will try to make you hear, at least I hope so, later.

And for the moment, referring simply to this specificity of the French language, I only want to rely on that something which must surely occur elsewhere too, if it occurs in our language. That is, for example, one might raise this point: if the result of this statement hinged on the fact that we could group “not everything,” in which case the meaning of the sentence would come down to this, making it somewhat superfluous — allowing one to elide, as happens in familiar conversation, I don’t say to suppress: to elide, to swallow down the “ne” — “I don’t know everything,” with “not everything” together — it would be the inseparability of the negation, which we can call included in the term “I am ignorant,” and which would then be the driving mechanism, and everyone would be quite content.

I don’t see why one wouldn’t be satisfied with this explanation if it were simply a matter of resolving this little riddle. It’s amusing, but still, maybe it doesn’t go as far as it seems. Yes! It goes further, as we will try to demonstrate by referring to another language — English, for example.

Let’s try to start with something that corresponds in meaning to the first sentence:

“I don’t know everything about poetry.”
and the other sentence:
“I don’t know anything about poetry.”

What will nevertheless appear to us, when considering the things expressed in this other language, is that, in order to produce these two meanings equivalent to the distance between the first two, the explanation we just invoked regarding the binding of the two signifiers together will necessarily be reversed, because this binding of “pas” with the term “tout” in the first example is here realized—at the level of the signifier, I mean—in what corresponds to the second articulation, the second proposition, the one we qualified as universal.

Anything—as everyone knows—is indeed there as the equivalent of something, something that transforms into anything insofar as it operates under a negative register. Consequently, our first explanation is not fully satisfactory since it is through something entirely opposite, it is through a binding that takes place at the level of the second sentence, the one that in this instance expresses the universal, that this binding occurs—this equally ambiguous detachment, moreover, since the don’t does not disappear to produce this meaning: “I don’t get a thing about poetry.” On the contrary, it is where everything is conjoined with I don’t know that the first meaning is realized.

This is well suited to make us reflect on something that concerns nothing less than, as I already told you, laying my cards on the table, what is at stake in the mystery of the relations between the universal and the particular. We will attempt to say shortly what the fundamental concern was of the one who introduced this distinction into history, namely ARISTOTLE. Everyone knows that on this subject—on the angle from which these two registers of statement must be approached—a sort of small revolution of thought has occurred, the one I have already several times pinpointed: the introduction of quantifiers.

There may be a few people here—I like to suppose it—for whom this is not simply an auditory tickle. But there must also be many for whom this is nothing more than the announcement I made that at some point I would speak of it. And—God knows how—I will have to speak of it to you from the point where it concerns us, the point where I currently am, the point, therefore, where it seemed to me that it could be of use to us, meaning that I cannot give you its entire history, all its antecedents, how it arose, how it emerged, how it was refined, and how—in the end, this is what I must limit myself to—it is thought by those who use it. How to know?

Because it is not at all certain that, just because they use it, they actually think it. I mean that they in no way situate what their way of using it implies at the level of thinking. So I will be forced to begin with the way I think it, at the level at which I think, which concerns you—that is, at the level where it may be of some use to us.

At ARISTOTLE’s level, everything rests on this, which is designated in something that is a sign. What he believes he can allow himself, he allows himself to operate in this way, namely that if he has said:

“All men are animals”

he can, for all practical purposes, if it seems to serve a purpose, extract from it:

“Some men are animals.”

This is what we will call—not quite the term he uses—since it involves a relationship that has been termed subordinate between the universal and the particular, an “operation of subalternation.” I will probably have occasion more than once to make a passing remark on the way we are beaten over the head with “Man” in the examples, the illustrations that logicians give of their elaborations, which is undoubtedly not without symptomatic value.

We can begin to suspect it, to the extent that we have made the observation that perhaps “Man” is not something we understand so well after all. Well, that would lead us…

The question of whether two sets—as is said nowadays—can have something in common is a serious question that is currently bringing about an entire revision of mathematical theory.

Because after all, we could very well, from the start, and without engaging in futile gestures—I dare say—like that of our friend Michel FOUCAULT giving absolution to a humanism that has long since burst and is drifting away downstream without anyone knowing where it ended up, as if it were still a question and as if that were the essential issue concerning structuralism—let’s move on…

Let’s simply say that logically we can retain only this, which alone matters to us, if we are speaking of the same thing when we say—logically, I mean:

“All men are animals”
or, for example:
“All men speak”

The question of whether two sets—I repeat to you—can have a common element is a question that is being raised very seriously insofar as it raises this: namely, what of the element, if the element itself cannot be…
this is the foundation of set theory
…anything other than something about which you can speculate exactly as if it were a set, this is where the question begins to emerge, but let’s leave it there…

You know that the fatherland is at once the most beautiful reality, and of course it goes without saying that:

“Every Frenchman must die for it.”
But it is from the moment you subalternate to ask whether:
“Some Frenchman must die for it”

that it seems to me you must notice that the operation of subalternation presents some difficulties, because

“Every Frenchman must die for it”
and
“Some Frenchman must die for it”

are not at all the same thing! These are things one notices every day.

It is here that one becomes aware of what ontology still clings to…
that is to say, something a bit more than what its aim was when constructing a logic, a formal logic
…what of ontology still lingers in logic.

I assure you, I’m avoiding many digressions; I want you not to lose my thread. Now, I’m going to introduce right away, by a rather sharp method of opposition. I’m pleased—perhaps wrongly—but usually, there’s an eminent logician here in the front row; I always look at him from the corner of my eye to see the moment he’s going to start howling. He’s not here today; I don’t think I see him. That reassures me, and on the other hand, annoys me a bit: I would have liked to know what he would have said to me about this.

At the end, usually, he shakes my hand and tells me that he completely agrees, which always does me a lot of good. Not at all that I need him to say so to know, of course, where I’m going, but everyone knows that when you venture into territories that aren’t strictly your own, you’re always within reach of… bang! bang!

Now of course, what matters to me is not infringing on territories that aren’t mine, but finding, at the level of logic, something that serves as an example, a thread, a guiding illustration of the difficulties we face—we, those in whose name I speak, those to whom I speak…
and this ambiguity is truly essential here
…namely, psychoanalysts, in relation to an action that concerns nothing less and nothing other than what I’ve tried to define for you as the subject.

The subject is not “Man.” If there are people who don’t know what “Man” is, it’s certainly the psychoanalysts. It’s even their entire merit to radically question it—I’m speaking as a man, insofar as this word still has even a semblance of meaning for anyone.

So, I move to the level of the logic of quantifiers and I allow myself, with that bulldozer style I sometimes use, to indicate that the radical difference in the way of opposing the universal to the particular, at the level of the logic of quantifiers, lies in this…
naturally, when you open books on the subject, you’ll find yourself in line with what I’m telling you,
you’ll see, of course, that it can be approached in a thousand other ways, but the essential thing is that you see that this is the main thread, at least for what concerns us
…that the universal—at least the affirmative one—must be stated thus: “No man who is not wise.”

There you have it…
believe me at least for a moment, the important thing is that you follow the thread to see where I’m going
…which gives the formula for the affirmative universal, namely what, in ARISTOTLE, would be articulated as: “Every man is wise,”
a reassuring statement that, in this context, is of no particular importance. What matters to us is to see the advantage we may find in formulating this statement otherwise. Right away, you can notice that this affirmative universal will bring into play, in order to be supported, nothing less than two negations.

It’s important for you to see in what order things are going to appear. Let’s place here the Aristotelian forms:

affirmative and negative universals are designated by the letters A and E in the tradition following ARISTOTLE,
and the letters I and O represent the particulars, I being the affirmative particular.

“Every man is wise” (A)
“Some man is wise” (I)

How, in our quantificational articulation, will “some man is wise” be able to be expressed? I had first said: “No man who is not wise.” We now articulate: “There is man who is wise” or “Man who is wise”
but this “man,” which would remain hanging in the air, we support as it should be with a “there is,” just as
“No man who is not wise” is “There is no man who is not wise.”

But you also see that there is more to the “not” at the level of “not wise”; it must be that way for the meaning
“who is wise” to be there. Or, if you wish to articulate further, “There is man such that he is wise,” this “such that” is not at all an abuse, because you can also use it at the level of the universal: “There is no man such that he is not wise.”

To, then, produce the equivalent of our Aristotelian subalternation, we have had to erase two negations.
This is very interesting because, first, we can see that a certain use of double negation is not at all meant to resolve into an affirmation but rather to allow…
depending on the sense in which this double negation is used: whether it is added or removed
…to ensure the passage from the universal to the particular.

This is quite striking and meant to make us wonder what exactly must be said so that, in certain cases, we may assimilate double negation to a return to zero—that is, to what was present as affirmation at the outset—and, in other cases, to this result.

But let us continue to examine what the operation we started from, the quantificational operation, offers us as a property, which we pinpointed…
because it is accurate, because it corresponds to exactly that.
Let us remove only one negation, the first: “There is man such that he is not wise.”

Here too, I particularize, and in a way that corresponds to the negative particular. This is what ARISTOTLE would call: “Some man is not wise.” In truth, in ARISTOTLE, this “not wise,” no longer by subalternation but by opposed subalternation—which is diagonal, the opposition of A to O, from “Every man is wise” to “Some man is not wise”—this is what he calls “contradictory.”

The use of the word “contradictory” interests us, analysts, all the more because…
as Mr. NASSIF reminded us in the last closed seminar…
it is an absolutely essential point for psychoanalysts that FREUD once offered them this assuredly primary truth: that the unconscious knows no contradiction.

Only drawback…
one never knows what fruit is borne by what you state as a truth, especially a primary one…
is that this had the consequence that psychoanalysts, from that moment on, believed themselves to be on holiday, so to speak, regarding contradiction, and believed that this in turn allowed them to know nothing of it themselves, that is, not to concern themselves with it in any degree. This is clearly an abusive consequence. It is not because the unconscious—even if it were true—does not know contradiction that psychoanalysts are not to know it, if only to understand why the unconscious does not know it, for instance!

Let us note finally that “contradiction” deserves closer examination, which logicians, naturally, have undertaken for a long time, and that it is something quite different to speak of “contradiction” at the level of the principle of non-contradiction…
namely, that A cannot be non-A from the same point of view and in the same respect…
and the fact that our negative particular is called “contradictory.” It is true, it is.

But you see that in the angle: “There is man such that he is not wise,” I only bring it…
in relation to the formula that served as our starting point, founded on double negation…
I only bring it to the position of exception. Of course, the exception does not confirm the rule, contrary to what is commonly said and what suits everyone. It merely reduces it to the value of a rule without necessary value,
that is, it reduces it to the value of a rule—that is even the definition of a rule.

So, you are beginning to see how these things may become interesting for us. Here I appeal to my psychoanalytic audience to help them not be bored. You see the interest of these articulations that allow us to nuance things as interesting as the following, for example: that it is not the same to say…
this is why I made this distinction at the level of contradiction…
“Man is not woman”…
there, of course, we are told that the unconscious knows no contradiction…
but it is not quite the same to say:
— universal: “There is no man—of course, we are speaking of the subject—who excludes the feminine position, the woman”
— or, the state of exception and no longer of contradiction: “There is man such that he does not exclude woman.”

This may show you, however, how much more tractable and how destined to reveal the interest of these logical investigations it can be, even at the level where the psychoanalyst believes himself…
a thing that surely deserves, over time, to be called obedience…
obliged to keep his gaze fixed on the horizon of the preverbal.

Let us continue—on our part—along our little path by conducting an experiment: “There is man such that he is not wise,” I said.
You may have noticed that we have, up to now, done without the “pas.” Let us try to see what that will do.
“There is man such that he is—for example—not wise.” That’s not problematic; it means the same: there are always some who are not wise. But let’s be cautious: this “not wise” might well serve as our passage toward something a bit unexpected.
If we reinsert the “ne,” it still works: “There is man such that he is not wise.” That can still go.

Let us now focus on “not wise” and return diagonally to A, ARISTOTLE’s affirmative universal being the quantificational expression:

“No man such that he is not wise.”

Now that gives a strange meaning, all of a sudden—it becomes the universal negative: they are all not wise.
What could have happened? This “not,” which was perfectly tolerable at the level of the negative particular, now, when we place it at the level of what was previously the affirmative universal…
which seemed entirely apt to tolerate this “not” as well…
now turns dark—and I don’t know what color “e” has in RIMBAUD’s sonnet—but at the Aristotelian level, it is black, it’s the universal negative: they are all not wise.

I will now immediately tell you the lesson we are going to draw from this. It is obviously something that brings us face to face with the fact that the relation between the two “ne”…
as it exists in the fundamental structure of the quantified affirmative universal,
which is this formula: “There is nothing that does not…”
…has something that is self-sufficient, and we have proof of this in the release of this “pas” which, suddenly, harmless elsewhere, is found here to have flipped one universal into the other.

This is what allows us to proceed and to affirm that the quantificational operation, when we assign it its guiding function,
the originating function of logical operation, is distinguished from ARISTOTLE’s logic in that it substitutes…
in the place where ousia, essence, the ontological is not eliminated—in the place of the grammatical subject…
the subject that interests us as divided subject, namely:
— the pure and simple division as such of the subject insofar as it speaks,
— the subject of enunciation insofar as distinct from the subject of the utterance.

The unity in which this presence of the divided subject is presented is nothing other than this conjunction of the two negations, and likewise it is what motivates that in order
to present it to you, to articulate it before you—whether you noticed or not, but now it is time to notice—
things could not be done without the use of a subjunctive: “There is nothing that be…”…wise or not wise, the particular matter doesn’t count:
it is this “be” that marks the dimension of the slippage, of what happens between those two “ne,” and which is precisely where the distance always at play between the enunciation and the utterance operates.

It is therefore not for nothing that, a few sessions ago, when I gave you the first example of what is at stake in
PEIRCE’s formulation, I clearly made you notice that what constituted, in that exemplification
I showed you of those little marks distributed, well chosen, in four boxes:

that the true subject of every universal is essentially the subject insofar as it is essentially and fundamentally that “non-subject” which is already articulated in our way of introducing it: “No man who is not wise.”

It is difficult to stay balanced on this edge. Strictly speaking, theory, of course, is designed to eliminate it. I mean
that what interests us is that the theory of quantifiers, if we articulate it, forces us to detect this relief and this irreducible slippage which makes it so that we do not know where the properly instituting nerve of what at first appears as repeated negation slips away—and which, on the contrary, is creative negation insofar as it is from it that is instituted the only thing truly worthy of being articulated in knowledge, namely the affirmative universal, that which always holds, and in any case, that alone interests us.

Thus you will see it formulated, under the pen of the logicians of quantification, that we may equate what is expressed by a ∀, namely the universal value of a proposition written as ;Fx,
we must write it in the algebraic terms of symbolic logic, namely that this universal truth: ∀ is “for all x,”
that x operates in the function Fx, meaning, for example in this instance, the function of being wise, and that man will be an x
that will always have its place in that function.

The transformation which is given to us as valid in the theory of quantifiers is represented as follows: :…
this : being the symbol that specifies for us, in quantification, the existence of an x, a value
of x such that it satisfies the function Fx
…and we are told that ;Fx can be translated by a :, namely that there does not exist an x such that it throws
the function Fx into the air: .

In short, that the conjunction of these two “minus” signs…
and it is indeed something that happens to cover the articulated, linguistically nuanced form in which I presented it to you
…suffices to symbolize the same thing, which is not at all true, because it is quite clear that—as “minus” as they are—in logical symbolization, these two “minus” signs do not have the same value, that there does not exist an x which—so I was led to tell you—
throws into the air, that is to say renders false, the function Fx. I symbolized that these two terms—that of non-existence (/) and that of , which results in the falsity of the function—are not of the same order. But it is precisely this that is at stake.

It is a matter of concealing something that is precisely the very fine fissure, absolutely essential for us to determine and to fix in its plane: the distance from the subject of enunciation to the subject of the utterance, as I will again make you notice, for example, in another way, at the level of other authors, in presenting a more tractable image of the function at the level of its properly predicative application, because in truth, Fx can designate all sorts of things, including all types of mathematical formulas that you can apply to it. It is the most general formula.

On the other hand, if you want to stay at the level of my “Every man is wise,” here is the formula: (h v s), with the disjunction sign “v” that I had already put on the board the other time, a formula to which, according to the logicians who introduced quantification, it would suffice to add the Π from pan or the Σ to make it a universal or a particular proposition: Π(h v s), which would mean that, in sum, what we are dealing with is the disjunction of “not man” and that s. That means that if we choose the opposite of “not man,” that is to say, “man,” we get the disjunction: “he is wise,” either in all cases or in certain particular cases.

If we take the negation of “wise,” that is, if we renounce “wise,” we are on the other side of the disjunction, namely on the side of “not man”: that can still work, up to that point. But this in no way implies the necessity of “non-wise” for what is “not man.” Yet this is not indicated in the formula. For that to be expressed, the disjunction would have to be marked, for example, like this:

—thus, a sign that would be the “inverse” of the square root sign—meant to show us that, in view of implication…
if we have here, in sum, at the level of the universal, that man implies wise
…non-wise, certainly, does not imply man, but wise is perfectly compatible, too, with not-man. That is to say, there may be something other than man that is wise—this is elided in the way the formula of the disjunction is bluntly presented, between a negated subject and a predicate that is not.

This is also the point where something is demonstrated which, in the so-called system of double negation, when expressed in the notation used by MITCHELL, always lets slip that “something” which, this time, far from sealing the fissure, unknowingly leaves it gaping—confirmation that what is at stake is always fissure. In other words, what is at stake—formally speaking in logic—is always this: to know what can be derived—and how far—from a statement, that is, to obtain a reliable statement. That is indeed where ARISTOTLE also started.

ARISTOTLE, of course—let’s not say he was at the dawn of thought, because the very essence of thought is that it has never had a dawn—it was already very old, and he knew something of it. He particularly knew this: that, of course, there would be no question of knowledge if language did not exist. That is not enough, of course, for knowledge to depend only on language, but what mattered to him was to know precisely—because thought was not born yesterday—what, from a statement, could make something necessary; on that point, there was no room for concession. The first ananké is ananké of discourse.

ARISTOTLE’s formal logic was the first step in knowing what, properly and distinctly at the level of the utterance, could be formulated as giving from this source—which does not mean it was the only one, of course—its necessity to enunciation, that is to say that, here, there is no turning back. Moreover, this is the meaning the term epistémé had at that time: it was that of a reliable utterance. The distinction between epistémé and doxa is nothing other than a distinction situated at the level of discourse.

That is its difference from what science is for us…
going in the same direction, namely toward a strictly reliable utterance
…and for us, of course, who have made some unprecedented contributions regarding what an utterance is—and not elsewhere than in mathematics.

These laws of utterance, however reliable they have become, are becoming even more demanding every day and thus are not without revealing their limits. I mean that it is to the extent that we have taken, in logic, a few steps—among which, of course, the one I am representing here—but it is the original step that interests us. Why? Because it is on this side of the attempt to capture enunciation through the networks of the utterance that we, analysts, find ourselves. But what luck that the work has been pushed so far elsewhere, if it may be through that that a few rules are delivered to us to better locate the fissure.

When I state that the unconscious is structured like a language, that does not mean that I know it, since what completes it for me is precisely what “one”—upon which I place emphasis and which is the one that gives vertigo to all psychoanalysts—
it is that “one” knows nothing about it, “one,” the subject-supposed-to-know, the one who must always be there to give us rest.
So it is not that I know it when I state it. It is that my discourse does, in fact, organize the unconscious. I say that the only discourse we have on the unconscious—the one from FREUD—makes sense, certainly, [but] that is not what matters,
because it makes sense like “one springs a leak”: from all sides. Everything makes sense, as I have shown you. “Colourless green ideas sleep furiously” makes sense too. It is even the best characterization one could give of the whole of analytic literature.

If this meaning in FREUD is so full, so resonant in relation to what is at stake—the unconscious—if, in other words, it is distinct from everything he had rejected in advance as occultism, if everyone knows and feels that this is not MESMER…
that is why it persists despite the nonsense of analytic discourse…
it is a miracle that we can only explain indirectly, namely through FREUD’s scientific training.

What matters is not its meaning, this discourse which must first exist, so that what I propose with “the unconscious is structured like a language” may have its reference, its Bedeutung, because it is there that we realize that the reference is language. In other words, everything that my discourse articulates about FREUD’s discourse on the unconscious leads to isomorphic formulas—those that are required if language is taken as object.

The isomorphism that the unconscious imposes on my discourse in relation to what discourse on language is, this is what is at stake, and what requires that every psychoanalyst be taken into this discourse, insofar as he engages in that field defined by FREUD for the unconscious. From there, we can hardly do more than state, before parting, a few points to be pinned down so that you don’t lose your head in this matter.

I hope that what I have just said at the end, concerning the formula “the unconscious is structured like a language,” will still retain its value as a turning point for those who have long heard it as well as for those who refuse to hear it. Of course, our science, the one that is ours, is not defined solely by these coordinates whereby there is no knowledge except through language.

Nevertheless, it remains that science itself can only be sustained by setting aside a purely linguistic knowledge, that is, a logic strictly internal and necessary to the development of its instrument, insofar as the instrument is mathematical, and that anyone can grasp tangibly at every moment the strictly linguistic impasses into which it is placed by the progress of the mathematical instrument itself, inasmuch as this progress both welcomes and is welcomed by each new field of these factual discoveries—this progress is a wholly essential spring of modern science.

It remains, then, that there is a whole level at which knowledge is of language, and that it is no vanity to say that this field is properly tautological, whether at the very origin of what marked the beginning of science—that is, a taking of measure of the division thus defined in discourse—of a logical asceticism that is called the cogito.

It is a sign that I have been able—that asceticism—to develop it sufficiently to ground in it the logic of fantasy, the one whose articulations were, I must say, quite well isolated last time during the closed seminar by one of those who work here in this field of my discourse. It is not, as he said—and as he said legitimately from the perspective of what he was trying to bring as a response to this discourse—a new negation that I would be producing.

Heaven forbid that I give anyone, with the introduction of a novelty, the opportunity to dodge what is at stake—which is precisely the opposite of something that could be plugged up, since it is something unpluggable.
Would that Heaven prevent me from giving the psychoanalyst yet another renewed alibi, when what is required of him is to be in the analytic discourse, that is to say, in the proper and Aristotelian sense, its hypokeimenon, its subjective support, certainly—but insofar as he himself assumes its division.