Hypertranslation: LACAN SEMINAR XIX, 8 March 1972

Lacan begins by reminding us of our focus: it is a discussion of the “One,” and so, for some reason he says that we must discuss the “Other.” Is the “One” therefore on the side of the “Other”?

Lacan recalls a conversation with a Marxist —  no doubt one of those staunch atheistic Marxists who, instead of examining the structure of power begins with the moral posturing of an atheist — whereby the Other can *only* be understood as God. This implies for Lacan that the Other is not necessarily God, although, God may be Other.


The Other is always also the Other of sexuation. This is why the signifier of the Other is barred, written with a line through the capital “A”: s(~A).

Jouissance always comes from the Other. It can come from no other place.

The existence of God is ineffable, within signification.

Jouissance does not come from the Other, sexually. In other words, we do not get sexual enjoyment from the Other (because there is no sexual relation).

Lalingua (the language, all as one word) is resistant to sexual enjoyment from the Other.

We derive enjoyment, jouissance, from the Other mentally (and not sexually).

S(~A) – it is the negation of the Other through the signifier: it is the same as saying that we derive jouissance from the Other mentally. This is also a way of writing something about the Other. It is because the Other vanishes — because the Other does not exist — that there can be a relationship written. One of the ways that we write the relationship is through the formal writing of the four discourses.

It is because the Other has to be emptied for it to be written mentally that it is not an idealism that Lacan is putting forward. It is quite different from the following position from George Berkeley: nothing of what is thought is thought unless by someone.

Jouissance comes from the Other, but not sexually. It comes mentally. But then Lacan says that jouissance comes only from your fantasies. Does this imply that the Other is in fact nothing but fantasy? Or is it that jouissance comes mentally to be written as fantasy because of the inexistence of the Other?

And then Lacan makes this even more difficult: “what is important is that your fantasies derive jouissance from you.” I’m not sure what this means: perhaps it means that the ideas — the signifiers — gather credibility because they are absorbed in your jouissance as an Other.


Lacan claims that Idealism asserts that there are nothing but thoughts (mentally). lalingua involves a queue — a series — of thoughts. This is why we should perhaps take lalingua seriously.

So what is involved in lalingua:

  • not that I think thoughts (Idealist position);
  • not that one thinks thoughts and therefore exists (I think therefore I am);
  • for lalingua: it is importnat that these thoughts think themselves.

Now we return to the point which Lacan used to close section 1 of the class. The thoughts — perhaps this is the symbolic order of signifiers, the serial numbers of Frege’s arithmetic system — think themselves. And how? Most likely they do so unconsciously.

It is because of this finally point about lalingua that Lacan claims he is not an idealist but rather a “realist.”

But here Lacan counts himself a realist psychoanalytically, rather than philosophically. Lacan is a realist in psychoanalytic discourse, and, as if to imply a relation to philosophical discourse, reminds us that a discourse takes its reference always from another discourse.

Lacan begins to make some really provocative statements about the “S,” which is, without a doubt, the letter for “Signifier.” The “S” — which is also the Master Signifier — is the shape of a chair, and Lacan said that it couldn’t have been otherwise because we sit on that chair, or, rather, we sit on it because there is no Other sitting on that chair. And then he points also to Hogarth to described the S as a “line of beauty.”

So this imply, then, that the “S” — as signifier — is also an aesthetic, a mark of beauty — that there is something about it as semblance, as art?

The series of thoughts — of signifiers — is also a “tail,” which means that something REAL “produces this comet effect that I have called the queue de pensees …” This is implies, doesn’t it, that the agency of the real produces the signifier, pushes the signifier out, like a flame attached to a comet moving in space.

For psychoanalysis, says Lacan, if you can’t follow him in the claim that the repetition of the signifying chain is what grounds psychoanalysis then there is no psychoanalysis.

Lacan revisits some of his earlier claims about Descartes and about the Freudian thing. You can’t speak about das Ding, the Freudian thing. The thing itself speaks. And, moreover, I make the thing itself speak. The thing states: “I, truth, speak.” So, it speaks the truth and yet we only catch glimpses of the thing speaking, of its truth, in “conundrums.” So – when one writes the thing it is not me who is writing but the thing that writes.

There exists an x that is no submitted to the phallic function, means that there is one who is not expressible in language.


Man needs the existence of something that negates him for him to exist at All. This is clearly expressed in the formula for masculine sexuation:

Ex ~Phi(x) <–there exists an x that negates the phallic function
Ax Phi(x) <–all men are submitted to phallic function

Lacan makes some very clever expressions here about those who “sit” (a reference, I think, to the master signifier, S) in the psychoanalytic associations.  And then he finally quites blabbering to get to the point that “the sexual relation cannot be written.”

The One has two faces. And we know this because of woman. Woman is “between centre and absence.” This “between centre and absence” is a “second bar” that Lacan writes “not-all.”

Does this second bar imply that for man, the first bar, is between “all men are submitted to castration” and “there exists one who has access to jouissance” ? So, it is a bar between himself and the jouissance of the Other? Whereas, for woman, it is between herself — “not all woman are submitted to castration” (or, rather, women are not entirely submitted to castration) — and “there does not exist a woman who is not submited to castration” (i.e., she is, nonetheless, castrated).

The “center” then is the phallic function, and she is between the phallic function of castration and its radical absence.

“jouissabsence” = there where the jouissance is in the “absence” (without the phallic function of the Other, the at-least-one).



Hypertranslation: LACAN SEMINAR XIX, 3 March 1972

Lacan opens with a discussion of what I have elsewhere named the property of “borromean dependence:” the borromean knot/chain is such that if one ring is detached the other two will also, by necessity, become detached, and the whole thing will fall apart.

The question that Lacan is pursuing seems to be the relationship of language and logic to topology. Indeed, this is what I tried to show in a recent paper published (kindly and with a great amount of risk, no doubt) by PsychoanalysisLacan, titled “A Portrait of Baudelaire as a ‘Man of Genius’: Ordinary Psychosis within the Age of Modernity” (here). In that article I tried to show that the logical formulations of the oedipal metaphor indicate a borromean knot already – they already point toward a topological understanding. Minimally, this is discovered by noticing the way in which the parentheses are nested within the formula.

In any case, Lacan says: “Should language be broached in its grammer? — in which case, this is certain, it hinges on a topology.”

Topology, as defined by Lacan, is mathematical but it does not deal with “units.” This is a curious statement given the focus on Frege in previous classes, and, indeed, Frege’s focus on “units” in his Foundations of Arithmetic. Thus, topology insists that “it can be pulled out of shape.”

And then Lacan claims that the tetrahedrons from the previous class were actually links, circles, rings even. “Each of them was a closed and flexible circle that only holds fast when linked to the others.” What does this mean? The pentagram from the previous class probably makes this very clear: these are two interlocking tetrahedrons.

But we can see the topology of the rings most clearly by imagining the ternary structure of the initial triangle, and each vector or vertex as an interlocking ring.


There are a few paragraphs on taking language “on the basis of signifying combinatorics” or “semantics,” which I can not understand whatsoever. And then there is something important that I am missing about the problem of being compelled to take very different types of action under the heading of “verbs.” I hope that somebody can make this comprehensible for me.

In any case, Lacan is putting forward something original and inventive: language having its origin in a topological structure. And he finds this only by pursuing the discovery of the impossible sexual relation.

And then we get those two modalities of the “real” define so easily by Fink in his book The Lacanian Subject: there is the “first order” real and the “second order” real. Lacan rather asks the question of a new real. For so long the real was that which limited the symbolic. Now, we have the following question: “does the speaking being speak because of this something that happened to sexuality, or did this something happen to sexuality because he is a speaking being?” It seems to me that the question might also be phrase in the following way: “does the speaking being speak because of the impossible real of sexual relations, or does the impossible real of sexual relations occur because he is a speaking being?”

On the one hand, there is a question of the real arises as a consequence of the symbolic (the imposition of the name-of-the-father, if you like). On the other hand, there is a question of the symbolic (signifier, name of the father, etc) arising as a consequence of the real itself. I believe that both are correct, but the latter is probably more correct because it accounts for the origin of the name of the father as signifier.

And then Lacan makes his famous statement about Simone de Beauviour’s work in The Second Sex. He says:

She called me by phone to tell me that she would certainly need my advice in order to enlighten her as to what the psychoanalytic contribution to her book would be. As I remarked to her that it would take at least a good five or six months for me to unravel the question for her — which is a minimum because I’ve been speaking about it now for twenty-years, and this is not by chance — she announced that of course it was out of the question for a book that was already being finalized to have to wait so long, the laws of literary production being such that it seemed to her that having more than three or four consultations with me was impossible. Following which, I declined the honour.

The fundament of what I’ve been coming out with for a while now, since last year, is very precisely that there is no second sex.

This final statement is fascinating: it is that the woman does not exist. He continues, returning to the function of language, to state that it is from the moment that language begins to function that the second sex ceases to exist.

Lacan introduces his infamous formulae of sexuation:

Ex! Phi(x) [whereby ! indicates a negation]

Ax Phi(x)


!Ex !Phi(x)
!Ax Phi(x)

Lacan makes a clever statement about the biblical meaning of “know,” which, it seems to me, means “to have sexual intercourse with” (a verb, then, from genesis in the old testament).

This is an ontology, then, for Lacan, since he believes it states something fundamental about Being. He points to the Chinese who have “long called upon two fundamental essences that are respectively the feminine essence, which they call Yin, in opposition to the Yang, […] underneath.”


There is a sense in which the feminine and masculine essences have a “one to one” relationship which corresponds with number. It seems that there is a one to one form of coupling among the senses — the “soul to soul” encounter, which, Lacan derives from the animistic model.

Lacan goes on to call this model a “fantasy.” And it is this fantasy that repeats, and it repeats the unique encounter of the speaking being. And what does the fantasy do? It tries to conceal the function of language, which sexuates the beings: “the fantasy is there to say language does not exist.” The fantasy is also that there is a sexual relation, which, it seems, amounts to the same thing as saying that language does not exist. 

Thus, that language does not exist implies also that there is a sexual relation. Yet, these are both fundamental to the fantasy.

Lacan claims that when it comes to the sexual relation … the Other is “an emptiness.” But he qualifies this: “by means of something extra.” Thus, the Other is an emptiness by means of something extra. This “something extra” relates to the homophone Lacan next produces: “the Hun,” which sounds like “the One” in French.

Lacan claims that Socrates is a hysteric! Lacan simply points to the reports of his “cataleptic manifestations.” Which is an embodied symptom. And then Socrates is also responsible for sustaining a discourse that gave way to the discourse of science. And how? It was by bringing “the subject to the place of semblance.” I am not sure what this means … I presume it means that the subject, instead of being located in the real, comes to the imaginary. Thus, he places the subject in the position of phallic signifier who stands in the way of enjoyment. This would explain Lacan’s point that “he had to adjure her kindly to withdraw so as to allow his death to take on its full political signification.”

It is the analytic discourse — not the hysteric’s discourse — that is able to claim, finally, that there is no such thing as sexual relation. This implies, does it not, that Lacan believes himself to be beyond Socrates (the hysteric) in some way. And perhaps he was! Thus, when my friend asks me: “what is socrates to the capitalist discourse?” My answer, here, might be: “a capitalist!, and what is the analyst within capitalist discourse?” Socrates seems no longer to be the hero that he may have once been for Lacan.

The analyst discourse observes that there is no sexual relation but also that there is a “phallic function,” phi(x,y). And it is the phallic function that spells out clearly the point of exception: there is “one” of the two terms that is not typified by sexual relation. What does this mean? He links this expression also to the homophonic “hun,” there is one, hun, that is not typified by sexual relation: and it is the woman. The hun is not Male or Yin/Yang. It is an organ — but only through its function.

Lacan makes a claim in passing that helps us to understand the discourse of science. First, as I wrote above, Socrates gave way to the discourse of science by bringing the subject to the place of semblance. Second, the discourse of science inserts “language onto the mathematical real.” Does this not imply, at some level, that there was no foreclosure? When foreclosure is absent then the symbolic — language — returns in the real. This, at least, was the position Lacan spelled out decades earlier in his psychosis seminar (sem. 3).

Although it is true that we continue, within language, to spell out the relation of the sexes through the materials of language — signifiers — as “man” and “woman,” in their “one-to-one” relation, this is a “mirage” of language. It does not accurately refer to the being of man and woman. Analytic discourse therefore rejects the ancient writing of man and woman. Lacan remarks that even he too is writing these down, in a way, but only, finally, with recourse to topology. And this is different! His writing moves from logic toward topology – and this is crucial. There is a difference, then, in logic and in topology. Topology gives us something that logic keeps only as mirage, fantasy.

It is topology that allows us to focus on the “empty place” and to see it as operative already within logic(al discourse). Moreover, topology permits us to see how the “empty place” determines the argument itself. It was, once again, the “empty place” of zero as the non-identity with 1 that determined the logic of succession for Frege.

It is not the phallic function that makes the sexes different, since both men and women are subject to the phallic function.

There are within propositional logic four fundamental relationships: negation, conjunction, disjunction, and implication. But Lacan points to a limitation in propositional logic: the relationship of “negation” can not be sustained: negation is not only falsehood, it is not only all that is not true. Why? Because truth is what is not written (which is different from that which is falsely written, or, rather written falsely). It is what is not written that challenges the supremacy of the phallic function.

In the relationship of man to woman, one always stands as an obstacle to the other — to the relationship as such.

A woman cannot be castrated, thus !Ax Phi(x) (Not All x are submitted to castration).

Lacan has gone through negation a bit, but turns to conjunction. Conjunction is grounded upon the bringing together of two true propositions. But this, claims Lacan, is not what is permitted by his formulae: there can be no conjunction of sexuation, of sexual relation. Or, perhaps, sexual relation is the mirage of conjunction.

Similarly, disjunction can not be operative in his formulae either. Disjunction occurs when it is impossible for two propositions are false at the same time. Disjunction can not allow for two propositions to be false at the same time.  Lacan goes on to give proof that disjunction is not operative in his formulae – I have opted not to think too hard about this stuff.

We return for a moment to the relation of 1 to 0. It is the relation of the phallus to the not-all, and this is also the “at least one.” “There is at least one x, …” and “there does not exist an x” … is this correct?

There is feminine jouissance and phallic jouissance; feminine jouissance does not concern the phallic function, and this is how Lacan chooses, at this time, to define it. And Lacan claims that Tiresias disclosed feminine jouissance when he came back Theresa. Tiresias was a blind prophet of Apollo who transformed into a woman for seven years.

When !E(x) (top level of the feminine formulae of sexuation), there is the possibility of sexual relation. But here, when there is sexual relation the Other ceases to exist: the Other is absent. Why? Because the Other would be the obstacle to the sexual relation? Because the Other would be the barred signifier of the Phallus?

0 and 1 makes 2, but on the symbolic plane. And this is where existence takes root: in the symbol.

The speaking being is ungraspable — and all the more so because he requires the symbol to support himself: Phi.

Existence is not Being, then. This is the statement Lacan returns to …

-to exist depends upon the Other.

-but Being does not depend upon the Other.

What does this mean: “All of you here, from some angle or other, do indeed exist,  but when it comes to your Being, you’re not so tranquil.” It means, I think, that existence does not guarantee Being. 

Aristotle maintains that existence can in no way be established except outside the universal, Ax. So existence is particular, rather than universal. This particular, which is associated with existence, is related to the use of the word some. 

“Some x …” implies “there exists some x…” and this is a particular proposition.

Lacan informs us that this is formalized as a quantifier. Apuleius argued that whenever Aristotle used all and some, we are dealing with quantifiers, with issues of quantity. But Lacan contends that all and some are not actually quantifiers. Rather, they are “two modes of […] the incarnation of the symbol.” Thus, you can incarnate the symbol all of the time, or you may incarnate the symbol some of the time. Or, rather: some symbols or all symbols. 

Every language uses “alls” and “somes.” This is fascinating. It is for this reason that Lacan believes that all languages have a “common root.” I wonder if his is lalangue? It is possible since lalangue is the babbling of language. This makes all the more sense for me since Lacan says that the common root has to be “related to something that is not language.” The real seems to be the common root, in some way.

There is a gap between the 0 and the 1 within Frege’s system, and that is the non-relation, which is also, one might say, non-identity (as a principle). Lacan likens this to the ternary structure … but this time for mathematics.


On the “at least one,” it is the “name of the father.” But here Lacan makes a really nice move by saying that the name of the father is “supported by” the “at least one.” Thus, the name of the father does have the primacy of place that it used to have for Lacan.

AxPhix indicates that “every male is serf to the phallic function.” We see here a way of transposing the formulae of sexuation into Marxian analyses, or economic analysis. However, it is not so simple: it is not that only men are “serfs,” clearly. But women are “serfs” too, perhaps, but in their own way.


Hypertranslation: LACAN SEMINAR XIX, 9 February 1972

Lacan gives a nice new phrase for what he discussed in the last class: “la lettre d’amur,” which is a homophone of “d’amour.” It sounds as though he is discussing the love letter but he is in fact discussing the love wall. The love letter is written, therefore, on the wall of discourse.


Lacan suggests that a love letter might read: “I ask you to refuse me my offering.” He goes on to claim that this is a “true” love letter, to “refuse my offering.”

From this I deduce, without reading further yet, that the “refuse” is the objet a, which is offering precisely as a rejection to the analysand by the analyst in the analytic discourse (a–>$). However, it carries for me also a biblical sense shared by the Abrahamic faiths and commented upon at length by Kierkegaard in his Fear and Trembling. It was Isaac, Abraham’s cherished son, who asked his father why he had no offering to God at Mount Mariah. And then comes Abraham’s response: “God himself will provide the offering, my son.” Abraham, rather than to tell a lie, opts to speak in a way that can not be understood.

These words — “I ask you to refuse me [me, the Ego] my offering [a posession, a having]” — also appear, in some form, within the Chinese script written on the board.

But Lacan adds one more part: “… because this isn’t it.” The “it” from this sentence alludes, it seems, to the Freudian “id.”

“I ask you to refuse me my offering … because this isn’t it” seems to me to have a similar structure — though I know not what to name that structure — as “love is giving what you don’t have … to somebody who doesn’t want it.” 

Except here it is inverted:

  • “I ask you to refuse me my offering” is subjective genitive of “somebody who doesn’t want it.” In this case you are asking somebody not to want what you are offering.
  • “… because this isn’t it” is objective genitive of “giving what you don’t have.” When you give what you don’t have you are giving what isn’t “it.”

So what makes this inverted? It is the fact of the demand. “I ask you to..” takes place at the level of demand, whereas “love is giving what you don’t have” is rather a response to the demand.

In any case, I return to the text.

Lacan tries to make a play on the French word “serious” as being related to the arithmetic “series,” or “serial,” which, as we know from previous classes, is used to understand the logic of the signifying chain (particularly through Frege’s work): “[s]erial is the sequence of integers …”

Lacan points to the problem: what “transfers” from “0 to 1”? He hints at something here, I think, when he says: “this is the goal I set myself […] …or worse.” He claims that he is still pursuing this question – as if to remind us – but then quickly turns to a lecture recently given by Jakobson. Jakobson points to the work of a Danish philosopher named Boetius de Dacia. The key concept here is “suppositiones,” which Lacan claims has something to do with the “supposition” of the subject by the signifier: “the subject that is radically supposed.”

de Dacia was a medieval semiotician. I tried to find something about de Dacia and this “suppositiones” and all I could find was something written in Latin, which I translated as: “it is by accepting these two suppositions [which two? Perhaps it doesn’t matter, but it matters that it is two] there is knowledge.” This certainly seems important, but I can not say for certain anything else about de Dacia. Dacia, incidentally, was accused of Averroism, which is, as I understand it, an attempt to make Aristotle’s philosophy work for Arab and Islam societies. I am learning more about Averroes lately because I have a colleague, a sociologist and social theorist, who has been pointing at his work for me (ibn Rushd). Lacan then makes a quick claim: “it would not be altogether accurate to say that the two things are related” (the thesis of the supposition and the philosophical association with Averroism). But why?

Could it be that Averroism does in fact introduce something new about this “supposition”? I think that Lacan was onto something — something that Miller’s work points in the direction of — namely that the movement from Jewish Atheism (Freud) through to Catholic/Christian Atheism (Lacan) has as its natural completion the movement to Islamic Atheism (…). This isn’t necessarily the worst of possibilities.

In any case, Lacan quickly claims that the “slip of the tongue” is a “serious matter,” which brings us back to its place in the “serial” chain of signifiers. It is a matter of the “series,” then. That is why it is “serious,” and why it must be taken seriously.


Lacan discusses communication as a “ternary” relationship – and uses this to offer a drawing where there is sender (S) and receiver (R) and the code, as the third, the mediator, that which must be deciphered for the two to reach an understanding, at the apex:

Screen Shot 2018-10-07 at 3.11.22 PM

The “code” is also the “message.” So, there is a sender, a receiver, and a message. There are a few paragraphs here that I simply did not understand. Lacan claims something about how the verb is also essential to the schema — how? Why? It is as if he is claiming that the ternary diagram is incomplete because it does not account for the verb’s function.

So – what is the function of a verb? Lacan returns to his opening expression: “I ask you to refuse me my offering because that’s not it.”

The verb is “to ask.” “I” is the Sender, ask is the Code, and “You” is the Receiver. Is this correct? Lacan says that “I” is “x” and “You” is “y” in the formula:

F (x,y)

F = “I ask you”

Ask (I, You)

Or, if I may put it in the triangle:

Screen Shot 2018-10-07 at 3.21.59 PM

To me, diagramming it in this way exposes the extent to which this relates to Lacan’s very early “Schema L.”

Lacan continues: “I ask you … to refuse to …” we can see here that there are two functions. The second verb function, “to refuse,” is actually nested inside of the first verb function, “to ask.” Thus:

F 1(x, y, F2(x, y …

F1 = “to ask”

F2 = “to refuse”

…and “x” and “y” remain “Subject” and “object,” “I” and “You.”

Lacan’s next move is a bit obscure. He indicates that to “end here,” that is, to end after “I ask you to refuse to me,” is to introduce Phi. I’m not sure why:

F(x,y f(x,y, Phi(x,y)))

What could it mean? My immediate thought is the following: whatever the noun is of this sentence (e.g., “I ask you to refuse me MY OFFERING”) is phallic. It is a possession, indicated by “my” and it is some-thing. So this makes it the phallus that one is potentially offering. Therefore:

F1 = “to ask”

F2 = “to refuse”

Phi = “whatever it is that one has,” the “phallic possession”

x = “I”

y = “you”

I don’t exactly have it right, but it looks something like this:

Screen Shot 2018-10-07 at 3.35.00 PM

I would appreciate a proper version of this image, if anybody can produce it. My attempt was done in haste and is obviously limited.

Lacan then claims that this formula is a “knot” and it introduces us to the “objet a.” Thus, is the objet a not found there in the “its not it” addendum: “I ask you to refuse me my offering because its not it.” The phallus, then, is a giving of “x” to “y” but “its not it,” which means that it occurs on the condition of the introduction of “objet a” in the final (x,y) of the Phi(x,y)? I need more clarity on this and I hope some of you will chime in.


Lacan unexpected opens the next part of his class with the famous Wittgenstein quotation — the anti-philosophical quotation par excellence, according to Badiou — “whereof one cannot speak, therefore one must remain silent.”

Lacan claims that “whereof one cannot speak” == “this isn’t it.” Thus, I see this as related to the “real,” and the following seems to be true:

Screen Shot 2018-10-07 at 3.50.05 PM

This implies that Lacan’s statement has the sentence clauses switched. Wittgenstein begins with that which one cannot speak about and deduces that one must remain silent about it. Lacan begins with a demand to refuse to remain silent about what isn’t the phallus: I demand that you refuse the phallus as an offering because that isn’t the objet petit a.

We begin with the statement: “I ask you .. to…” It seems to me that the “to” is the moment that links us into the next function, the next, “f2(x,y),” and, therefore, I suspend this first function and denote it as “1” as in the following:

Screen Shot 2018-10-07 at 3.56.16 PM

This brings us to the next stage, “2,” or, rather, the next function, “f2(x,y)”: “refuse me my offering” … which is produces the “objet a” in the place of “i” as “this isn’t it.” [I should point out that my diagram is in fact a simplified version of Lacan’s diagram]

43225765_1899462280145788_4037740549296357376_n (1)

Lacan then claims that he will take this up in a more accurate diagram: “I ask you to refuse me my offering” becomes “I demand you to refuse,” or “I ask you to refuse ….

Screen Shot 2018-10-07 at 4.06.00 PM

The “I” moves toward the “you” and then up to the “R” for “refuse” (or real) and, through the dotted line, “demand.” If I trace this path, or vectorize it, it looks like this:

Screen Shot 2018-10-07 at 4.09.41 PM

I think that this shows more clearly how the following logic closely aligns itself to the early teachings, once again, for “schema L.”

But, next, we have two tetrahedrons. On the one hand, there is the aforementioned tetrahedron “I ask you to refuse.” On the other hand, there is the “refuse my offering to you.”

DEMAND: “I ask you to refuse …” [Asking]

SUPPLY: “refuse my offering …” [Offering]

And Lacan points to the distance that separates “DEMAND” from “SUPPLY.”  In other words, there is a distance between what is asked, or the “asking,” and what is offered, or the “offering.”

And in a remarkable diagram — truly remarkable — Lacan draws an unfinished pentagram and names it the “diagram of the double tetrad”:


The two circuits of DEMAND [asking] and SUPPLY [offering] overlap here to demonstrate the lack of a relationship between them [“…because that isn’t it”]. I believe it is the missing vector that would/could have been traced from “D” to “S” that is meant to show the real, that which one must not speak of, or, put better …

Lacan said: “it is impossible to sustain the relation between asking and refusing, between refusing and offering.” That he used the word “impossible” is very important for me because it gives credibility to the claim I have been advancing: that all of this has something to do with the real.

Lacan wanted to begin to close the class by insisting that “my offering is perhaps not at all what I am offering you.” What one offers, rather, is the very fact of offering as such. It is not the content of what one offers but rather the fact of offering itself. This is where we often get things wrong, then. I ask you to refuse the content of my offering because that’s not it. I take this very simply: if I offer you a gift and that gift is a chocolate bar, then, you should not see the offering as the chocolate but rather: it is the act of offering, the verb itself, that one should see.

To offer is not to “give” purely at the level of a verb. It is also not to “take,” purely at the level of the verb.

One offers only so that one will reciprocate. 

This, after all the work we’ve done in this class, resonates almost as an axiom. One offers something only so that something will be reciprocated – one gives only to receive. This means that one loves — offers love — only to receive love in return.

And Lacan makes a gesture toward the work of Bataille and his colleagues when he says: “this is precisely why the potlatch exists.”

So – it is not what I am offering but rather the fact of offering as such. 

In language, if we remove one of the functions — the demand — then the offering, as a function, ceases to have meaning.

F1(x,y F2(x, y .. ))

If F1 disappears, because F2 is nested within that functional imperative, it will cease to exist. Thus, one can only offer because there was a demand. The supply exists here only because of the demand.

And then Lacan introduces the Borromean knot. He claims that it was given to him like a ring slid on his finger, which means, in other words, that it is the crowning jewel of his work. I can sense the pride and excitement with which he shares it with his audience. He says: “there you go,” and offers it to us.

The rest of this part I am going to skip discussing only because it has become fairly commonplace knowledge on Lacan and I do not see much new here.

Lacan claims only that Demand, Refusal, and Supply form the three strands of the knot, and all of them are operative. You can’t have any two without the third — this is the Borromean property: if you cut any one from the chain then all of them fall apart from one another. I have elsewhere referred to this as the property of Borromean dependence.

One wonders if Demand = Imaginary, Refusal = Real, and Supply = Symbolic. It is not clear that these align so easily, afterall.

Lacan’s provocative final words for this class: “I once quipped, ironically — with supply, the analyst creates demand. But the demand that he satisfies is the recognition of the fundamental fact that what is being asked for, this isn’t it.

This was a truly extraordinary class.

Hypertranslation: LACAN SEMINAR XIX, 3 February 1972

What is a “quadripode”? It means, quite simply, “four legs.”

We know that a discourse has four legs to stand upon — and that any fewer legs will make it difficult for the discourse to sit up on its own.

Lacan claims that you can sit on them, the discourses. And it has something to do with the four discourses. But then Lacan claims something very interesting: the four discourses are only discovered because of the emergence of the discourse of the analyst. Thus, it is the analytic discourse that discovered the preceding discourses.

And then Lacan claims that he has arranged the courses via topology. Well, this is new, as far as I can tell, I do not believe he specified that the discourses are arranged topologically before this point. The topology of the discourses is based on a simple monad, which has “no more than” four points.

There are four vertices and four surfaces. And these vertices are equidistant.

Lacan makes a humorous remark: there are two ways to sit on a monad of this sort, both are uncomfortable. The one has the tip up, and the other has the tip on the base. Well, these are two possibilities for the formation of a social link: “this is where we have to begin for everything that is involved in what constitutes a type of social base that is supported by what is called a discourse.” I should say here that the social base is precisely the discourse, since, topologically, they bare the same structure. The social link is always an uncomfortable one, and yet, as Lacan puts it, we’ve gotten used to it for so long that we hardly notice how uncomfortable the social bond really is.

So this “monad” is, then, tetrahedral.

There is a property of the tetrahedral that Lacan wants to draw attention to: if you “vectorize” the edges, which means, in topology, to give them a direction, then you have to presume that not one of those edges will be the privileged vertex. Privileging a vertex involves permitting all of the vectors (edges) to point toward it. So we have introduced here some rule: “nowhere shall there be a convergence of 3 vectors that depart from the same vertex.”

For the tetrahedron, then, this implies that there will be four vertices:

  1. Vertex “A” will have 2 incoming vectors and 1 outgoing vector
  2. Vertex “B” will have 2 incoming vectors and 1 outgoing vector
  3. Vertex “C” will have 1 incoming vector and 2 outgoing vectors
  4. Vertex “D” will have 1 incoming vector and 2 outgoing vectors

I have drawn the corresponding tetrahedron, after applying the rules:

As you can see from the image above, I tried this for myself. It is true – all tetrahedrons that follow these rules for vectorization will be equivalent. Next, Lacan claims that if you remove one of the edges (and thus, one of the vectors) then you will have the “formula” for the four discourses. This is the “template” or the “key” for the discourses. Now, here Lacan does not at all state why he removed one of the edges. Is it because the other edge is actually always obscured (indicated by the dotted line)? I have no idea. It seems like a move that requires some explanation – but he does not provide any whatsoever.

At each vertex there is the following:

  • Semblance (2 incoming, 1 outgoing)
  • Jouissance (2 incoming, 1 outgoing)
  • Surplus Jouissance (1 incoming, 1 outgoing; the other outgoing is obscured)
  • Truth (2 outgoing; the 1 incoming is obscured)

This, claims Lacan, is the fundamental topology for discourse — for speech.

Lacan claims again that the analyst discourse discovered, in a sense, the other discourses. He extends this now: the analyst’s discourse is the “support” of the other discourses, it is the “supposed” discourse.

Lacan asks the question: where does meaning come from? And then he opens a different topic.

The analytic discourse is related to the science known as linguistics, on the condition that linguists never discuss the origin of language itself. Lacan claims that this has something to do with his position that the unconscious is structured like a language. I recall Freud once writing, somewhere, that the unconscious is eternal (picked up later by Althusser to discuss ideology). Maybe this is the connection that Lacan is trying to make.

Lacan is interested in the function of speech. Speech, claims Lacan, is “the only form of action that posits itself as truth.” Speech speaks as a fact, and all facts are determined by the unfolding of speech. Moreover, speech speaks all my itself.

Speech functions even when there is no fact though. Speech may assumes certain facts of saying, but that does not imply that all of speech is itself made up of facts. For example, speech that commands, prays, insults, etc, doesn’t necessarily constitute for itself a fact.

When a man gets aroused by a woman he does so by “taking her as the phallus,” Phi(x).

Okay, so speech doesn’t just denote facts, but it can denote facts. It can not denote things. But Lacan adds: it can denote things once every so often, “by chance.”

Jouissance in discourse is “phallic jouissance” but not at all “sexual jouissance.” The “poles” of discourse are arranged so that on the one side there is “semblance” and on the other “jouissance,” and in the middle a gap separates the relation of semblance to jouissance. There is no harmonious conjunction of man and woman. Man has a relation with Phi rather than with the other (woman).

Homosexuals, claims Lacan, have better, firmer, and more frequent hard-ons — and this is because they take the other for what it is: Phi. (this is my understanding of Lacan’s argument; I am not sure it is correct).

The analyst discourse needed the university discourse. And not only that, the analytic discourse arises out of extreme urgency. Now, something new for me is said: the discourse of the master, of the analyst, of the university, and so on, indicate the object of the discourse. It is the discourse *about* the master, *about* the analyst. In the case of the analytic discourse: it is discourse about the analyst as objet petit a (that is what the analyst is made into as an object by the analysand). The objet petit a is an object in the analyst discourse of semblance.

The speaking-being doesn’t know what determines his discourse: it is the objet a. This is what divides him as a subject and gives way to desire. The objet a is produced by discourse as the cause of desire.

The objet a is also a metonymic object. This is because, I believe, it keeps sustaining the chain of signifiers. We can see this clearly in the movement of the empty set within the logic of succession (see Badiou). When the succession is interrupted, when it becomes less coherent, then the objet a becomes revealed for what it is. I like how Lacan put this because it relates perhaps also to capitalist discourse: “until it [discourse] stumbles and peters out.” This is what later Lacan calls “burn out” in capitalist discourse.

God is here described as the one who disrupts the pleasure of others (each of us, little ones). The Epicureans, according to Lacan, tried to find a method to avoid being disrupted in their pleasure — but it failed. The stoics tried to go the other way: to obtain divine pleasure/jouissance. But that fails too. The natural environment is such that one can’t get any jouissance. No jouissance — but you do get some pleasure. It is this pleasure that grounds the primary process.

Leonardo de Vinci says to “look at the wall.” Lacan finds a profound truth in this statement. On the wall there may be stains and obscure figures. These stains are the basis for figuration, for art. I recall as a child an art game that I would frequently play. I would ask somebody to make a bundle of lines or obscure shapes on a page and then I would transform that mess into a figure: a bird, a dragon, a tree, etc. This is, of course, to transform the stain into Phi.

“The stain in question is figuration itself.”

Everything that is written reinforces the wall, claims Lacan. This is why the “love letter” is ultimately writing on the wall. Love, in french, sounds like “wall.”

What is beyond the wall? Beyond the wall is the real, the impossible. It is the impossibility of reaching the real beyond the wall.

The emergence of the One: it is related to S1, since the master signifier is the first signifier. But there is the problem: can there be a master signifier (any more than a master discourse) without an S2? You first need 2 for there to be 1. The one comes from the two: nought (zero) and 1 make two.

Language and speech are before the wall. The discourse of science has found a way to construct itself behind the wall: in the impossible, in the real. Science proposes that meaning can not approach the real. It is impossible to give meaning to algebra or topology. This is why it is behind the wall.

Discourses (language, speech)  ||WALL||      Science (Topology, Algebra)

A signified always comes from a signifier in another discourse.

Knowledge: “it is the numbers that know” (I think he is referencing Frege’s arithmetic logic).

Castration is the means of adapting to survive. The analyst’s knowledge is “an ocean of false learning” because learning has no meaning (which implies, here, that it is behind the wall, in the zone of science), and that any meaning of discourse is partial because it is sustained by another discourse. I recall here the wonderful motto of Trent University: “nunc cognosco ex parte.”

The knowledge, S2, of the analyst is in the position of truth, then, since truth is in the real: and it is always partial, always castrated, always half-said between the wall of another language/discourse and truth. On the other hand, the analyst digs up scraps of knowledge — bits of knowledge — from the analysand’s unconscious.

Hypertranslation: LACAN SEMINAR XIX, 19 January 1972

Lacan defines logic: it is the “art of producing a necessity of discourse.” And “discourse,” which is produced, by necessity, through the art of logic, has a meaning that remains veiled — or, put another way, discourse is produced precisely because its meaning is radically absent. Lacan claims that the meaning of a discourse is always positioned elsewhere: “there is no discourse that must not receive its meaning from another discourse.”

Thus, discourses interact with one another, and they do so, it would seem, because of a primary motivation: meaning, which was absent and must come to be revealed through the other discourse.

I suspect that this stuff all has something to do with sexuation. There are two discourses which are not at all in a relation with one another but who, by way of their lack of relation, come to reveal some meaning.


The logic of necessity can only occur when discourse is on the scene. This is because necessity begins with the speaking being, the speaking being who speaks through discourse. Necessity, according to Lacan, occurs only — exclusively — among speaking beings.

“The art of producing a necessity of discourse,” … the word “producing” is related to a demonstration of what was already there to begin with, namely the master’s discourse. The master’s discourse was already constituted before the speaking-being arrives on the scene, and yet, it seems to me that this produce indicates that it is “achieving through labour” that the discourse of the master arrives precisely as already constituted.

I find most of this discussion regarding necessity and “inexistent” very difficult to understand. I think it is because I am not all that familiar with Aristotle’s logic. In any case, Lacan asks himself directly: “What is necessity?”

Necessity is supposed to be “inexistent” before it is produced.

We repeat our “bricolage” (what is this? By bricolage does he mean the discourse in question?) and this is also what Lacan names a “symptom.” It is also called “automatism.”

If I am following correctly, and I doubt I am, then Lacan is suggesting that we repeat our symptom through discourse which is a supposition that the master discourse does not exist. To presume the inexistence as preliminary to necessity then it is to reject that the unconscious exists. We suggest that there is something inexistent behind the symptom. Lacan continues: “what lies behind the principle of the symptom is the inexistence of the truth that it presupposes, even though it marks out its place.”

If I am having difficulty with the terms — Aristotle’s terms — then it is probably because Lacan is engaged here in a “hypertranslation” of Aristotle. Lacan seems to be trying to force Aristotle’s insights into the psychoanalytic discourse that he is employing, while, at the same time, torturing those insights to reveal something specific to his own discourse. That is precisely what Alain Badiou calls “hypertranslation.”

Next, Lacan links “truth” in a new way — it is no longer simply the truth of the master signifier, or the truth of the symbolic unconscious — we have a new invention here that I find striking: “it is the inexistence of jouissance that the so-called automatism of repetition brings to the light of insistence, of this stamping at the door that is designated as the exit towards existence.” Thus, it is jouissance — enjoyment, if you like — that appears to be inexistent from the necessity of discourse. Lacan says: “it is rather jouissance [beyond the door of existence], such as is necessitated by discourse.” The necessity of discourse produces the jouissance that is its beyond. We still have a notion of jouissance here that is the production of a discourse rather than that which inspires discourse (as a cork).

Jouissance operates as inexistent.

But then Lacan cautions: “it still remains, however, that you cannot get down to the bone of structure when you stay at this level.” This, for me, implies that the notion of jouissance as the necessary production of of inexistence (truth) … is not the whole story on discourse.

Lacan points to the limitation: “inexistence only becomes a question on account of already having a response [discourse].” So inexistence is always the production of a discourse. Inexistence is not produced by jouissance or by truth, but by the necessity of discourse; inexistence is not nothingness.

Nothingness inspires belief – and logical discourse produces inexistence not as nothingness but as symbol (nought, zero). So, “inexistence is not nothingness, it is […] a number that is part of the series of integers.” And it goes the other way too — as we saw with Jacques-Alain Miller’s 1950s paper on “suture” and Frege — “there can be no theory of integers if you don’t take into account what is involved in nought.” Indeed, Lacan continues: “This is the path that was opened by a certain Frege […] through examining logically what is involved in the status of number.”

As it happens I wrote extensively about this in my book Lacanian Realism (Bloomsbury). Indeed, it was in Frege’s Foundations of Arithmetic that a logic of number was articulated on the basis of the non-congruence of zero and 1 within a logical operation of “succession” (what Badiou names “the count”).

Finally, my hypothesis about the retroaction of truth/inexistence is confirmed: “inexistence is only produced in the retroaction from which there first arises the necessity, namely from a discourse in which it manifests itself prior to the logician reaching it himself as a second consequence, that is, at the same time as inexistence itself.”

The necessity is the repetition itself [does this occur at the level of discourse? It seems to me that the “tuche” of jouissance, if I am correct, is not the repetition, the repetition is in the discursive response to the touch of jouissance, to the truth]. What is repeated, in this case, is the inexistence — the repression. It is what maintains the system and structure of discourse.

Life is on the side of the repeated sequencing of its discourse, whereas jouissance, the touch of death (drive), is not on this side. This is what Lacan calls the “reproduction of life.” And Lacan is not at all afraid to place it on the side of biology and bacteria. This is a crucial move, especially for sociologists to study, because for a long time sociologists rejected Freud’s “death drive” for being too “biological.” Lacan is here, perhaps without knowing it, posing a reversal: the biological drive is precisely at the level of discourse. “death drive,” jouissance, is an interruption in the life of the body/bacteria/bios.

Lacan’s next statements are fascinating. He turns to the world of animals and relates them to “one living being” who “colours all his basic needs with jouissance, needs which in other living beings are merely ways of sealing off jouissance. If the animals feed on a steady basis, it’s quite clear that this is so as to avoid knowing the jouissance of hunger. With jouissance, he who speaks […] colours all his needs […] by which he fends off death.”

This implies, to me, that the speaking-being, unlike the animal, makes use of jouissance to fend off death. But isn’t death linked with jouissance? So is jouissance here at war with itself? The animal, on the other hand, eats to fend off jouissance (of hunger/death). So is the speaking-being here equated with the same basic impulses as the animal? We speak like the animal eats: to fend off jouissance?


Lacan makes to different points of emphasis, marked by the genitive (used to express, in this case, “possession” of something).

On the one hand, there is the objective genitive: “A desire of a child” indicates that it is a child (as object) that one desires, that is the object of one’s desire.

On the other hand, there is the subjective genitive: “A desire of a child” indicates that it is the desire of a child, that it is the child who is desiring, it is a child who partakes in the act of desiring.

Lacan seems to be making the point that when one writes “A desire of a child” there is both a subjective and objective genitive implied. Well, in the phrase “the signification of the phallus” there is both objective and subjective genitive possibilities. Lacan wants us to notice, I think, is the following: “what the phallus denotes is signification.”

Frege, by examining number, was able to “found the number 1 on the concept of inexistence.” I think this is probably found in Frege’s claim that “nought [zero] is the number which which belongs to the concept of ‘not identical with itself'” (S74) — Frege continues, “Nought is the Number which belongs to a concept under which nothing falls. No object falls under a concept if nought is the Number belonging to that concept” (S75). For Frege, it is the next move in the succession that is truly interesting: “1 is the Number which belongs to the concept ‘identical with 0′” (S77). We can only have 1 if we suppose that it is identical with the concept of not being identical with itself, and being identical with not having any objects belong to that concept.”

It is this inexistence that, it seems to be, forms the basis of the real for Lacan (and, by extension, for Jacques-Alain Miller).

I am taking a detour — I paused reading Lacan for a moment — to think about the fact that “being identical with that which is not identical with itself” grounds the number 1.

0 = “not identical with itself” and “no object falls under …”
1 = “identical with 0” (which means: “identical with not being identical with itself.”)

To be identical with that which is not identical with itself — to be identical with non-existence — is precisely to form an identity out of non-existence, out of that which is inconsistent and not identical.

Lacan continues: for people to be counted as 1 they have therefore to be “divested of all qualities.” This was Marx’s position, of course: quality is eclipsed by quantity, use-value by exchange-value. For Frege, for something to be counted it must be transformed into a “unit.” Frege defines a unit as that which excludes the properties of objects. For example, Frege was fond of claiming that a “white cat” and a “black cat” each form an independent unit “cat” without any associated properties of being “white” or “black.”


Lacan goes through some work on the arithmetic triangle to show, among other things, that the addition line will always be a number not included in the preciding lines. For Frege, though, the concept of number 7 denotes 7 repetitions of no objects, 7 repetitions of that which is inexistent. The problem, as Lacan sees it, is that this does not answer how it is that something like “1” comes into existence in the first place — it only proves that we can repeat inexistence 7 times. Perhaps another way of putting this is to claim that it can prove inexistence but it can not prove existence.

Frege only accounts for the repetition of the integers and not for the actual sequence of the integers. By this, perhaps, Lacan means that Frege does not indicate or think about where the name of the concept — each new name — comes from. And so, it does not show us where 1 comes from except as a reflexive repetition of inexistence.

This class was a really difficult one for me.

Hypertranslation: LACAN SEMINAR XIX, 12 January 1972

Lacan is interested in logic and its ability to articulate the unconscious and its sexual “values” (I wonder, here, what the French word was for the English “values”).

Lacan immediately addresses my question: by “sexual values” he indicates the universality within language of “man” and “woman.” And he does not shy away at all from distinguishing “man” and “woman” as a foremost matter of language. This, unlike the position of Judith Butler, does not imply, it seems to me, that he is taking a “linguistic constructionist” approach, because that would reduce the field of inquiry only to language, when, for Lacan, there is always more at stake, namely the real.

Next, Lacan claims that the “he” and the “she” always exist relative to language, in all of the languages of the world, and this is the “principle behind the functioning of gender.” In other words, gender is here always relative to language, and always functions to split the genders. The “hermaphrodite” is just an attempt to playfully bring “he” and “she” into “the same sentence.” That is Lacan’s claim. I am not sure what it means – but I do not follow Lacan in this argument. He goes on to suggest that the hermaphrodite can not be an “it” but rather a bridge of the “he” and “she,” a bridging of the sexual relation, perhaps, but never in a neutral sense.

Castration can not be reduced to “anecdote” or to “mishap” or even to a “clumsy intervention.” I can only guess that the reference to “anecdote” implies that it is never temporary, or fleeting, it has staying power. It can also not be an accident – whatever that means.

The question that Lacan pursues next concerns the “object of logic.” I presume that this brings us back to the variable “x,” the birth of the signifier in the real, the birth of the subject, and the birth of the objet petit a. At this point it is worth listing all of the qualifications that Lacan has given to this little variable, this little object of logic which is often written f(x):

  1. the signifier
  2. the objet petit a
  3. the subject (in its notch, ditch)

Lacan adds the following: “I propose to define the object of logic as what is produced by the necessity of a discourse.”

So, my reading: if a discourse is a social bond then it always produces something like the (x), the objet petit a, the scrap of the real as a necessary consequence. Here we can see the return to the classical Lacanian version of the real as objet petit a, as that which is produced as the excrement of discourse.

Lacan confirms this but goes a step forward: “the real — a category from the triad with which my teaching got under way, the symbolic, the imaginary, and the real — is affirmed in the impasses of logic.

We also see here the word “suture,” which guaranteed Jacques-Alain Miller his statements on the “logician’s logic,” and his theory of “suture” via Frege and Lacan in the 1950s.

Within the logic of arithmetic we can find a designation of the Lacanian real: “in arithmetic something can always be stated […] which is articulated as though it stood in advance of the very thing which premises, axioms, grounding terms, whereby the said arithmetic can find a base [a foundation, a suture], enable us to presume to be provable and refutable.”

This base for Frege, I believe, was: 0 = 1. The whole net of logic — the system of numbers, in Frege’s case — is grounded, founded, upon this premise that 0 = 1 and this opens up a path to set theoretical logic wherbey the 1 always includes within itself the empty set.

Lacan then points explicitly to Godel’s incompleteness theorem. The basic argument from Godel, which he went on to prove, was that there is a limitation to every formal axiomatic system within mathematics. But Lacan phrases this in a more precise and more interesting way, which gives more credibility, no doubt, and more precision, to his concept of the real: “there will always be something that can be stated in the specific terms in comprehends which does not lie within the scope of what it posits to itself […].” So here we have a statement on the real as a piece of excess, what, in another later seminar, Lacan refers to as a “bit of the real.”

So – the real is defined as “impossible” within the limits of the logician’s logic, within the limits of a given discourse itself. This is the real that Lacan wants to “favor” within psychoanalysis. He explicitly states as much, implying, also, in the process, that this is not the only real. This I think is a very important point.

The psychoanalyst should be concerned with the real as impossible within logical discourse.

We return to discourse, but this time examining it not just as a logic but also that which establishes a social bond. Discourse is that which establishes a social bond through language – and, as such, always produces something impossible. And this impossible, this real, is related quite fundamentally to the unconscious.

So here we have a statement from Lacan that begins to examine the unconscious as real and as impossible rather than simply as a symbolic repository of signifiers. In fact, Lacan finds a problem with the symbolic version, which leads, often times, as we have seen in popular readings of Freud’s Dream book, and also in the work of Jung on architype: a certain type of “rut:” “Jung thought they would be able to revive [the sexual symbolism of the unconscious] by sliding back into the most ancient rut.”

The next few statements are very difficult for me to understand. Lacan seems to be opposes the position that there is something universal and symbolic about the sexuality of the unconscious. He is also in opposition to the position which claims that there is something “anecdotic” about the unconscious: rather, what he favours, is the approach which views the unconscious as rendering “impossible” (this is linked to the real) the “sexual bipolarity” as such.

So, the unconscious renders the impossibility of the sexual relation at the level of discourse.

Lacan confirms a suspicion of mine. He links the phallic function precisely with castration, as if, basically, they are the same thing. “All men are defined by the phallic function, the phallic function being specifically what obturates sexual relation.”

This is denoted: Ax Phi(x)

Woman, on the other hand, are “Not All woman..”

This is denoted: /Ax Phi(x) [whereby the / is used for negation]

This indicates not that woman do not have some relation to the phallic function, as some eager readers of Lacan seem to suggest (and they suggest it to respond, in haste, to charges of Lacan’s anti-feminism). Rather, it implies something more precise: “somewhere, and nothing more, woman has a relation to the phallic function.”

“Nothing can adapt this all to this not all,” Lacan says, indicating the “impossible” bar that separates man from woman via sexuation.

And why? The real — the impossible — has something to do with their different modes of jouissance: “there remains the wide gap of an indeterminancy in their common relation to jouissance.”

So the problem is already within the level of the real, of the real of the body, and its jouissance. There are different modes of enjoyment with respect to language, the signifier.

Next, we find the “one,” which appears “in spite of all”: there is “at least one” for whom truth does not concern the phallic function. This is denoted:

Ex /Phi(x) [negation of phallic function for this ‘x’]

Typically, this is the at least one of the father, of god, and so on. It was explained clearly in the work of Freud, at the level of Myth [remember, Lacan’s provide is to translate Freud’s myths into logical or topological articulations], in Totem and Taboo. If I remember correctly: there is at least one leader of the horde who has access [jouissance] to all of the women.

Lacan jumps a bit further here: this at least one enjoys precisely “what does not exist, namely all the women.”

On the side of the woman, there is:

/Ex /Phi(x)

Lacan explains, simply: “women cannot be castrated because they don’t have the phallus.” But, for woman, “it is not impossible that woman should know the phallic function.”






A question for you: who gave Lacan the pen at the beginning of the seminar?

Lacan makes a tri-fold distinction on writing:

  1. There is the written, as in, for example, written notes produced for teaching. Lacan is clear that he does not write something down in order to prepare for his lectures. At least, he does does not do it in order to spare himself strain or risk. If he did, he maintains, it would only produce bad results. It is actually better to not prepare anything written, in this respect. The writing that he does for his seminars is not therefore the sort of writing that one would consider to be “preparation.” It is something different – something that relates to “findings.”
  2. The written for “print” is altogether different again.
  3. Finally, there is the written [is it proper to write “the”?] as the return of the repressed. This is truly Lacan’s “idea of the written.”

Lacan attempts next to provide some clarity regarding a confusion, indeed it was a confusion I made for a long time (I blame Derrida): the signifier is not a letter. I made this claim many years ago during one of my personal analysis and I was quickly corrected by my analyst. That moment stays with me. However, the signifier “touches me most” as a letter, that is, as a signifier that comes back; one that comes back because it has been repressed. Thus, in L’instance de la lettre Lacan does indeed imagine the signifier as a letter.

So – what does this mean? It means that the so-called signified is nothing but here the turning back of a signifier. The signified is beneath the bar, then, because it is in a sense repressed. The letter is nothing but the imprint of the repressed signifier as an artifact, or, in other words, as an apparent signified.

Lacan points to Aristotle’s Prior Analytics, wherein he uses letters rather than “terms” (i.e., “A belongs to every B,” and so on). I can see how this relates to the previous class from Lacan on the variable, or, on the Fregean “x.”

The letter is here related to the little piece of the real, objet a, because “it comes to mark out a place” using a signifier that is just “lying around” (like a scrap sound-image). This is how the letter first manifests itself, then. Lacan is pointing in a way to a theory of the origin of language, of signification, as it emerges out of the real from the scraps that are just lying around to be used. These scraps are no doubt transmitted from the Other and picked up by the subject to express the want or desire as objet a.

Lacan opens up a question: how does the signifier transform into a letter?: “there has to be a kind of transmutation that occurs, from signifier to letter, when the signifier isn’t there, when it’s gone off course, when its scarpered.”

What I take from this is the following: the “transmutation” when, paradoxically, the signifier is no longer there, when it is lacking, when, so to speak, it runs away; this is when the letter stands in its place.

To put it in classical psychoanalytic mythical terms: it is when the mother runs away that the letter comes to stand in for her absence, and, therefore, comes to express her presence.

But when it comes to the letter one can not just write anything. This is why the field of mathematics is important, claims Lacan, and why, moreover, the “matheme” is a “pivotal point” of all teaching. It is because it anchors together a discourse, provides it with its meaning, and, moreover, reduces everything else to “banter.” I think Lacan might have meant to say “babble” here, but I can not be sure.


Lacan goes on at length about doltishness. the “Matheme” is doltish, and so too is, in a way, the letter. We can find doltishness in Atistotle’s Metaphysics, and we should allow ourselves doltishness in our political system. There is perhaps a separation of meaning within texts written out of doltishness. One can read Metaphysics in this way: “evidently they are capable of reading the text with a certain way of barring themselves off from the meaning, and when you look at the text, well, you are beset by doubts.”

An axiom, of sorts: “doltishness is a mark of proof when it comes to authenticity” … “There is nothing more authentic than doltishness.”

Lacan reminds us of the etymology of the word “authentic,” which means, to my mind, “authorized,” or, relating to the “author” (not far from being a homophone for other in French).

The essential function of doltishness is to “fill in everything that has been left gaping wide by the fact that there can be no such hing as sexual relation […].”

Doltishness is therefore related to the function of a letter. The letter comes after the sexual relation has been left separated, when the signifier ‘runs way.’


Lacan turns to the blackboard and writes the symbol for “phi” and the variable “x.”

Phi(x) [I am writing it my own way here because I can not write the symbol easily]

The Phi, letter, is what poses a barrier to the sexual relation.

A distinction seems to be made: sexual jouissance and jouissance: “for the speaking being, sexual jouissance opens the door to jouissance.” So jouissance is not always sexual, then. This is a Lacanian invention, it seems to me, and a way of moving beyond Freud.

Jouissance is always “of a body.” It is “the embracing, the clutching, the fragmenting of the body.” And this is “the most regular mode of jouissance.”

So jouissance always has some relation to the body. This is also a nice new move for Lacan.

The “x” in the formula is a variable, yes, but it is also a signifier – and, since the signifier is related to the subject for another signifier, we can claim that the is the place of the subject within the phallic function above. Lacan said: “each of you here can be a signifier, precisely at the slender level at which you exist as sexuated.”

The “x” is a signifier, but it is also the “hole in the signifier.” It is not that “x” is man and “y” is woman, then, because that would give them the same status as a variable, as a signifier. There must be something about the difference included in the discussion, then.

There are some “x-es” which are subject to the phallic “for all,” that is phi(x). And lacan writes this in his set notation:


Phi(x) may now also be referred to as the “function of castration.” Thus, when referring to masculine sexuation, A(x)Phi(x) refers to the fact that all men as castrated.

Lacan makes a casual observation: why is it that the popular expression is “be a man,” indefinite article? Whereas, for women, the expression has more to do with “the woman,” as a group. We do not hear very often, then, “be man,” or “be a woman.”

When man passing through the phallic function, as a consequence of castration, he no longer has access to the rich repository of signifiers. They have been limited. Given any x, that is, given any man, this functions.

Next, “there exists at least one for whom castration does not function.” Lacan claims that this is the place of God. There exists god, claims Lacan. It is on the basis of there exists at least one that “all the rest can function.” The myth is that the father does not get castrated.

Lacan closes the seminar by quickly introducing the feminine terms, without naming them as feminine sexuation.

/Ex “there exists not”

/Ex /Phi(x) “without the exception of this signifier position” … “it is not true that castration dominates everything.”



Hypertranslation: Lacan Seminar XIX, 8 December 1971

Lacan remarks upon the title of the seminar: … ou pire, which nicely translates into English as “… or worse.” He remarks, emphatically, that it is not … ou le pire [or the worst] (which introduces the definite article “the” or le into the title). In English the distinction is much more obvious because the only translation would end up being: “or the worst” — where it is no longer “worse.” In the French, in both cases, the word is pire, but in English the shift is marked by a different word. The adverb would, in this case, change to a possible noun or an adjective. But Lacan specifies that pire must remain an adverb if it is going to be used the way he intends it to be used in the seminar.

An adverb is a modifier that qualifies a verb by adding a place, time, circumstance, manner, cause, degree, etc. So if the verb is “run,” then the adverb would modify the “running” to include perhaps a manner of running: “I ran worse.” Yet, in the title the adverb is “disjoined,” because the verb in question is missing and replaced, curiously, by an elipsis: “…”


There is something about the missing verb that Lacan wants to highlight. He indicates right away that it relates to the fact that “this is the only way to say something with the aid of language.” It is not clear what he means here. Perhaps he means that one can only say something by replacing what can not be said. The “empty place” is important because that is where language enters: “the remark that this empty place is the only way to catch hold of something [das Ding?] by means of language allows us to precisely penetrate the nature of language.” It now becomes clearer: it is only when there is an empty place within language that we catch hold of the thing in the real, which implies, conversely, that when language apparently corresponds to the thing it actually misses its mark.

Lacan then turns to logic and makes a truly fascinating claim: “as soon as logic first succeeded in facing up to something that sustains a reference to truth, it produced the notion of the variable.” This gives us a better appreciation, I think, for Badiou’s insistence — and perhaps also Lacan’s at times — that mathematical logic has a privileged grasp on the real. In any case, the variable is precisely this stand-in for the concept. Lacan moves on to discuss more specifically the apparent variable. We should remark that the “apparent variable” refers quite directly to the work of Giuseppe Peano, the founder of mathematical logic. I was not able to find anything further about “apparent variables,” except that they were marked by an “x” to discuss an “empty place.”

Lacan also points out that the only way it can work is if we use the same “x,” the same signifier, in every place where this empty place exists: “only in this way can language get to something, and this is why I employed the formula – There is no such thing as metalanguage.” I need to break this passage down:

  • the empty place in language is given a special signifier “x”
  • this special signifier must be used, as a rule, in all cases where the empty place occurs
  • it is only by using the signifier “x” in all cases where language fails that language can in fact touch hold of some-thing

It is the final stage of the argument that I can not connect: this is why there is no such thing as metalanguage. Perhaps some insight will be forthcoming. Could it be the following:

  • if there were a metalanguage — a language that could ‘say it all,’ so to speak — then from what place would it speak? Naturally, it would be from somewhere outside of the ’empty place,’ and yet this is what it can not do — it is tethered to the empty place. Only the signifier ‘x’ is truthful, only it corresponds to something in the real.

Lacan continues by suggesting that metalanguage implies that there is “one” language. But language is never “one”: “Since I am saying it in language, this would already be sufficient affirmation that there is one language from which I can say so. And yet this is clearly not the case.”

Okay, I want to take another step forward: “whenever logic is at issue, it is necessary to create the fiction of metalanguage.” Within the study of logic a metalanguage is said to consist of an “object language,” which is the language being studied by the meta- language. So metalanguage constructs a division between itself and the object language that it seeks to study. Discourse, on the contrary, is “common,” such that there can be no division between language as such and the objects it seeks to study. This is what Lacan means when he writes: “There is no such thing as metalanguage denies that this division can be upheld.” Moreover, it produces, through its division, paradoxically, the fact that language has an empty place, that it is itself divided: “that there can be any discordance in language is foreclosed by this formula.”

Lacan’s next claim is that logic does not permit the possibility of eliding a verb, so logic can not deal with the title of his seminar: ” … or worse.” Lacan said: “eliding the verb by means of three dots is the one thing that may not be done in language once it is being examined in logic.” The next argument is very complicated for me because I am not trained in philosophical/mathematical logic: “when you try to turn a proposition into a function, the verb becomes a function, and you form an argument from what lies around it. So, by emptying out the verb, I’m turning it into an argument, that is to say, I’m turning it into substance. It’s not saying per se, it’s one fact of saying.” I hope that the pages that following help to explain this a bit more.

There is the proposition: there is no such thing as sexual relation. If you try to say anything else, that is, if you say anything positive about the sexual relation it will be worse in the sense that it will not be as truthful. If the proposition is truthful, as Lacan claims it is, then the only way to actually say it is to half-say it in language — like the “x,” I suppose, which is still a signifier.

Lacan then makes what seems to me to be a really funny joke: “So, what I’m saying is that, all in all, what the other half says is worse. How much simpler things would be if there were no worse!” He is indicating that this fact of saying regarding the “x” is related quite fundamentally to sexuation and sexual object choice.

The proposition is as follows: there is no sexual relation indicates that the truth is that sex does not define any relation in speaking beings (parletre). This seems to me to be a positive affirmation on the sexual relationship. It leads to be consider two propositions Lacan has made in his career:

  1. love is what makes up for the lack of a sexual relation
  2. love is giving what you don’t have

In the first case, love fills the empty space of language and of sexual reality. In the second case, love speaks through the empty place. The one is a negative proposition on the side of language (and truthful for that reason) and the other is an affirmative one on the side of truth itself. Giving what you don’t have is entirely without signification. These are the two positions open to the speaking being with regards to truth.

The “small difference” — I have not heard this expression before except in the concept of Freud’s narcissism of small differences, where, now, it takes on a new resonance — has something to do with the small difference of the “organ,” which, finally, is the signifier. The signifier is precisely this “x” which stands in place of the concavity (I borrow Frege’s expression) within language. Indeed, it is at this point in the seminar that Lacan turns toward Frege’s work on “assertions” and “judgment strokes.” It is the “not-all,” hitherto discussed by Lacan in previous seminars, that takes on a new meaning in view of logic: the “not-all” is situated there within the ditch, the concavity, of the statement (beyond the judgment stroke).

Aristotle began by introducing to us the word “all” within logic. This is most famously discussed in “Aristotle’s Square”:


Lacan’s claim is that “it was with the all that the empty place I was speaking about earlier was established.” For Frege, the “all” was situated there in the concavity, as an “x,” an argument.

Lacan’s addition is to suggest that the “not-all” is not a “universal” that has been denied. It is also not a “none.” It is something closer to Aristotle’s “some,” but also a bit different: “not all women are …”

Okay, but the “not-all” is rejected, as if by necessity, for all “speaking beings.” They reject it through all sorts of identifications. Here we can see that the concavity, the “x,” is filled over by an imaginary substance. But the distinction for speaking beings is not constructed by themselves, they are dinstinguished: “it is not they who distinguish themselves. One distinguishes them.” It is interesting that Lacan chose here the word “one” as determinative of their distinction. The “one” is the small difference that distinguishes the sexes.

The one pre-exists the little boy and little girl, in, for example, the parents who address the children by the distinction of the one. Children are therefore recognized by their parents and by their society by way of a linguistic construction, by the signifier, of an “x,” which is, really, just a small difference.

Lacan makes some very interesting remarks concerning the “transexual’s passion:” the transexual wants to be rid of the signifier itself. The transexual suffers because of an error: he perceives the signifier to be the real thing. It is a common error. The transexual wants to “free himself from the error.” Lacan seems to reserve some praise, in fact, for the transexual for recognizing the error as such. However, the transexual can not see that he must be signified within sexual discourse: “he is wrong in just one respect, in wanting to force, by means of surgery, sexual discourse which, qua impossible, is the point of passage to the real.” It seems that the transexual is incapable of seeing the signifier as already an error and takes it for more than it actually is — and so he wants to remove the signifier from the real, without realizing that the signifier was never in the real to begin with (it was a place holder for the real).

I’m going to try to decipher this in my own words. I believe that Lacan is claiming that the transexual sees the error in the real instead of the symbolic. Consequently, the transexual attempts to remove the signifier from the real — remove the signified — without realizing that it was never there to begin with except as an error. The neurotic, on the other hand, fears that it was never there to begin with and so keeps attempting to posture as the signified.


Lacan seems to spend a considerable amount of time critiquing the pscyhoanalyst’s discourse. It is probably the case that he is not necessarily critiquing his psychoanalysis, insofar as by “his” I do not mean involving his ego. He mentions that women “amputate” psychoanalytic discourse, and that psychoanalyst’s “stay lashed to a mast,” in the phallic sense. I think Lacan is getting at the point that women are without the textual reference, to some degree. He is moving toward the point that women are “not all” with respect to psychoanalytic language, and that, moreover, psychoanaltic discourse was probably too much phallic in orientation, tied to the logic of the “All.”


Lacan begins to introduce a “new logic.” I am under the impression that this “new logic” is what will lead toward Lacan’s more famous chart of sexuation. The new logic is founded upon the assumption of the “not-all”: “The new logic is to be constructed from what occurs on account of the following having been posited at the outset. Nothing of what occurs due to the instance of language can in any case whatsoever give rise to any formulation of relation that would be satisfactory.”

Lacan seems to be interested in pushing in two directions. On the one hand, there is the direction of the negative proposition, if I understand correctly: “what imposes a limit on language in its apprehension of the real.” On the other hand, there is something very interesting about the other half (affirmative proposition): “the aspect of the real that lies in the fact of having determined language.”

I map these in two ways:

  1. love is what makes up for the lack of sexual relation == what imposes a limit on language in its apprehension of the real
  2. love is giving what you don’t have == the aspect of the real that lies in the fact of having determined language

And why? I am avoiding the accent on love, which is a very complicated area in Lacan’s work, and focusing rather on the relationship of love to lack / hole. Already in this class there is the mention of a “hole in language,” which, I think is relevant given the point that Lacan seems to be making about the real as (1) a limit on language and (2) the real as the foundation of language.

It seems to me that Lacan is demonstrating again that he always had both dimensions into consideration (maybe this is why his teaching is a “third way” as he implies in this class) when he discussed the real. However, there are certain popular theorists out there who will give you the flattened version of the Lacanian real.

Lacan is here interested in “three” registers:

  1. the “not-all” — which is a “function of jouissance,” which implies that it is in the real.
  2. modality: as I understand it, in philosophy, “modality” refers to how things could have been, could be, or must be. Aristotle introduces the following categories of modality: “possible” versus “impossible,” “necessary” versus “contingent.” Lacan believes that these need to be tossed away. Lacan wants to address something which “can not be able not to.”
  3. negation.

Finally, Lacan wants us to realize that his function, written in the symbolic, “phi(x)” concerns the speaking being and it affirms that the sexual relation is always a question. Moreover, Lacan’s claim is that the sexual relation determines everything by way of discourse.





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