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(All parts in English)

Recanati

[On the board]

‘What is said – as act – remains forgotten behind what is spoken, in what is heard.’

Lacan

Naturally, this statement, which is assertive in its universal form, pertains to the modal for what it posits of existence. So, make an effort, since it seems, like last time, not to be working very well. Am I managing to make myself heard this time? A little more? Good! I will do my best. Hello, Sibony, come a little closer then. Come a little closer, you never know, it might be useful in a moment.

So, taking into account what I called earlier ‘the mixing’, the communications that might have taken place between my audience here and the one at Sainte-Anne, I suppose that now they have unified, as the saying goes. You may have seen that we have moved from what I once called here, from a predicate formed for your use, namely ‘the unian’ [wordplay: unien is coined from ‘un’, one, and mimics ‘union’], last time at Sainte-Anne we moved to another construct which would advance from the term, from the form ‘unier’ [again, a neologism from ‘un’, one, and the verb ending ‘-ier’]. What I spoke to you about, what I brought up last time at Sainte-Anne, is the pivot that takes hold in this order that is founded, put founded, found it, finally, let it be, let it be something of the founded-melted.

Lacan – What is it?

X In the audience: We can’t hear anything!

So I say that this ‘unier’ that is founded, and I asked you not to let this ‘founded’ appear too fundamental to you, it is what I called leaving it in the melted, this ‘unier’ that is founded, there is One, there exists One who says no.

That is not quite the same as denying, but this coinage of the term ‘unier’, like a verb that is conjugated and from which we could in sum advance as to the function, the function represented in analysis by the myth of the father, f.a.t.h.e.r.: he unites, that is what those who managed to hear, through the fireworks, the point on which I would precisely today, finally, like to allow you, let us say, to adjust.

The father unites then. In the myth, he has this corollary of all, ‘all women.’ It is there, if one follows my quantum inscriptions, (q.u.a.n.t.u.m.), that a modification is to be introduced. He unites them, certainly, but ‘not all’ precisely.

Here, one touches at once on what is not my own, to say, namely the kinship – of logic – and of myth, it only marks that one can correct the other. That is work that remains ahead of us.

For the moment, I remind you that with what I allowed myself, after all the approximations of the father, with what I inscribed of the é-pater [wordplay: ‘é-pater’ can mean both ‘to amaze’ and is homophonic with ‘the father’], you see that the way which sometimes joins myth with derision is not foreign to us. That in no way affects the fundamental status of the structures involved.

It is amusing that, just like that, there are people who discover, who discover late, what I can well say from where I stand is rather general for now, all this effervescence, this turbulence that is happening around terms like the signifier, the sign, the signification, semiotics, all that occupies for the moment the forefront of the scene, it is curious, the singular delays that are revealed there.

There is a very good little journal, well, no worse than another, in which I see appearing under the title of The Writing Workshop an article, my God, no worse than another, called ‘The Agony of the Sign’… Do you hear? …called ‘The Agony of the Sign.’

Agony is always very touching. Agony means struggle. But also agony means one is fainting, and so The agony of the sign makes, it makes pathetic. I would have preferred, finally, that it did not all turn towards the pathetic. It starts from a charming invention, from the possibility of forging a new signifier that would be that of “ant, antastic” [wordplay: in French, fourmi (ant) + formidable = fourmidable]. Indeed, this whole article is antastic and it begins by asking what the status of antastic could possibly be.

I quite like that. Especially since it is someone who, after all, has been well informed for a long time about a certain number of things that I put forward and who, in sum, at the beginning of this article, feels obliged to play innocent, that is, to hesitate, regarding antastic, to classify it either as metaphor or metonymy and to say that there is something which is therefore neglected, in Jakobson’s theory, namely that which would consist in stamping words together.

But I have long since explained that! I wrote The Instance of the Letter precisely for that, S over small s with the result, one, parenthesis, effect of meaning, [long sigh from Lacan, laughter from the audience] it’s displacement, it’s condensation.

That is precisely the way by which one can indeed create… which is, after all, a little more amusing and useful than “antastic”… one can create “unier” [Laughter].

And then it serves a purpose. It serves to explain to you by another way what I have entirely given up approaching by that of the Name-of-the-Father. I gave it up because I was prevented at a certain point, and because it was precisely those to whom it might have been useful who prevented me. It could have been useful to them, in their, in their personal intimacy.

These are people particularly involved on the side of the Name-of-the-Father. There is a very special clique in the world, like that, which can be pinned to a religious tradition, it is they who would have been refreshed by it, but I don’t see why I should devote myself especially to them.

So I explain the story of what Freud tackled as best he could, precisely, to avoid his own story… “El shaddaï” in particular, it’s the name by which he designates “he whose name is not spoken”… he turned to myths, then he did something rather proper, somewhat antiseptic, he did not take it further, but that is indeed the point, it is that we let pass the opportunities to pick up what directed him, and what should now make the psychoanalyst be in his place in his discourse. His chance has passed. I have already said it.

So that in the plane there, that was bringing me back from I don’t know where, that was bringing me back from Milan where I returned from last night… well! I didn’t bring the thing… it’s really very good, it’s in the plane, in a thing called Atlas and which is distributed to all travelers by Air France: there’s a very, very nice little article… fortunately I don’t have it, I forgot it at home, fortunately because it would have led me to read you some passages and there is nothing as boring as hearing things read out, there is nothing as boring as that! …anyway, there are psychologists, psychologists of the highest order, aren’t there, who in America devote themselves to surveys on dreams. Because dreams are surveyed, aren’t they.

Surveys are conducted and it turns out, finally, that sexual dreams are very rare. [Laughter] These people dream about everything: they dream about sports, they dream about all sorts of jokes, they dream about falls, well, there is not an overwhelming majority of sexual dreams. [Laughter]

From which it follows, naturally, that since the general conception – so we are told in this text – of psychoanalysis is to believe that dreams are sexual, well, the general public… the general public which is, precisely, formed by psychoanalytic dissemination, you too are a general public… well, the general public is naturally going to be flabbergasted, isn’t it, and all the soufflé is going to fall like that, flatten at the bottom of the pan.

It is still curious that no one, in sum, in this supposed general public, for all this is supposition, after all it is true that in a certain resonance all dreams, that is what Freud would have said, that they were all sexual.

He never actually said that… never, never said that! He said that dreams were “dreams of desire.” He never said it was sexual desire!

Only, to understand the relationship between the fact that dreams are “dreams of desire” and this order of the sexual, which is characterized by what I am in the process of putting forward, because it took me time to approach it and not throw disorder into the minds of those charming people, didn’t it, who, after 10 years of me telling them things, didn’t it, only thought of one thing: joining the bosom of the International Psychoanalytical Association.

Everything I might have told was of course beautiful exercises, exercises in style. They were serious: seriousness is the International Psychoanalytical Association.

Which means that now I can assert—and let it be heard—that there is no sexual relationship, and that is why there is a whole order that functions in the place where that relationship would be. And it is there, in this order, that something is consequent as an effect of language, namely, desire. And maybe we could advance a little bit, and think that when Freud said that “the dream is the satisfaction of a desire”: “satisfaction” in what sense?

When I think that I am still at that point, isn’t it, that no one… of all those people who spend their time muddling what I say, making noise out of it… no one has yet ever thought to advance this thing which is, however, the strict consequence of everything I have put forward, which I have articulated in the most precise way… if my memory is correct, in 57… wait, not even: in 55! …regarding the “dream of Irma’s injection”: I took it, to show how one treats a Freudian text, I explained very clearly what was ambiguous in it, that it was there, precisely… but not at all in the unconscious: at the level of his present preoccupations… that Freud interprets this dream, this dream of desire which has nothing to do with sexual desire, even if there are all the implications of transference that suit us.

The term “intermixture of subjects,” I advanced in 55, can you imagine: 17 years, eh…

And then it is clear that I will have to publish it as it is, because if I haven’t published it, it’s because I was absolutely disgusted by the way it was taken up in a certain book published under the title “Self-Analysis,” it was my text, but put back together in such a way that no one could understand anything.

What does a dream do? It does not satisfy desire! For fundamental reasons… which I am not going to start developing today because, because it’s worth 4 or 5 seminars… for the reason that is simply this and that is tangible, and that Freud says: that the only fundamental desire in sleep is the desire to sleep. [Laughter]

That makes you laugh, because you have never heard that. Very well! Yet, it’s in Freud…

How is it that it does not come immediately to your mind, what does it mean to sleep? It consists in this: that what, in my tetrad, the semblance, the truth, and enjoyment, and surplus-jouissance… I don’t need to rewrite it on the board, right?… what is to be suspended… that’s what sleep is for, anyone only needs to watch an animal sleep to notice… what is to be suspended, precisely, is this ambiguous thing in the relationship of the body with itself: enjoyment.

If there is a possibility that this body accesses self-enjoyment, it is obviously everywhere: – when it bumps itself, – when it hurts itself, – that is jouissance. Then man has little entry doors there that others do not have, he can make it a goal.

In any case, when he sleeps, it’s over. It is precisely about making this body curl up, make itself into a ball.

To sleep is not to be disturbed.

Jouissance, after all, is disturbing. Naturally, one is disturbed, but as long as one sleeps, one can hope not to be disturbed.

That is why, from there, everything else fades away: there is no longer any question – nor of semblance, – nor of truth since all that, it holds together, it is the same thing, – nor of surplus-jouissance.

Only here it is… what Freud says is that the signifier, itself, keeps on running during that time. That is exactly why, even when I sleep, I prepare my seminars. Monsieur Poincaré discovered the Fuchsian functions…

What is it?

X in the audience – It is a pollution!

Who just said that precise word?

X in the audience – It was me.

Yes, that’s right, but I am particularly pleased to see you choose that word, you must be particularly intelligent [Laughter].

I have already publicly delighted in the fact that one of my analysands… who is somewhere around here, who is a particularly sensitive person… did indeed speak, regarding my discourse, of “intellectual pollution.”

It is a very fundamental dimension, you see, pollution.

I probably would not have pushed things that far today, but you seem so proud to have brought up this word “pollution” that I suspect you must not understand a thing about it. Nevertheless, you will see that I will at once, not only make use of it, but rejoice a second time that someone has made it appear, for that is precisely the difficulty of analytic discourse.

I note this interruption, I seize upon it, I embark on something which, in the urgency of the end of the year, I will then find the occasion to say.

It is this: since it is in the place of semblance that analytic discourse is characterized by situating the object little(a), imagine, Sir, who believes you have pulled off a coup here, that you are precisely agreeing with what I have to advance.

That is to say that the most characteristic pollution in this world is very exactly the object little(a) from which man draws, and you too draw your substance, and that it is from having to… from this pollution which is the most certain effect on the surface of the globe… from having to make of it—in his body, in his existence as analyst—a representation, that he must look at it more than once. The dear little ones fall ill from it, and I must tell you that I myself am not much more at ease in this situation.

What I am trying to show them is that it is not altogether impossible to do it a little decently. Thanks to logic, I manage, if only they would let themselves be tempted, to make that position supportable to them that they occupy as little(a) in analytic discourse, so as to allow them to conceive that it is obviously no small thing to raise this function to the position of semblance which is the key position in any discourse.

That is where lies the mainspring of what I have always tried to make felt as the resistance… and it is all too understandable… of the analyst, to truly fulfill his function.

One must not think that the position of semblance is easy for anyone; it is really only tenable at the level of scientific discourse and for a simple reason, it is that there, what is brought to the position of command is something entirely of the order of the real, insofar as everything we touch of the real, – it is the Spaltung, – it is the split, – in other words, it is the way I define the subject.

It is because in scientific discourse, it is the capital S, the barred S [S] that is there, at the key position, that it holds together.

For university discourse, it is knowledge:

There, the difficulty is even greater, because of a kind of short-circuit: because to pretend to know, one must know how to pretend. And that wears out quickly.

That is exactly why, when I was there, there where I just returned from as I told you earlier, namely in Milan, I had an audience obviously much smaller than yours, let’s say a quarter, but there were many young people there, many of those young people who are called “in the movement,” there was even a completely respectable figure of rather high stature who happens to be the representative there, does he know or does he not know… I was told he was only there afterwards, I did not want to ask him… does he know or does he not know that by being there at that point, what he wants is like all those here who are a little interested in the movement, it is to restore university discourse to its value.

As the name indicates, it leads to “units of value.” They would like us to know a little better how to pretend to know. That is what guides them. Well indeed, it is respectable and why not?

University discourse is of a status as fundamental as any other. Simply what I point out is that it is not the same, because it is true: it is not the same as psychoanalytic discourse. The place of semblance is held differently there.

And so that is how I was led over there… My God, what to do with a new audience and especially if they might confuse things? I tried to explain to them just a little what my place was in the story.

I started by saying – that my Écrits was “trashlication” [wordplay: poubelle = trash, publication; “poubellication”], – that they should not believe they could find their bearings in it.

There was still, and then the word “seminar.” Of course, how to make them understand that… what I was forced to explain, to admit… that the seminar is not a seminar, it is a thing I rattle off all by myself, my good friends, for years now, but that there once was a time when it deserved its name, when there were people who intervened? So that is what drove me beside myself, to be forced to come to that. And as on the way back someone pressed me to tell me: “Ah well, what was it like when it was like a seminar?” I said to myself, today I am going to tell them… for the second-to-last time that I will see you, because I will see you one more time… good God, let someone come and say something!

On that note I receive a letter from Mr. Recanati… I am not making up a story for the moment, I am not pretending to make an intervention arise from the floor, I am simply saying that I received a letter, which was moreover a reply to one of mine… from Mr. Recanati who is here, who proved to me, to my great surprise—wasn’t it?—that he had heard something of what I said this year.

So I will give him the floor because he has something to say to you about something that has the closest relation to what I am trying to work out, with set theory in particular, isn’t that so, and with mathematical logic, he will tell you which.

François Recanati

The letter to which Dr. Lacan has just alluded was in fact a few remarks and comments on three texts by Peirce that I gave him, not because he was unfamiliar with them—that is obvious—but because these texts, precisely, differed from those to which he might otherwise have referred.

These were, on the one hand, cosmological texts, and on the other, texts relating to mathematics. I will first clarify a little the content of these three texts before coming to the way in which I might speak about them. As for mathematics, Peirce provides a critique of the definitions of continuous sets known to him. He examines three definitions, namely Aristotle’s, Kant’s, and Cantor’s, all of which he critiques, and based on a single criterion.

The criterion is that he wants, in each definition, the very fact of the definition to be marked, since, he says, in defining a continuous set, one cannot help but determine it in a certain way and this is important for the outcome of the definition. The very process of definition must be marked somewhere, as such.

As for cosmology, Peirce speaks of a fairly similar problem, of a similar preoccupation concerning the problem of the genesis of the universe. His problem is that of the before and after. One cannot access what was before by simply performing the analytical operation that consists in removing from what came after everything that constitutes the character of this after, since this would only result in a crossed-out after and it is precisely in the mode of this crossing-out that the after is constituted, which differs only by a specific inscription, here in the mode of crossing-out, of the before.

In other words, the before is in a sense an after… or rather the after is an inscribed before and one will absolutely not be able to deduce the before from the after since the before that is inscribed in the after is precisely the after which, in this sense, no longer has anything to do with the before whose very property is not to be inscribed. In other words, it is the inscription that counts, I mean that the before is nothing.

That is what Peirce says, when he speaks of the genesis of the universe: before there was nothing, but this nothing is nevertheless a specific nothing, or rather precisely it is not specific, because in any case it is not inscribed, and one can say that everything that came after is nothing either, but as nothing is inscribed. This non-inscribed in general, which he finds more or less everywhere, and not only in cosmology, Peirce calls the potential and that is what I will say a few words about now.

But before doing so, I would like to say a few words about my position here, which is obviously paradoxical, since I am clearly a specialist in nothing, no more in Peirce than in anyone else, and everything I will say about this author and others, since I will speak of others, will be what I can take up from the discourse held by Dr. Lacan. In my own speech, I maintain my status as listener.

And how is this possible? Precisely by signifying in my discourse only the fact of having listened. This raises the problem of to whom I am speaking. For clearly, if I address myself to those who, like me, have listened, it will serve them nothing, and if I address myself to those who have not listened, I will only inscribe the nothing of their non-listening and thereby allow an elaboration which will of course make use of it later and which will have nothing to do with the pure nothing that was at the start. In this case, then, nothing will change, [Laughter] and it is inasmuch as my intervention as listener disturbs nothing, that I can indeed represent the audience.

Since after all, all the interventions of Aristotle are only supposed in the discourse of Parmenides, and that precisely the sooner they are finished the better, generally speaking, as for the interventions of Aristotle, rather so that he himself can hold a true discourse, he must in turn have a mute listener in whom, in what he can identify himself, which explains why the other Aristotle in the Metaphysics says “We Platonists…,” because it is after Plato has spoken, or if you like after Parmenides has spoken for the other, that he himself can begin to do so. Hence the paradox here, but as this paradox is not my doing, I will leave Dr. Lacan to comment on it afterward, because I myself can say nothing about it.

One cannot, says Peirce, oppose the void, the 0, to something, because 0 is something, this is well known. The void represents something and Peirce says that it is among those secondness concepts, important concepts for Peirce and which I will come back to a bit later. It is not a monad, as inscribed void, but it is relative. Indeed, if one posits this void, one inscribes it. In this case, the inscription of the empty set can be given as {Ø}. This is recognized as the empty set considered as an element of the power set of the empty set.

So, if the void is constituted as 1 and if one were to repeat the operation a little and make the power set of the power set of the empty set, one would quickly have something like this: {Ø, {Ø}}, which gives roughly this: {{Ø}}, and this can very well be recognized as representing 2. Just as well, this can represent 1.

It is in this way that one is led to repeat this remark, that of course it is the repetition of a nonexistence that can found many things, and notably, in this case, the sequence of whole numbers, but what interests Peirce in this remark is that what is repeated is not nonexistence as such, or rather not exactly, it is the inscription of nonexistence, inasmuch as nonexistence is marked by this inscription.

And this is what he will develop on many occasions, in several texts, and I will speak about it. This links us back to his mathematical argument. When, he says, one wants to define a system where this nonexistence is repeated, it must be specified that it is repeated as inscribed. At the start, there is an inscription of a nonexistence. And this is very important for logic.

The universal quantifier, by itself, could define nothing. The universal quantifier, for Peirce, is something of secondness, as paradoxical as that may seem, as he says, it is relative to something. What grounds this quantifier is the “prior and inscribed nullification of the variables” that contradict it. Thus, from a purely methodological point of view, Peirce takes on Cantor.

Cantor is wrong because his definition of the continuum refers specifically to all the points of the set. Peirce specifies that the definition must be varied from a logical point of view. An oval line is only continuous because it is impossible to deny that at least one of its points must be true for a function that absolutely does not characterize the whole set. For example, when it is a matter of going from the outside to the inside, one must necessarily pass through one of the boundary points. This is, in a way, a lateral approach. One cannot simply posit the universal quantifier like that; it is necessary to pass through a prior nullification, which itself passes through a prior function.

Negation here is itself erected as a function, and the set of sets relevant for this function… in this case, insofar as it is impossible to deny, etc…. is the empty set, which inscribes negation as impossible. The same type of example could be taken in topology as well. If one listened to Peirce, the fixed point theorem should be stated as follows, I will write it:

It is impossible to deny that in a deformation of a disk onto its boundary, at least one point escapes the deformation that authorizes it, by the very fact of escaping it.

Lacan – Repeat that properly.

François Recanati

The fixed point theorem, if one takes for example something like a disk, it is, in a way, a matter of deforming a disk continuously onto its boundary. It is certain—and it is given as a theorem—that at least one point of the disk escapes the deformation, that is to say, remains fixed, and it is by this fact that there is this point that remains fixed that one can carry out the general deformation. Otherwise, it would not be possible, and here there is obviously a contradiction. Let’s say that there is a very clear connection between this point that escapes the function that authorizes it.

Lacan

That is a demonstrated theorem. It is not only demonstrable, it is demonstrated. Moreover, this theorem is symbolized—you might perhaps comment on how it is symbolized by this:… because it is a formula that is very close, in sum, to the one I am used to writing…: such that one must deny—that there is not: such that one must deny that there is no existence of X—such that ΦX is denied.

François Recanati

There is indeed a double negation, certainly, but the two negations are not equivalent, they are not exactly the same. And on the other hand, especially this double negation, insofar as it is inscribed, it is not the same as simply affirming it. One could have affirmed it. There, that is why I cited at the beginning the critique of the universal quantifier, as it were, as given like that. If it is the product of a double negation, this first uninscribed negation, it bears on a negation erected as a function.

For example: the points do not remain fixed. Well, there is a point that precisely escapes this function, and in this respect, the necessity is above all to inscribe them. That is why I did so there. And perhaps it would be necessary to mark, perhaps in a specific way, what I said to be an impossibility. But at the same time, here, it is simply here the empty set posited as the only set functioning for the function of negation.

Lacan

I think what must be emphasized here is this: the bar placed here on each of the two terms as negated is an “it is not true that,” an “it is not true that” frequently used in mathematics, since it is the key point, it is what the so-called proof by contradiction leads to. It is, in short, a matter of understanding why, in mathematics, it is accepted that one can found, but only in mathematics, because everywhere else, how could you base anything affirmable on an “it is not true that”?

This is exactly where the objection comes within mathematics to the use of proof by contradiction. The question is how, in mathematics, proof by contradiction can found something, which is indeed proved as such by not leading to contradiction.

This is where the proper domain of mathematics is specified. So under this “it is not true that”—it is a matter of giving status to the negative bar, which is the one I use at a point in my schema, to say that this is a negation, / §: there does not exist an x that satisfies this: Φx negated.

François Recanati

In Peirce’s terms, that bar is what comes first, it is the first inscription. Because he says, the potential… and I was going to come back to that in the course because it is a concept that is ultimately rather elaborated… it is the field of inscription of impossibilities, but before there are impossibilities, impossibilities not yet inscribed, it is the field of possible impossibilities.

And in this field, something comes to subvert it by this mark, as it were, which is here impossibility, which is a kind of cut, a cut made within a domain which, beforehand, is in a sense unique, and that is why, says Peirce, the first impossibility must be inscribed first. That determines everything.

And then, possibly, negation and all these specifications continue to determine, but it is already there, inside, of the impossible. In other words, he says there are two fields:

– on the one hand there is the field of the potential, which is the element of pure 0, one could say of pure void, I will come back to that,

– and on the other hand, the impossibles, which are those that are born from the potential, but to oppose it very clearly, and within the impossibles one can say things like this, that is to say: there does not exist x such that not Φx, or there exists x such that not Φx.[/ §, or: §]

But he makes an opposition of these two fields as fundamentally opposed, one being the element of pure 0, the other being the element that I will call the 0 of repetition, and it is on this point that I would like to arrive.

Lacan

You admit, for example, that I transcribe everything you have said by saying that the potential equals the field of possibilities as determining the impossible.

François Recanati

As determining, but I immediately specify that he said, it is this field of possibilities that determines the impossible but not in the Hegelian sense, one must be careful, as he himself says, it determines it not necessarily, but potentially, that is to say, one cannot say: “necessarily it had to happen,” one notes that it happened. We know that it is this potential that determined this impossible, but not necessarily, we agree. So it is exactly what I meant, the potential…

Lacan

We could perhaps transcribe it like this: potential = field of possibilities as determining the impossible.

François Recanati

So, it is with this kind of consideration that Peirce constructs the concept of the potential. It is therefore the place where impossibilities are inscribed, it is the general possibility of unrealized, that is to say, non-inscribed, impossibilities. It is the field of possibilities as determining the impossible. But it involves, as has just been said, with regard to the inscriptions that occur in it, no necessity, which means, notably, for a mathematical problem, that 2 cannot be accounted for rationally, in the Hegelian sense, that is, necessarily. The 2 came, one cannot say where it came from, one can simply relate it to the 0, to what happens between 0 and 1, but to say why it came, impossible.

The potential allows for this, to define the paradox of the continuum, and this is in a text by Peirce… I cite this, but in fact, I haven’t looked at it very closely so I will not elaborate… if a point of a potential continuous set is given a precise determination, an inscription, a real existence, then continuity itself is broken.

And this was interesting not from the point of view of the continuum, but from the point of view of the potential. It is that the potential truly exists as potential and that as soon as it is inscribed in one way or another, there is obviously no longer any potential, that is to say, it is itself the product of an impossible that has come from itself.

X – There, Cantor is wrong!

François Recanati

As for cosmology, absolute 0, pure nothingness, as Peirce says, is different from the 0 that is repeated in the sequence of integers. The 0 that is repeated in the sequence of integers is none other than the general order of time, and I will return to this, whereas absolute 0 is the general order of the potential. Thus absolute 0 has its own dimension, and Peirce tries to emphasize that this dimension should be inscribed somewhere, at least marked, presented in mathematical definitions. The problem is obviously…

Lacan – There, Cantor is not opposed.

François Recanati

The problem is obviously: how can one move from one dimension, that of the potential for example, to the other, which I will call that of the impossible or that of time, or whatever one wishes. Peirce thus presents the problem: how to think, non-temporally, what was before time? This certainly recalls Spinoza and Saint Augustine, but it recalls above all the empiricists. And here I must say it has often been noted that Peirce took up the style of the empiricists and their concerns.

But to truly situate Peirce’s originality, this has never been related to the empiricists, no one has ever sought what in them could have prepared all this. Yet these two dimensions… one potential and the other, if you will, temporal, or rather one dimension of absolute 0, and a dimension of the 0 of repetition… this is present from the very start of the empiricist epic. And this is what I would like to say a word about to show how it can be brought out.

Lacan- Say it well, thunder it out!

François Recanati

I will do so, and after that I will return to Peirce’s semiotics in connection with all this. Yes, the object of empirical psychology—it is a first point that we have made a point, each time, to evacuate—is signs and nothing else, it is the system of signs. It is an extension, one could say, of the quaternary system of Port Royal, such that, all in all, Saussure is also only an extension of it at the limit:

– the thing as thing and as representation,
– the sign as thing and as sign,
– the object of the sign as sign being the thing as representation.

It is the same thing that Saussure says—I was saying this but I will not elaborate—the sign as concept and as acoustic image. Only, with scholasticism we have evacuated the general problem of “the thing in itself,” and have even gone so far as to see in the world—and this, with all the theories of the Great Book of the World—the sign of thought.

From then on, one arrives at something like this: the world as representation—insofar as the world can only be known as representation—replaces the thing, in the quaternary system of the sign, and the thought of the world in general replaces the representation, which amounts to putting face to face thought of the world—world of thought.

Now, it is evident that the thought of the world and the world of thought, which may differ in certain respects, are the same thing. So, there is a problem for the quaternary system because there is an irreducible duality in the quaternary system; it is necessary either to abandon it or to change it, and we know that Berkeley abandons it, precisely by establishing a system of identity between the thought of the world and the world of thought.

As for Locke, he changes it. When he says, and I apologize for lingering a bit on this introduction, what he says is that representations, ideas, do not represent things, they represent each other.

Thus the most complex ideas represent the simpler ones. There are faculties, for example, for the representation of ideas among themselves, and it is highly developed, there is an entire topic that is roughly as has been said about it, a hierarchy of ideas and faculties.

But what I would like to emphasize a little, and what has not been noticed in Locke, and which is precisely the most interesting, since it allows Condillac and in this way Condillac precedes Peirce in a sense, is that there is another faculty for Locke, which enables all this. Because how does it work? It apparently functions on its own, something is needed for the system to function.

And there is a new faculty, a new operation that he calls—and which has never been noticed because it is not in his classifications, it is always in the notes—“observation,” observation, which is something that works on its own, operates at all levels, is found everywhere, and is also intrinsic to all the elements, something rather incomprehensible, and which is at once the process of transformation and the milieu, the general element of the transformed.

It is at once the milieu… by this observation, in a sense, a simple idea is transformed into an image of itself, that is to say, into a complex idea since its objectivity is placed alongside it in the idea, and in this general idea through which it is transformed, there is an inscription, there is a connotation of the inscription of its transformation. That is to say, the idea, once it is transformed, is in a sense inscribed, it is in that that it becomes a complex idea and no longer a simple idea.

So, the whole problem at this point is: what makes this possible? Either: – what was there at the start, – what is transformed at the start, – from what does one transform to obtain the first cause? – What is the very first, in a sense?

And Locke poses it in these terms when he speaks of the irreducible sensation of an original reflection. If a reflection is original, what is reflected that is pre-original? Either what is the pre-original, or what allows, strictly speaking, what allows this faculty?

And here Condillac takes over. His method was absolutely exemplary: he will zero in on this something he saw in Locke, this unattainable something, by giving it a name, making it function as an unknown in an equation. And subsequently, when authors wanted to criticize Condillac, they said that his system was not at all merely psychology, it was profoundly logic, that he had made it a logical system, a system where there was no content, etc., you see, that is precisely the interest of Condillac.

And especially this sensation, from which he says everything derives, at least in one of his major treatises, this sensation there, ultimately, is nothing, at no point does he define it precisely, on the contrary, the entire development he gives it, everything he shows as deriving from it, is a kind of contribution to its definition. But what strictly speaking enables it—and everything else derives from it, all that are strictly speaking the attributes of sensation—everything that enables this attribution, is what he points to as the 0 element that is always given at the start, always given in sensation, and about which he wonders what it is, and we will ask ourselves with him.

He will characterize, in order to try to reach this irreducible element, everything that happens with the help of this element, but with more than this element, that is to say, in a word, as he says, everything that happens in understanding. With this, we will be able to see what truly founds the originality of sensation, if indeed it is from sensation that everything that happens in understanding is derived.

Now, what is characteristic of understanding, he says, and this in his first essay—I insist because there was a slight divergence afterwards, he distanced himself from this idea which is obviously his greatest originality—what is characteristic of understanding is order, it is connection in general, connection as connection of ideas, connection of signs, connection of needs, in fact it is always a connection of signs, it is always the same thing.

For humans, order functions on its own, he says, and he explains it a bit, whereas for animals, to set order in motion, a punctual external impulse is required, and Condillac specifies: “between humans and animals—and it is quite a fine phrase he says—between humans and animals, there are the imbeciles and the mad”:

– the former cannot latch onto order—they are the imbeciles—systematically they cannot latch onto order,
– and the latter can no longer detach themselves from it. They, they are completely drowned in order, they can no longer take any distance, they can no longer detach themselves from it.

Order in general is what allows the passage from one sign to another. It is the possibility of having an idea of the boundary between two signs. And Condillac has a conception of the sign, but as always, inadequate, always a metaphor, and he says it, this time expressly, in a short study where he praises tropes, perhaps taking up—I am not sure—terms from Quintilian.

In any case, for him, a sign is what comes to fill the interval between two other signs. In this sense, in a sign, what is considered? It is the two other neighboring signs, at least two which are considered, but not as signs in so far as they could induce a representation, from the point of view of their own edges, that is to say, from the formal point of view. And he makes it clear that these cannot be, strictly speaking, representations, but only signs, since he says:

– there is no formal representation,
– there is no abstract representation,
– there is always a representation that represents a representation, that is to say, there is always a mediation of the representation of the sign, but never an immediation of the content, for example.

As he himself says, the image of a perception, its repetition is only its hallucinatory repetition. He says it is the same thing. One cannot differentiate a perception and its image, and in this way he critiques all previous theories. So order is what the sign represents, in that the sign substantiates an interval between two signs. Only, signs in general are supposed, by all the theories from which he inherits, Condillac, to represent something.

And this, of course, is a problem for him, he cannot manage to disentangle himself from it, how is the connection made between the formal sign and its reference in general? This connection itself—says Condillac to get rid of it—it derives from the unknown, it derives from sensation. So, the unknown is already a relation between the sign as event and the sign as inscription of the event. And I specify, this is not Condillac who says it, but he implies it, it is Destutt de Tracy, his exegete, who asserts it, and I find that it is not bad. And Maine de Biran who, for his part, was a student…

Lacan

The two sentences that I had begun to write throughout the thing, which some may perhaps have copied, are directly the statement that Recanati reproduces here…

François Recanati

Maine de Biran, himself a disciple of Destutt de Tracy, is first nourished by this difference between the event and the inscription of the event. And one sees how it is the pivot of the whole theory.

There is, he says, a perpetual gap between the inscription and the event. This gap, says Maine de Biran, comes from the gap in the speaking being—and I am not joking—between the subject of the statement and the subject of the enunciation. It is in the foundations of Maine de Biran’s psychology, where he shows more or less that, in representing the self, insofar as in every representation there is already a self, that at that moment, there are two. As soon as one tries to represent the “I,” it means that automatically, there are two, it means that immediately there are two, it means that mediately there is never… that there is never one except mediately.

For Condillac, the order of signs, insofar as the order of signs is the order of this gap, has as its model the multidimensional space of time, as he calls it, and I will not elaborate on that. Time, one can say, is nothing but the infinite repetition of punctualities. Punctuality as time-zero is the same problem that arises above.

It is not the same punctuality:

– the one that repeats in time,

– and the one from which time issues: zero-punctuality—the one from which time issues—zero-punctuality as transparency, precisely, between inscription and event.

The punctuality that repeats in time, always for Condillac, is relativized by being considered in time as this punctuality here, present, past, or to come. It too is considered from the point of view of its edges, from the point of view of its boundary. Time, rather than being a series of punctualities, is therefore the series of interpunctual boundaries, inasmuch as the boundary is precisely the marking of the respective edges of two punctualities or just as well of two signs.

Thus, there is the same difference between absolute punctuality and time as between the empty set and the set of its subsets. It is the inscription of the 0 which is an element of the latter, just as it is the inscription of punctuality that is the element of time. Thus, there is a gap that is given at the beginning of all this theory and which Maine de Biran was perhaps trying to discern more clearly. The system of signs is nothing but the infinite repetition of this gap, as such, pure gap, and that repeats itself in all the writings of the Empiricists, it emerges from the experience and investigation of their school, that is: it is not talked about.

Condillac too, though it rarely happens, speaks of human nature at one moment, saying that he would very much like to know how, at the beginning, this relation and this order come about, why, precisely, since it fails, the order between inscription and event, why, since it fails, since it doesn’t fit, why nevertheless does it exist? Why is there an inscription of what is only 0? This is clearly his problem, and at that point he responds, after a little display of bravado: I don’t know, it is human nature.

It is this gap in general which allows for the self-motricity of the system of signs, according to Condillac, who said, the system of signs, there, works on its own, whereas in his Treatise on Animals he recounts all sorts of things to show how in animals, there is also a system of signs and how it is dependent on all external objects, dependent on all the [?]

This brings us back to Peirce’s semiotics from where we started. Peirce calls phaneron—from the Greek word φανερόν—the totality of everything that is present to the mind, which is more or less the sense of phaneron, real or not, the immediately observable. And he starts from there, he breaks down the elements of the phaneron. There are three elements in the phaneron, inseparable, which he calls:

—on the one hand, what one could translate as the priman, the monad in general, I believe he uses the word monad, an element complete in itself,

—on the other hand, the second, static force, opposition, static tension between two elements, that is, each element, immediately, evokes the other with which it is in relation and it is in a sense a whole, an absolutely inseparable whole,

—and the most important, the tertian, an element immediately relative to both a first and a third and Peirce specifies, all continuity, all process in general, comes under ternarity. From there, from this conception of ternarity, which one can show derives from his astronomical theories, which he produced at the beginning of his life, but in any case I will not discuss that.

Lacan—Peirce as astronomer…

François Recanati

So, starting from this ternarity he constructs a logic which is specified as semiotics, Logic of semiotic, semiotics itself being specified at certain levels as rhetoric. And that is important for Peirce. Everything depends on his definition of the sign in general, the sign, he calls representamen, I am sorry to quote:

“It is something, the representamen, which, for someone, stands for something else, from a certain point of view or in some manner.”

In this, there are four elements, for someone is the first, and I quote Peirce again:

“This means that the sign creates in the mind of the recipient a more equivalent sign, or even more developed.”

The second point follows from that: the reception of the sign is thus a second sign functioning as interpretant.

X in the audience – That’s nonsense!

Third, the thing for which the sign stands is called “its object.” It is these three elements that make up the three corners of the semiotic triangle. The fourth term that comes in is more discreet but no less interesting.

Lacan – You think Peirce is wrong too?

X in the audience – I think he’s going too far.

Lacan – What does that mean?

François Recanati

The fourth term, more discreet, is what Peirce calls the ground. The sign stands for the object, not absolutely but with reference to a kind of idea called the ground, that is, the basis, the background of the relation between the sign and the object. These four terms, taken together, define three relations. And these three relations are the respective objects of the three branches of semiotics. First relation, the sign-ground relation, sign-ground. This is pure or speculative grammar, says Peirce. It’s a matter of recognizing…

Lacan

Because speculative grammar wasn’t invented just a few years ago, as this gentleman would have us believe and…

François Recanati

It’s a matter of recognizing what must be true of the sign for it to have meaning, the idea in general is the focusing of the representamen on a determined object according to the ground or the point of view.

Thus, one can see that meaning is, in a way, projected on a differentiated background and that the ground, the determination of the ground, is almost the determination of the first point of view that determines the inscription, all this on potential. That is to say, the ground in general is already the potential. Likewise, the representamen is, in relation to its background, the determination of a certain point of view which commands the relation to the object. The ground is thus the preliminary space of inscription.

The second relation, representamen-object, is the domain of pure logic for Peirce. It is the science of what must be true of the representamen for it to stand for an object.

The third, which is the most important for what we are considering here, is the relation between the representamen and the interpretant, which Peirce ingeniously calls pure rhetoric, which recognizes the laws—it works at the level of laws—according to which a sign gives birth to another sign that develops it according to the course of the interpretant, as we will see. And this question of pure rhetoric, Peirce approaches with the help of his semiotic triangle: representamen, interpretant, object.

I will clarify each of these terms so that we can understand them better. I am following Peirce regarding this relation.

“The representamen, first, has a primitive relation to a second, the object.”

The object to which the second, the sign, is first given.

“But this relation can determine a third, the interpretant, to have the same relation to its object as the sign itself maintains.”

In other words, the relation of the interpretant with the object is commanded to be, by the relation of the representamen with the object, to be the same relation. The same from the point of view of order, but different nonetheless, different, that is, more specified, that is, in a certain way the field of possibilities of this new sign is somewhat reduced, and like that, it continues to infinity, we will see that.

The ground is absent here, it determines the relation of the representamen to the object itself. And the representation of the representamen to the object determines as repetition the relation of the representant to the object which in turn determines as repetition itself… what was I saying? Did I say “representant”? …Yes, so representamen-object determines interpretant-object.

And in a certain way, one can say, and Peirce says it, that the object of the relation between the interpretant and the object is not exactly the object that is the object of the interpretant, but it is the whole of this relation, that is to say:
— on the one hand, all of that is the object of this,
— and, on the other hand, this must repeat that, it must repeat it generally in the form and have it for its object.

And we can take an example; Peirce gives an example.

Lacan – That is what I translate by saying that existence is insistence.

François Recanati

We see that the whole problem is the beginning. It is what happens between the representamen and the object. Now, it is precisely impossible to say anything about what happens there, impossible to come back from what happens there. All we know is that this, what happens in there, between the two, entails everything else. I will end by writing out the rest because that continues to infinity.

As soon as we want to know, as soon as… for this to make sense [R-O], says Peirce… the process of signification takes place from there… for this to have meaning, in one way or another, it is necessary that from the relation… if we take the object as “justice,” and if we take the representamen as “scales”… it is precisely necessary that this relation, which in itself is nothing, be interpreted by its interpretants.

These interpretants can be anything; it could be “equality,” and in that respect, the general relation, that is, of the interpretant here will itself be interpreted by a second interpretant. We could put “communism,” we could put whatever we want, and it continues endlessly. So that at the start, all the data are there, there is a kind of ground, a background that is chosen within an undifferentiated background, and from there there is an absolutely impossible attempt to exhaust this background from the first step that is given in the whole.

The semiotic triangle, as you see, is very clear, reproduces the same ternary relation you cited about the Borromean rings. That is to say, and Peirce says it—well, he does not say the Borromean rings but he uses the same terms—the three poles are linked by this relation in a way that does not admit multiple dual relations, but an irreducible triad. I quote:

“The interpretant cannot have a dual relation to the object, but to the relation that is commanded for it by the sign-object relation, which it cannot have, however, in an identical but degenerate form. The sign-object relation will be the proper object of the interpretant as sign.”

Thus the triangle develops in a chain as endless interpretation… and the phrase is Peirce’s, “endless interpretation” as an expression is still fantastic… that is to say, each time it is what you trace as a new hypotenuse that is taken as the object of the new interpretant each time.

This, which is only sketched out here, so to speak, then becomes affirmed as the object for the new interpretant, and this triangle continues to infinity. In the example I gave, the relation equality-justice is of the same order as the relation scales-justice, but it is not the same. Equality targets not only justice but also the relation scales-justice.

So, to return to Locke for example, we see that it is precisely this, this is taken as the object of an interpretation, but what is new, in a sense, in the terminal point of view, in the result of the interpretation, is that the inscription of the object is marked as such, because precisely, the general relation scales-justice is set beside the object itself, namely justice.

Such is the model of the process of signification inasmuch as it is interminable.

From a first gap—the one given by a first mark within the ground, representamen-object—from a first gap arise a series of others, and the pure element of this first gap was this ground analogous to pure 0.

Here again arises the double function of the void. Given the time, I am not going to continue because there would perhaps be plenty of examples to give, both all over Peirce and throughout all theories, here I have chosen empiricism, but one could have chosen almost anything. You have notably looked at Berkeley, which is a good idea because it is very rich. We could multiply these examples, but that would only amount to commentary.

Lacan said that his discourse made it possible to give meaning again to older discourses.
That is certainly the first fruit that can be drawn from it.
But the identification of what has generally happened as a pathway, under Peirce’s pen for example, is still only an inscription in what, until then, counted for nothing, up to then, up to Peirce, up to Lacan, as one wishes.

From now on, from this inscription of what until then was zero, an enormous infinite series must arise and it is for this series that one must make room.

[Applause]

Lacan

I had to go to Milan to feel the need to get a response.

I find that the one I have just received is more than sufficiently satisfying for you to be able, for today, to be satisfied with it too.