We may try to introduce another principle to [[understand]] these things. If we rarely try to [[understand]] things from the point of view of the [[unconscious]], it is because the [[unconscious]] tells us something articulated in [[word]]s and perhaps we could try to search for their principle.
I suggest you consider the [[unity ]] in another light. Not a <i>unifying</i> [[unity ]] but the countable unity one, two, three. After fifteen years I have taught my pupils to count at most up to five which is difficult (four is easier) and they have [[understood ]] that much. But for tonight permit me to stay at two. Of course what we are dealing with here is the question of the integer, and the question of integers is not a simple one as I think many people here know. To count, of course, is not difficult. It is only necessary to have, for instance, a certain number of sets and a one to-one correspondence. It is true for example that there are exactly as many people sitting in this room as there are seats. But it is necessary to have a collection composed of integers to constitute an integer, or what is called a natural number. It is, of course, in part natural but only in the sense that we do not understand why it exists. Counting is not an empirical fact and it is impossible to deduce the act of counting from empirical data alone. [[Hume ]] tried but Frege demonstrated perfectly the ineptitude of the attempt. The real difficulty lies in the fact that every integer is in itself a unit. If I take two as a unit, things are very enjoyable, [[men ]] and [[women ]] for instance — [[love ]] plus [[unity]]! But after a while it is finished, after these two there is nobody, perhaps a [[child]], but that is another level and to generate three is another affair. When you try to read the theories of [[mathematicians ]] regarding numbers you find the formula "n plus 1 (n + 1)" as the basis of all the theories. It is this question of the "one more" that is the key to the genesis of numbers and instead of this [[unifying ]] [[unity ]] that constitutes two in the first case I propose that you consider the real numerical genesis of two.
It is necessary that this two constitute the first integer which is not yet born as a number before the two appears. You have made this possible because the two is here to grant existence to the first one: put <i>two</i> in the place of <i>one</i> and consequently in the place of the <i>two</i> you see <i>three</i> appear. What we have here is something which I can call the <i>mark</i>. You already have something which is marked or something which is not marked. It is with the first mark that we have the status of the thing. It is exactly in this fashion that Frege explains the genesis of the number; the class which is characterized by no elements is the first class; you have one at the place of zero and afterward it is easy to understand how the place of one becomes the second place which makes place for two, three, and so on. The question of the two is for us the question of the subject. and here we reach a fact of psychoanalytical experience in as much as the two does not complete the one to make two, but must repeat the one to permit the one to exist. This first repetition is the only one necessary to explain the genesis of the number, and only one repetition is necessary to constitute the status of the subject. The unconscious subject is something that tends to repeat itself, but only one such repetition is necessary to constitute it. However, let us look more precisely at what is necessary for the second to repeat the first in order that we may have a repetition. This question cannot be answered too quickly. If you answer too quickly, you will answer that it is necessary that they are the same. In this case the principle of the two should be that of twins — and why not triplets or quintuplets? In my day we used to teach children that they must not add, for instance, microphones with dictionaries; but this is absolutely absurd, because we would not have addition if we were not able to add microphones with dictionaries or as [[Lewis Carroll]] says, cabbages with kings. The sameness is not in things but in the <i>mark</i> which makes it possible to add things with no consideration as to their differences. The mark has the effect of rubbing out the difference, and this is the key to what happens to the subject, the unconscious subject in the repetition; because you know that this subject repeats something peculiarly significant, the subject is here, for instance, in this obscure thing that we call in some cases trauma, or exquisite pleasure. What happens? If the "thing" exists in this symbolic structure, if this unitary trait is decisive, the trait of the sameness is here. In order that the "thing" which is sought be here in you, it is necessary that the first trait be rubbed out because the trait itself is a modification. It is the taking away of all difference, and in this case, without the trait, the first "thing:" is simply lost. The key to this insistence in repetition is that in its essence repetition as repetition of the symbolical sameness is impossible. In any case, the subject is the effect of this repetition in as much as it necessitates the "fading," the obliteration, of the first foundation of the subject, which is why the subject, by status, is always presented as a divided essence. The trait, I insist, is identical, but it assures the difference only of identity — not by effect of sameness or difference but by the difference of identity. This is easy to understand: as we say in French, <i>je vous numérotte</i>, I give you each a number; and this assures the fact that you are numerically different but nothing more than that.
It is necessary that this two constitute the first integer which is not yet born as a number before the two appears. You have made this possible because the two is here to grant existence to the first one: put <i>two</i> in the place of <i>one</i> and consequently in the place of the <i>two</i> you see <i>three</i> appear. What we have here is something which I can call the <i>mark</i>. You already have something which is marked or something which is not marked. It is with the first mark that we have the status of the thing. It is exactly propose to intuition in this fashion order to show that Frege explains the genesis of the number; the class which is characterized by no elements is the first class; you have one at the place of zero and afterward it is easy to understand how the place of one becomes the second place which makes place for two, three, and so on. The question of the two is for us the question of the subject. and here we reach a fact of psychoanalytical experience trait be found in as much as the two does not complete the one to make two, but must repeat the one to permit the one to exist. This first repetition is the only one necessary to explain the genesis of the number, and only one repetition is necessary to constitute the status of the subject. The unconscious subject is something that tends to repeat itself, but only one such repetition which is necessary to constitute it. However, let us look more precisely at what is necessary for the second to repeat the first in order that we may have a repetition. This question cannot be answered too quickly. If you answer too quickly, you will answer that it is necessary that they are the same. In this case the principle of the time one or two should be that of twins — and why not triplets or quintuplets? In my day we used to teach children that they must not add, for instance, microphones with dictionaries; but this is absolutely absurd, because we would not have addition if we were not able to add microphones with dictionaries or as Lewis Carroll says, cabbages with kings. The sameness is not in things but in Consider the <i>mark</i> following diagram which makes it possible to add things with no consideration as to their differences. The mark has the effect of rubbing out the difference, and this is the key to what happens to the subject, the unconscious subject in the repetition; because you know that this subject repeats something peculiarly significant, the subject is here, for instance, in this obscure thing that we I call in some cases trauma, or exquisite pleasure. What happens? If the "thing" exists in this symbolic structure, if this unitary trait is decisive, the trait of the sameness is here. In order that the "thing" which is sought be here in you, it is necessary that the first trait be rubbed out because the trait itself is a modification. It is the taking away of all difference, and in this case, without the trait, the first "thing:" is simply lost. The key to this insistence in repetition is that in its essence repetition as repetition of the symbolical sameness is impossible. In any case, the subject is the effect of this repetition in as much as it necessitates the "fading," the obliteration, of the first foundation of the subject, which is why the subject, by statusan inverted eight, is always presented as after a divided essence. The trait, I insist, is identical, but it assures the difference only of identity — not by effect of sameness or difference but by the difference of identity. This is easy to understandwell-known figure: as we say in French, <i>je vous numérotte</i>, I give you each a number; and this assures the fact that you are numerically different but nothing more than that.
You can see that the line in this instance may be considered either as one or as two lines. This diagram can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the subject. This goes much further than you might think at first, because you can search for the sort of surface able to receive such inscriptions. You can perhaps see that the sphere, that old symbol for totality, is unsuitable. A [[torus]], a Klein bottle, a cross-cut surface, are able to receive such a cut. And this diversity is very important as it explains many things about the structure of mental disease. If one can symbolize the subject by this fundamental cut, in the same way one can show that a cut on a torus corresponds to the neurotic subject, and on a cross-cut surface to another sort of mental disease. I will not explain this to you tonight, but to end this difficult talk I must make the following precision.
What can we propose I have only considered the beginning of the series of the integers, because it is an intermediary point between language and reality. [[Language]] is constituted by the same sort of unitary traits that I have used to intuition in order to show that explain the one and the one more. But this trait be found in something which language is at not identical with the same time one or two? Consider the following diagram which I call an inverted eightunitary trait, since in language we have a collection of differential traits. In other words, after we can say that language is constituted by a well-known figure: set of signifiers — for example,</pi>ba, ta, pa<p align="center" style="line-height: 150%"/i><img src="moebius) etc., etc.gif" width="111" height="75"></p><p style="text-align: justify — line-height: 150%">You can see a set which is finite. Each signifier is able to support the same process with regard to the subject, and it is very probable that the process of the integers is only a special case of this relation between signifiers. The definition of this collection of signifiers is that they constitute what I call the Other. The difference afforded by the existence of language is that each signifier (contrary to the unitary trait of the line integer number) is, in most cases, not identical with itself — precisely because we have a collection of signifiers, and in this instance collection one signifier may be considered either as one or as two linesmay not designate itself. This diagram can be considered is well known and is the principle of Russell's [[paradox]]. If you take the basis set of a sort all elements which are not members of essential inscription at themselves, the origin[[set]] that you constitute with such elements leads you to a paradox which, as you know, leads to a contradiction. In simple terms, this only means that in a universe of discourse nothing contains everything, and here you find again the knot which gap that constitutes the subject. This goes much further than you might think at first, because you can search for The [[subject]] is the sort introduction of surface able to receive such inscriptions. You a [[loss]] in [[reality]], yet nothing can perhaps see that the sphere, introduce that old symbol for totality, since by status [[reality]] is unsuitableas full as possible. A torus The notion of a [[loss]] is the effect afforded by the instance of the trait which is what, with the intervention of the [[letter]] you determine, a Klein bottleplaces — say al, a cross-cut surfacea2, a3 — and the places are able to receive such spaces for a cut[[lack]]. And When the [[subject]] takes the place of the [[lack]], a [[loss]] is introduced in the [[word]], and this diversity is very important as it explains many things about the structure definition of mental disease. If one can symbolize the [[subject by this fundamental cut]]. But to inscribe it, it is necessary to define it in a circle, what I call the [[otherness]], of the same way one can show sphere of [[language]]. All that is [[language]] is lent from this [[otherness]] and this is why the [[subject]] is always a [[fading]] thing that runs under the [[chain]] of [[signifier]]s. For the definition of a cut on [[signifier]] is that it represents a torus corresponds to [[subject]] not for another [[subject]] but for another [[signifier]]. This is the only definition possible of the [[signifier]] as different from the neurotic subject[[sign]]. The [[sign]] is something that represents something for somebody, and on but the [[signifier]] is something that represents a cross-cut surface to [[subject]] for another sort [[signifier]]. The consequence is that the [[subject]] [[disappear]]s exactly as in the case of mental disease. I will not explain this to you tonightthe two [[unitary trait]]s, but to end this difficult talk I must make while under the second [[signifier]] appears what is called [[meaning]] or [[signification]]; and then in sequence the following precisionother [[signifier]]s appear and other [[signification]]s.
The question of [[desire]] is that the [[fading]] [[subject]] yearns to find itself again by means of some sort of encounter with this miraculous thing defined by the [[phantasm]]. In its endeavor it is sustained by that which I call the [[lost object]] that I evoked in the beginning — which is such a terrible thing for the imagination. That which is produced and maintained here, and which in my vocabulary I call the [[object]], lower-case, [[a]], is well known by all [[psychoanalyst]]s as all [[psychoanalysis]] is founded on the [[existence]] of this peculiar [[object]]. But the relation between this [[bar]]red [[subject]] with this [[object]] (<i>[[a]]</i>) is the [[structure]] which is always found in the [[phantasm]] which supports [[desire]] in as much as [[desire]] is only that which I have called the [[metonomy]] of all [[signification]].
I have only considered the beginning of the series of the integers, because it is an intermediary point between language and reality. Language is constituted by the same sort of unitary traits that I have used to explain the one and the one more. But this trait in language is not identical with the unitary trait, since in language we have a collection of differential traits. In other words, we can say that language is constituted by a set of signifiers — for example,<i> ba, ta, pa</i>) etc., etc. — a set which is finite. Each signifier is able to support the same process with regard to the subject, and it is very probable that the process of the integers is only a special case of this relation between signifiers. The definition of this collection of signifiers is that they constitute what I call the Other. The difference afforded by the existence of language is that each signifier (contrary to the unitary trait of the integer number) is, in most cases, not identical with itself — precisely because we have a collection of signifiers, and in this collection one signifier may or may not designate itself. This is well known and is the principle of Russell's paradox. If you take the set of all elements which are not members of themselves, the set that you constitute with such elements leads you to a paradox which, as you know, leads to a contradiction. In simple terms, this only means that in a universe of discourse nothing contains everything, and here you find again the gap that constitutes the subject. The subject is the introduction of a loss in reality, yet nothing can introduce that, since by status reality is as full as possible. The notion of a loss is the effect afforded by the instance of the trait which is what, with the intervention of the letter you determine, places — say al, a2, a3 — and the places are spaces for a lack. When the subject takes the place of the lack, a loss is introduced in the word, and this is the definition of the subject. But to inscribe it, it is necessary to define it in a circle, what I call the otherness, of the sphere of language. All that is language is lent from this otherness and this is why the subject is always a fading thing that runs under the chain of signifiers. For the definition of a signifier is that it represents a subject not for another subject but for another signifier. This is the only definition possible of the signifier as different from the sign. The sign is something that represents something for somebody, but the signifier is something that represents a subject for another signifier. The consequence is that the subject disappears exactly as in the case of the two unitary traits, while under the second signifier appears what is called meaning or signification; and then in sequence the other signifiers appear and other significations. The question of desire is that the fading subject yearns to find itself again by means of some sort of encounter with this miraculous thing defined by the phantasm. In its endeavor it is sustained by that which I call the lost object that I evoked in the beginning — which is such a terrible thing for the imagination. That which is produced and maintained here, and which in my vocabulary I call the object, lower-case, a, is well known by all psychoanalysts as all psychoanalysis is founded on the existence of this peculiar object. But the relation between this barred subject with this object (<i>a</i>) is the structure which is always found in the phantasm which supports desire in as much as desire is only that which I have called the metonomy of all signification. </p><p style="text-align: justify; line-height: 150%"><spacer size="20" type="horizontal" />In this brief presentation I have tried to show you what the question of the [[structure ]] is inside the [[psychoanalytical ]] [[reality]]. I have not, however, said anything about such dimensions as the [[imaginary ]] and the [[symbolical]]. It is, of course, absolutely essential to understand how the [[symbolic ]] [[order ]] can enter inside the<i>vécu</i>, lived experienced, of [[mental ]] [[life]], but I cannot tonight put forth such an explanation. Consider, however, that which is at the same time the least known and the most certain fact about this [[mythical ]] [[subject ]] which is the sensible phase of the [[living ]] [[being]]: this fathomless thing capable of experiencing something between [[birth ]] and [[death]], capable of covering the whole spectrum of [[pain ]] and [[pleasure ]] in a [[word]], what in [[French ]] we call the <i>[[sujet ]] de la [[jouissance]]</i>. When I came here this evening I saw on the little neon sign the motto "Enjoy Coca-Cola." It reminded me that in [[English]], I think, there is no term to designate precisely this enormous weight of [[meaning ]] which is in the [[French ]] [[word ]] <i>[[jouissance]]</i> — or in the [[Latin ]] <i>[[fruor]]</i>. In the dictionary I looked up <i>[[jouir]]</i> and found "to possess, to use" but it is not that at all. If the [[living ]] [[being ]] is something at all thinkable, it will be above all as [[subject ]] of the <i>[[jouissance]]</i>; but this [[psychological ]] [[law ]] that we call the [[pleasure principle ]] (and which is only the [[principle ]] of [[displeasure]]) is very soon to create a [[barrier ]] to all <i>jouissance</i>. If I am enjoying myself a little too much, I begin to feel [[pain ]] and I moderate my pleasures[[pleasure]]s. The organism seems made to avoid too much <i>[[jouissance]]</i>. Probably we would all be as quiet as oysters if it were not for this curious organization which forces us to disrupt the [[barrier ]] of [[pleasure ]] or perhaps only makes us [[dream ]] of forcing and disrupting this barrier. All that is elaborated by the [[subjective ]] [[construction ]] on the scale of the [[signifier ]] in its relation to the [[Other ]] and which has its root in [[language ]] is only there to permit the full spectrum of [[desire ]] to allow us to approach, to test, this sort of [[forbidden ]] <i>[[jouissance]]</i> which is the only valuable [[meaning ]] that is offered to our [[life]].
[[Category:Jacques Lacan]]
