No one without those precise conceptions of analysis which only a personal analysis can provide has any right to concern himself (or herself) with it. Ladies and Gentlemen, doubtless you fully conform to the strength of that ruling by Freud in the?New Introductory Lectures.

沒有那些只有個人分析才能提供的關于分析的精確概念，沒有權利涉及它。女士們先生們，毫無疑問，你們完全符合弗洛伊德在《（精神分析）新論》中的下的這個規(guī)矩。

Thus, articulated as a dilemma, a question raises itself for me in your regard.

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因此，在涉及到你們的問題時（這是一個難題），我會有一個疑問。

If, contravening this injunction, it is of psychoanalysis that I am going to speak, - then, by listening to someone whom you know to be incapable of producing the credentials which alone would authorize your assent, what are you doing here?

如果我要違反這個規(guī)矩不去談論精神分析的話 - 那么，只想拿到資格證書的你卻在這里聽一個無法給你提供證書的人講的話，是在這兒做什么呢？

Or, if my subject is not psychoanalysis, - then you who so faithfully attend here in order to become conversant with the problems which relate to the Freudian field, what are you doing here!

或者，如果我的主題不是精神分析 - 那么，你們這些為了熟悉與弗洛伊德領域相關問題而如此熱誠地參加這里的活動的人，是在這兒干什么呢！

And you above all, Ladies and Gentlemen the analysts, what are you doing here, you to whom Freud specifically addressed the warning not to rely on those who are not confirmed in the practice of your science, on those so-called authorities, those literary intellectuals, who bring their soup to warm at your fire, without so much as recognizing your hospitality? Even if he who reigns in your kitchens as head-chef could amuse himself by letting someone lower than the lowest kitchen boy get hold of the pot with which you are so naturally concerned since it is from it that you draw your sustenance, it was still uncertain - and I confess that I myself doubted - that you would be ready to drink in a soup merely cooked up in that way. And yet you are here. Permit me to marvel a moment at your presence, and at the privilege of your having lent me for a while that most precious of the organs at your disposal, your ear.

而分析師們，女士們和先生們，你們在這里做什么呢？弗洛伊德明確警告過你們，不要依賴那些沒有在你們的科學實踐中得到承認的人，不要依賴那些所謂的權威，那些文科知識分子，他們只是來尋求庇護而已，甚至沒有認識到你們的殷勤。即使掌管你們廚房的大廚可以玩笑般地讓比最低級的廚房男孩還低的人拿到你們關心的鍋，因為你們從中獲取生計，但仍然不確定（我承認我自己也懷疑）你們是否愿意喝那樣煮出來的湯。然而，你們還在這里。請允許我驚嘆一下你們的在場，以及非常榮幸你們借給我你們可支配的最寶貴的器官——你們的耳朵的特權。

Which I must now attempt to justify to it, and with reasons which are at least admissible.

現在我必須試圖向它（耳朵）證明，并且提出至少可以接受的理由。

I will not keep you waiting. The justification lies in this, which will come as no surprise after the developments which have so enchanted your hearing at this seminar since the start of the academic year, that the Freudian field is not representable as a closed surface. The opening up of psychoanalysis is not the effect of the liberalism, the whim, the blindness even of he who has set himself as its guardian. For, if not being situated on the inside does not relegate you to the outside, it is because at a certain point, excluded from a two-dimensional topology, the two surfaces join up and the periphery or outer edge crosses over the circumscription.

我不會讓你等太久。這個理由在這里，對于這個研討會自學年開始以來一直讓你們著迷聽到的發(fā)展，這并不會讓你們感到驚訝，那就是弗洛伊德領域無法被表示為一個封閉的表面。精神分析的開放不是自由主義的結果、也不是自命為它的守護者的心血來潮，甚至是盲目。而是因為如果不在內部并不使你被排除在外，那是因為在一個特定的，被排除在一個二維拓撲結構之外點上，兩個表面會相互連接，周邊或外緣會穿過界限。

That I can recognize and occupy that point is what releases you from the dilemma I presented to you, and entitles you to be listening to me today. Which will enable you to grasp, Ladies and Gentlemen, to what extent you arc implicated in my undertaking and how far its successful outcome concerns you.

我能夠認識并抓住這一點，這就將你們從我提出的難題中釋放出來，并使你們今天有權聽我講話。女士們和先生們，這將使你能夠理解你在我的事業(yè)中涉及到的程度以及它的成功結果對你的影響有多大。

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Concept of the Logic of the Signifier

能指之邏輯的概念

What I am aiming to restore, piecing together indications dispersed through the work of Jacques Lacan, is to be designated the logic of the signifier - it is a general logic in that its functioning is formal in relation to all fields of knowledge including that of psychoanalysis which, in acquiring a specificity there, it governs; it is a minimal logic in that within it are given those pieces only which arc necessary to assure it a progression reduced to a linear movement, uniformally generated at each point of its necessary sequence. That this logic should be called the logic of the signifier avoids the partiality of the conception which would limit its validity to the field in which it was first produced as a category; to correct its linguistic declension is to prepare the way for its importation into other discourses, an importation which we will not fail to carry out once we have grasped its essentials here.

我試圖通過整合散布在雅克·拉康的著作中的線索，來恢復所謂“能指的邏輯” - 它是一種普遍的邏輯，因為它的功能在所有知識領域中都是形式化的，包括精神分析領域，它在那里獲得了特殊性并起支配作用；它是一種最小邏輯，因為它只給出了那些必要的部分，以確保它的進展僅限于線性運動，在其必要序列的每個點都均勻地生成。將這種邏輯稱為“能指的邏輯”，避免了那種僅將其有效性限制在首次作為一種范疇出現的領域的局限性；修正它的語言變化，是為了為其引入到其他話語中鋪平道路，一旦我們在這里理解了它的要點，我們就不會放棄將它引入到其他領域的努力。

The chief advantage to be gained from this process of minimisation is the greatest economy of conceptual expenditure, which is then in danger of obscuring to you that the conjunctions which it effects between certain functions are so essential that to neglect them is to compromise analytic reasoning proper.

這種最小化處理的最大優(yōu)勢是概念使用的最大節(jié)約，但這也有可能會使你忽視它所實現的某些功能之間的聯結是如此重要，以至于忽略它們會損害分析推理的正確性。

By considering the relationship between this logic and that which I will call logician's logic, we see that its particularity lies in the fact that the first treats of the emergence of the second. and should be conceived of as the logic of the origin of logic - which is to say, chat it does not follow its laws, but that, prescribing their jurisdiction, itself falls outside that jurisdiction.

通過考慮這種邏輯（能指的邏輯）和我會稱之為“邏輯學家的邏輯”之間的關系，我們可以看出它的特殊性在于第一個處理了第二個的出現，并應被看作是邏輯的起源 - 換句話說，它不遵循邏輯法則，而是規(guī)定它們的管轄范圍，它本身則超出了那個范圍。

This dimension of the archeological can be grasped most succinctly through a movement back from the field of logic itself, where its miscognition. at its most radical because closest to is recognition is effected.

這種考古學的維度可以通過從它的誤認處返回自身的運動來最簡潔地把握，最根本是因為最接近它的認識被影響了。

That this step repeats something of that which Derrida has shown to be exemplary to phenomenology?[1]?will conceal to none but the most hasty this crucial difference, that here miscognition finds its point of departure in the production of meaning. We can say that it is constituted not as a forgetting, but as a repression.

這一步驟重復了德里達所展示的現象學的典范[1]，只有最草率的人會忽略了這個關鍵的區(qū)別，即這里的誤認是以意義的產生為出發(fā)點，它不是一種遺忘，而是一種壓抑。

To designate it I choose the name of suture. Suture names the relation of the subject to the chain of its discourse; we shall see that it figures there as the clement which is lacking, in the form of a stand-in. For, while there lacking, it is not purely and simply absent. Suture, by extension - the general relation of lack to the structure - of which it is an element, inasmuch as it implies the position of a taking-the-place-of.

我選擇使用“縫合”這個名稱來指代它?？p合指的是主體與其話語鏈的關系；我們將看到，它在那里被描繪為缺失的元素，以代理的形式存在。因為雖然它缺失，但它并不純粹地或簡單的缺席。從廣義上講，縫合——缺失與結構的一般關系，它是其中的一個元素，因為它意味著一個可被填充（替代）的位置。

It is the objective of this paper to articulate the concept of suture which, if it is not named explicitly as such by Jacques Lacan, is constantly present in his system.

本文的目的是闡述縫合的概念，盡管它并沒有被雅克·拉康明確地命名為縫合，但在他的體系中一直存在。

Let it be absolutely clear that it is not as philosopher or philosopher's apprentice that I am speaking here - if the philosopher is as characterized by Heinrich Heine in a sentence quoted by Freud, "with his nightcaps and the tatters of his dressing-gown, patching up the gaps in the structure of the universe". But take care not to think that the function of suturation is peculiar to the philosopher: what is specific to the philosopher is the determination of the field in which he operates as a "universal structure". It is important that you realize that the logician, like the linguist. also sutures at his particular level. And, quite as much. anyone who says "I".

讓我們非常清楚，我在這里講話并不是作為哲學家或哲學家的學徒 - 如果哲學家就像海因里?！ずＤ诟ヂ逡恋乱玫囊痪湓捴兴枋龅哪菢樱按┲乃焙退鄣钠撇?，修補宇宙結構中的缺口”。但是注意不要覺得縫合的功能是哲學家特有的：特定于哲學家的是確定他所操作的領域作為“普遍結構”。重要的是，你們要意識到，邏輯學家和語言學家在其特定的層面上也進行縫合。同樣，任何一個說“我”的人也是如此重要的縫合者。

In order to grasp suture we must cut across what a discourse makes explicit of itself, and distinguish from its meaning, its letter. This paper is concerned with a letter - a dead letter. It should come as no surprise if the meaning then dies.

為了理解縫合，我們必須跨越話語所明確表達的東西，并從其意義中區(qū)分出其字符。本文涉及一封信 - 一封無法到達的信。如果意義隨后消失，這并不會讓人感到驚訝。

The main thread of this analysis will be Gottlob Frege's argument in?Grundlagen der Arithmetik,?[2]?crucial here because it puts into question those terms which in Peano's axiomatic, adequate for a construction of a theory of natural numbers, are taken as primary - that is, the zero, the number, the successor.?[3]?This calling into question of the theory, by disintricating, from the axiomatic where the theory is consolidated, the suturing, delivers up this last.

本分析的主要線索會是戈特洛布·弗雷格在《算術基礎》中的論證[2]，這里是至關重要的，因為它對皮亞諾公理中被認為是基礎的那些術語提出了質疑 - 即零、數字和后繼數[3]。這一對理論的質疑，通過從統(tǒng)一的公理中解脫出來，縫合，最后得出了這個。

The Zero and the One

“零和一”

Here then is the question posed in its most general form;

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下面就是以最一般的形式提出的問題；

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what is it that functions in the series of whole natural numbers to which we can assign their progression?

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在我們可以指定其級數的整個自然數序列中，它的作用是什么？

?

And the answer, which I shall give at once before establishing it:

?

在確立它之前，我將立即給出答案：

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in the process of the constitution of the series,
in the genesis of progression,
the function of the subjet, miscognized is operative.

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在構成系列的過程中，

在級數的起源中，

在主體的功能中，誤認在起作用。

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This proposition will certainly appear as a paradox to anyone who knows that the logical discourse of Frege opens with the exclusion of that which is held by empiricist theory to be essential for the passage of the thing to the unit, and of the set of units to the unit of number: that is, the function of the subject, as support of the operations of abstraction and unification.

弗雷格的邏輯話語排除了經驗主義理論認為的對事物到單元以及單元集到數字單元之間的過渡至關重要的功能，即支持抽象和統(tǒng)一操作的主體功能，對于任何知道這一點的人來說，這個命題肯定會表現為一個悖論。

For the unity which is thus assured both for the individual and the set, it only holds in so far as the number functions as its name. Whence originates the ideology which makes of the subject the producer of fictions, short of recognizing it as the product of its product - an ideology in which logical and psychological discourse are wedded, with political discourse occupying the key position, which can be seen admitted in Occam, concealed in Locke, and miscognized thereafter.

因此，對于個體和集合而言，這種確保的統(tǒng)一只有在數字作為其名稱時才存在。這種意識形態(tài)的根源在于將主體視為虛構物的制造者，而不承認它是其產品的產物，這種意識形態(tài)將邏輯和心理話語結合在一起，并將政治話語置于關鍵位置，其在奧卡姆處被承認，又在洛克那兒被掩蓋，再被（人們）誤認為是正確的。

A subject therefore, defined by attributes whose other side is political, disposing as of powers, of a faculty of memory necessary to close the set without the loss of any of the interchangeable elements, and a faculty of repetition which operates inductively. There is no doubt that it is this subject which Frege, setting himself from the start against the empiricist foundation of arithmetic. excludes from the field in which the concept of the number is to appear.

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因此，一個主體，由其作為政治屬性的另一面定義，具有權力，具有閉合集合而不丟失任何可互換元素所必需的記憶能力，以及以歸納方式運作的重復能力。毫無疑問，正是這個主體，弗雷格從一開始就反對算術的經驗主義基礎，將其從數字概念出現的領域中排除出去。

But if it is held that the subject is not reducible, in its most essential function, to the psychological, then its exclusion from the field of number is assimilable to repetition. Which is what I have to demonstrate.

但是，如果認為主體在其最基本的功能上不可還原為心理學，則將其從數字領域中排除也是類似的重復。這就是我需要證明的。

You will be aware that Frege's discourse starts from the fundamental system comprising the three concepts of the concept, the object and the number, and two relations, that of the concept to the object, which is called subsumption and that of the concept to the number which I will call assignation. A number is assigned to a concept which subsumes objects.

你可能已經知道，弗雷格的論述從包括概念、對象和數字三個基本概念以及兩個關系構成的基本系統(tǒng)開始，即概念與對象之間的包含關系，以及我將稱之為指定關系的概念與數字之間的關系。數字被指定給包含對象的概念。

What is specifically logical about this system is that each concept is only defined and exists solely through the relation which it maintains as subsumer with that which it subsumes. Similarly, an object only has existence in so far as it falls under a concept, there being no other determination involved in its logical existence, so that the object takes its meaning from its difference to the thing integrated, by its spatio-temporal localization, to the real.

這個系統(tǒng)的邏輯特點在于每個概念只能通過它與所包含的對象之間的包含關系來定義和存在。同樣地，一個對象只有在它屬于一個概念的范疇時才存在，它的邏輯存在中沒有其他的規(guī)定性，因此對象（客體）通過其時空定位將其意義從其差異帶到事物的整體，再帶到真實。

Whence you can see the disappearance of the thing which must be effected in order for it to appear as object - which is the thing in so far as it is one,

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從那里你可以看到為了使它作為對象出現而必須實現的事物的消失——就這個物它被記為一而言

It is dear that the concept which operates in the system, formed solely through the determination of subsumption, is a redoubled concept: the concept of identity to a concept.

很明顯，在該系統(tǒng)中起作用的、僅通過包含關系的規(guī)定而形成概念，是一個加倍的概念：概念與概念的同一性。

This redoubling. induced in the concept by identity, engenders the logical dimension, because in effecting the disappearance of the thing it gives rise to the emergence of the numerable.

這種由同一性引起的概念的加倍，在概念中引起了邏輯維度，因為它在實現物的消失的同時引起了可計數性的出現。

For example, if I group what falls under the concept "child of Agamemnon and Cassandra", I summon in order to subsume them Pelops and Teledamus. To this set I can only assign a number if I put into play the concept "identical to the concept: child of Agamemnon and Cassandra". Through the effect of the fiction of this concept, the children now intervene in so far as each one is, so to speak, applied to itself - which transforms it into a unit, and gives to it the status of an object which is numerable as such. It is this one of the singular unit, this one of identity of the subsumed, which is common to all numbers in so far as they are first constituted as units.

例如，如果我將屬于“阿伽門農和卡珊德拉的孩子”概念的東西分組，我需要召喚珀羅普斯和泰勒達姆斯以便將它們歸入其中。只有當我運用“概念的同一性：阿伽門農和卡珊德拉的孩子”這個概念時，我才能給這個集合指派一個數字。通過這個概念的虛構效應，孩子們現在介入到彼此之間，每個孩子可以被視為應用于自身，這將其轉化為一個單位，并賦予它作為可計數對象的地位。正是這個單一的、與被包含者的同一性相關的單元，是所有數字所共有的，因為它們首先被構成為單元。

From this can be deduced the definition of the assignation of number: according to Frege "the number assigned to the concept F is the extension of the concept identical to the concept F". Frege's ternary system has as its effect that all that is left to the thing is the support of its identity with itself, by which it is the object of the operative concept, and hence numerable.

由此可以推導出數字的指定定義：根據弗雷格的說法，“指定給概念F的數字是與概念F相同的概念的外延”。弗雷格的三元系統(tǒng)其作用是，令事物只剩下與自身的同一性的支撐，因此成為可操作概念的對象，并由此獲得可計數性。

The process that I have just set out authorizes me to conclude the following proposition, whose relevance will emerge later, - the unit which could be called unifying of the concept in so far as it is assigned by the number is subordinate to the unit as distinctive in so far as it supports the number.

我剛剛闡述的過程使我得出以下命題，其相關性將在后面顯現出來：可以稱為概念統(tǒng)一的單位，只要它是由數字指定的，就從屬于支持數字的區(qū)分單位。

As for the position of the distinctive unit, its foundation is to be situated in the function of identity which, conferring on each thing of the world the property of being one, effects its transformation into an object of the (logical) concept.

至于區(qū)分單位的位置，它的基礎應該位于同一性的功能中，同一性賦予了世界上每個事物存在的屬性，使其成為（邏輯）概念的對象。

At this point in the construction, you will sense all the importance of the definition of identity which I am going to present.

在建構的這一階段，你將意識到我即將提出的同一性定義的所有重要性。

This definition which must give its true meaning to the concept of number, must borrow nothing from it?[4]?- precisely in order to engender numeration.

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這個定義必須賦予數字概念真正的意義，而絕不能從中借用任何東西——這正是為了產生計數功能。

This definition, which is pivotal to his system, Frege takes from Leibniz. It is contained in this statement:?eadem sunt quorum unum potest substitui alteri salva veritate. Those things are identical of which one can be substituted for the other?salva veritate?without loss of truth. Doubtless you can estimate the crucial importance of what is effected by this statement: the emergence of the function of truth. Yet what it assumes is more important than what it expresses. That is, identity-with-itself. That a thing cannot be substituted for itself, then where does this leave truth? Absolute is its subversion.

這個定義是弗雷格系統(tǒng)的關鍵所在，他從萊布尼茨那里借鑒了這個定義。它包含在這個陳述中：eadem sunt quorum unum potest substitui alteri salva veritate。（它們是相同的，其中一個可以代替另一個而不保留真理。）那些可以相互替換而不丟失真理的事物是同一的。毫無疑問，你可以估計到這個陳述所產生的至關重要性：真理功能的出現。然而，它所假定的比它所表達的更為重要，即自我同一性。一個事物不能代替它自己，那么這把真理留在了什么地方呢？（那）絕對是它的顛覆。

If we follow Leibniz's argument, the failing of truth whose possibility is opened up for an instant, its loss through the substitution for one thins of another, would be followed by its immediate reconstitution in a new relation: truth is recovered because the substituted thing, in that it is identical with itself, can be the object of a judgement and enter into the order of discourse: identical with itself, it can be articulated.

如果我們遵循萊布尼茨的論證，真理的失敗僅是一瞬間的可能性，真理的失去發(fā)生在一個事物被另一個事物替代時，但它會立即在一種新的關系中重建：真理被恢復是因為被替換的事物與自己同一，可以成為判斷的對象，并進入話語秩序中：與自身同一，它可以被清晰表達。

But that a thing should not be identical with itself subverts the field of truth, ruins it and abolishes it.

但是，如果一個事物不能與自己同一，就會顛覆真理領域，破壞它并廢除它。

You will grasp to what extent the preservation of truth is implicated in this identity with itself which connotes the passage from the thing to the object. Identity-with-itself is essential if truth is to be saved.

你會理解到，如果要保持真理，自我同一性對于從事物到對象的轉變至關重要。只有自我同一性是必不可少的，才能拯救真理。

Truth is. Each thing is identical with itself.

真理存在。每個事物都與自己同一。

Let us now put into operation Frege's schema, that is, go through the three-stage itinerary which he prescribes to us. Let there be a thing X of the world. Let there be the empirical concept of this X. The concept which finds a place in the schema is not this empirical concept but that which redoubles it, being "identical with the concept of X". The object which falls under this concept is X itself, as a unit. In this the number, which is the third term of the sequence, to be assigned to the concept of X will be the number 1. Which means that this function of the number 1 is repetitive for all things of the world. It is in this sense that this 1 is only the unit which constitutes the number as such, and not the 1 in its personal identity as number with its own particular place and a proper name in the series of numbers.

現在讓我們按照弗雷格的方案進行操作，走完他指導我們進行的三個階段的流程。假設世上有一個事物X。假設有這個X的經驗概念。在這個計劃中找到一個位置的概念不是這個經驗概念，而是將之加倍的概念，即“與X的概念同一”的概念。屬于這個概念下的對象是X本身作為一個單元。在此，指定給 X 概念的數列的第三項將是數字 1。這意味著數字1對于世界上所有事物來說都是重復的。從這個意義上說，這個1只是構成數字本身的單元，而不是作為數字的個人身份的1，作為個人身份的1的意思是它在數字系列中有自己的特定位置和專用名稱。

Furthermore, its construction demands that, in order to transform it, we call upon a thing of the world - which, according to Frege, cannot be: the logical must be sustained through nothing but itself.

此外，它的構建要求我們，為了轉化它，我們要調用世界上的一個物體，而根據弗雷格的說法，這是不可能的：邏輯必須只通過自身得到維持。

In order for the number to pass from the repetition of the 1 of the identical to that of its ordered succession, in order for the logical dimension to gain its autonomy definitively, without any reference to the real, the zero has to appear.

為了讓數字從相同的1的重復到有序的后繼中傳遞，為了讓邏輯維度最終獲得完全的自主性，而沒有任何對真實的參考，零就必須出現。

Which appearance is obtained because truth is, Zero is the assigned to the concept "not identical with itself". In effect, let there be the concept "not identical with itself". This concept, by virtue of being a concept, has an extension, subsumes an object. Which object? None. Since truth is, no object falls into the place of the subsumed of this concept, and the number which qualifies its extension is zero.

這種出現的獲得是因為真理存在，零被指定到了“與自身不同一”的概念。事實上，假設存在一個“與自身不同一”的概念。由于這個概念是一個概念，因此它有一個外延，包含一個對象。哪個對象？無。由于真理存在，沒有對象落入這個概念的被包含者的位置，限定其外延的數字是零。

In this engendering of the zero, I have stressed that it is supported by the proposition that truth is. If no object falls under the concept of non-identical-with-itself, it is because truth must be saved. If there are no things which are not identical with themselves, it is because non-identity with itself is contradictory to the very dimension of truth. To its concept, we assign the zero. It is this decisive proposition that the concept of not-identical-with-itself is assigned by the number zero which sutures logical discourse.

在零的產生過程中，我強調了它是由真理存在的命題所支持的。如果沒有對象落入“與自身不同一”的概念下，那是因為真理必須被拯救。如果沒有事物與自身不同一，那是因為與自身不同一與真理的維度相矛盾。對于它的概念，我們指定零。正是這個決定性的命題，即“與自身不同一”的概念通過被數字零所指定，縫合了邏輯話語。

For, and here I am working across Frege's text, in the autonomous construction of the logical through itself, it has been necessary, in order to exclude any reference to the real, to evoke on the level of the concept an object not-identical-with-itself, to be subsequently rejected from the dimension of truth.

因為，在邏輯通過自身的自主構建中，為了排除任何對實在的參考，就必須在概念層面上喚起一個與自身不同一的對象，隨后將其從真理維度中排除。這里我正在跨越弗雷格的文本進行分析。

The zero which is inscribed in the place of the number consummates the exclusion of this object. As for this place, marked out by subsumption, in which the object is lacking, there nothing can be written, and if a 0 must be traced, it is merely in order to figure a blank, to render visible the lack.

被零所標記的數字位置完成了對這個對象的排除。至于這個被包含者所標記的位置，在這個位置上對象是缺失的，沒有任何東西可以被書寫，如果必須繪制一個0，那僅僅是為了描繪一個空白，使缺失變得可見。

From the zero lack to the zero number, the non-conceptualisable is conceptualized.

從零的缺失到零這個數字，非可概念性被概念化了。

Let us now set aside the zero lack in order to consider only that which is produced by the alternation of its evocation and its revocation, the zero number.

現在我們暫時擱置零的缺失，只考慮它的喚起和撤銷的交替所產生的東西，即零的數字。

The zero understood as a number, which assigns to the subsuming concept the lack of an object, is as such a thing - the first non-real thing in thought.

零被理解為一個數字，將對象（客體）的缺失指定給包含概念，（其）會作為一個物，思維中的第一個非真實的物。

If of the number zero we construct the concept, it subsumes as its sole object the number zero. The number which assigns it is therefore 1.

如果我們從數字零構造概念，它所包含的唯一對象是數字零。指定給它的數字因此是1。

Frege's system works by the circulation of an element, at each of the places it fixes: from the number zero to its concept, from this concept to its object and to its number - a circulation which produces the 1.?[5]

是的，弗雷格的系統(tǒng)通過這種元素循環(huán)來工作，每個位置都有其固定的元素，從數字零到其概念，從概念到其對象和數字，最終產生數字1。

This system is thus so constituted with the 0 counting as 1. The counting of the 0 as 1 (whereas the concept of, the zero subsumes nothing in the real but a blank) is the general support of the series of numbers.

因此，這個系統(tǒng)是由0計為1所構成的。0被計為1（盡管零的概念在現實中僅包含一片空白），這是數字序列的普遍支撐。

It is this which is demonstrated by Frege's analysis of the operation of the successor, which consists of obtaining the number which follows n by adding to it a unit: n' the successor of n, is equal to n + 1, that is, ... n... (n + 1) = n'... Frege opens out the n + 1 in order to discover what is involved in the passage from n to its successor.

正是這一點，弗雷格通過對繼承者操作的分析證明了這一點，這個操作包括通過加上一個單元來獲得后繼的數字：n'是n的后繼，等于n + 1，即...n...（n + 1）= n'...弗雷格展開n + 1，以便發(fā)現從n到其后繼所涉及的內容。

You will grasp the paradox of this engendering as soon as I produce the most general formula for the successor which Frege arrives at: "the Number assigned to the concept?member of the series of natural numbers ending with n?follows in the series of natural numbers directly after n".

一旦我提出弗雷格得出的繼承者的最一般公式，你就會理解這種產生的悖論：“被指定給以n結尾的自然數系列成員的概念的數字，在自然數系列中直接跟在n后面。”

Let us take a number. The number three. It will serve to constitute the concept?member of the series of natural numbers ending with three. We find that the number assigned to this concept is four. Here then is the 1 of n + 1. Where does it come from? Assigned to its redoubled concept, the number 3 functions as the unifying name of a set: as reserve. In the concept of "member of the series of natural numbers ending with 3", it is the term (in the sense both of element and of final element).

讓我們以數字三為例。它將用來構成以三結尾的自然數系列成員的概念。我們發(fā)現被指定給這個概念的數字是四。這里就是n + 1的1來自哪里。數字3被指定給它的加倍概念，作為集合的統(tǒng)一名稱：作為儲備。在“以3結尾的自然數系列成員”的概念中，它是術語（在元素和最終元素的意義上）。

In the order of the real, the 3 subsumes 3 objects. In the order of number, which is that of discourse bound by truth, it is numbers which are counted: before the 3, there are 3 numbers - it is therefore the fourth.

在現實的秩序中，數字3包含3個對象。在數字的秩序中，即受真理約束的話語的秩序中，被計數的是數字：在數字3之前，有3個數字，因此它是第四個數字。

In the order of number, there if an addition the 0 and the 0 counts for 1. The displacement of a number, from the function of reserve to that of term, implies the summation of the 0. Whence the successor. That which in the real is pure and simple absence finds itself through the fact of number (through the instance of truth) noted 0 and counted for 1.

在數字的秩序中，如果進行加法運算，則0會計為1。數字從儲備的功能轉變?yōu)樾g語的功能，意味著0參與求和。這就是后繼的含義。在現實中純粹的缺席通過數字的事實（通過真理的實例）被標記為0并計為1。

Which is why we say the object not-identical with itself invoked-rejected by truth, instituted-annulled by discourse (subsumption as such) - in a word, sutured.

這就是為什么我們說，那個由真理喚起并拒絕的不同一于自身的對象，由話語（包含作為這樣的）建立和廢除 - 一言以蔽之，縫合。

The emergence of the lack as 0, and of 0 as 1 determines the appearance of the successor. Let there be n; the lack is fixed as which is fixed as 1: n + 1; which is added in order to give n' - which absorbs the 1.

缺失作為0的出現，以及0作為1決定了后繼的出現。假設有n；缺失被固定為1：n + 1；這個1被加上以給出n'，它吸收了1。

Certainly, if the Lot n + 1 is nothing other than the counting the zero, the function of addition of the sign + is superfatory, and we must restore to the horizontal representation of the engendering its verticality: the 1 is to be taken as the primary symbol of the emergence of lack in the field of truth, and the sign + indicates the crossing, the transgression through which the 0 lack comes to be represented as 1, producing, through this difference of n to n' which you have seen to be an effect of meaning the name of a number.

確實，如果數字n + 1不過是對零的計數，那么加號符號的功能就是多余的，我們必須恢復水平表征以生成垂直方向：1被視為真理領域中缺失出現的主要符號，加號符號表示跨越、違反，通過這種差異，零的缺失被表示為1，產生了n到n'的差異，而你已經看到這是一個數字名稱的意義的產物。

Logical representation collapses this three-level construction. The operation I have effected opens it out. If you consider the opposition of these two axes, you will understand what is at stake in logical suturing, and the difference of the logic which I am putting forward to logician's logic.

邏輯表示使這個三層結構崩潰。我所進行的操作展開了這個結構。如果你考慮這兩個軸的對立，你就會理解邏輯縫合所涉及的問題，以及我提出的邏輯（能指的邏輯）與邏輯學家的邏輯的區(qū)別。

That zero is a number: such is the proposition which assures logical dimension of its closure.

零是一個數字：這是保證邏輯維度封閉的命題。

Our purpose has been to recognize in the zero number the suturing stand-in for the lack.

我們的目的是在數字零中識別出縫合代替缺失。

Remember here the hesitation perpetuated in the work of Bertand Russell concerning its localization (interior? or exterior to the series of numbers?).

在這里，記住伯特蘭·羅素在他的工作中關于零的定位（內部？還是外部于數字系列？）所持續(xù)的猶豫。

The generating repetition of the series of numbers is sustained by this, that the zero lack passes, first along a vertical axis, across the bar which limits the field of truth in order to be represented there as one, subsequently cancelling out as meaning in each of the names of the numbers which are caught up in the metonymic chain of successional progression.

數字系列的生成中的重復是以此為支撐的，即零的缺失首先沿著垂直軸通過限制真理領域的障礙為了以1的形式被表示在那里，隨后取消了在每個數字的名稱中的含義，這些數字被卷入了連續(xù)進行的轉喻鏈中。

Just as the zero as lack of the contradictory object must be distinguished from that which sutures this absence in the series of numbers, so the 1, as the proper name of a number, is to be distinguished from that which comes to fix in a trait the zero of the not-identical with itself sutured by the identity with itself, which is the law of discourse in the field of truth. The central paradox to be grasped (which as you will see in a moment is the paradox of the signifier in the sense of Lacan) is that the trait of the identical represents the non-identical, whence is deduced the impossibility of its redoubling,?[6]?and from that impossibility the structure of repetition, as the process of differentiation of the identical.

正如零作為矛盾對象的缺失必須與在數字系列中縫合這種缺失的東西區(qū)分開來一樣，數字1作為一個數字的專用名稱也應該與將不同于自身的零通過自身的同一性縫合在特征中的東西區(qū)分開來，這是真理領域話語的法則。需要理解的中心悖論（正如你馬上會看到的，這是拉康所說的能指的悖論）是，同一個特征代表了不同的東西，從而推導出其加倍的不可能性，從這個不可能性中推導出重復的結構，作為同一的差異化的過程。

Now, if the series of numbers, metonymy of the zero, begins with its metaphor, if the o member of the series as number is only the standing-in-place suturing the absence (of the absolute zero) which moves beneath the chain according to the alternation of a representation and an exclusion - then what is there to stop us from seeing in the restored relation of the zero to the series of numbers the most elementary articulation of the subject's relation to the signifying chain?
現在，如果數字系列是對零的轉喻，并從它的隱喻開始，如果數字系列中的0成員僅作為數字的代表位置來縫合缺失（絕對的零）的缺席，其根據表征和排斥的交替在轉喻鏈條下方運動 - 那么在零與數字系列的恢復關系中，我們有什么理由不將其視為主體與能指鏈的最基本表達？

The impossible object, which the discourse of logic summons as the not-identical with itself and then rejects as the pure negative, which it summons and rejects in order to constitute itself as that which it is, which it summons and rejects wanting to know nothing of it, we name this object, in so far as it functions as the excess which operates in the series of numbers, the subject.

邏輯話語召喚不同一于自身的不可能對象，然后將其拒絕為純粹否定。邏輯召喚并拒絕它以構成它之所是，它召喚并拒絕希望對它一無所知。我們將這個對象稱為主體，就其作用而言，它是在數字系列中運轉的多余部分。

Its exclusion from the discourse which internally it intimates is suture.

它從它在內部暗示的話語中被排除，這種排除就是縫合。

If we now determine the trail as the signifier, and ascribe to the number the position of signified, the relation of lack to the trait should be considered as the logic of the signifier.

如果我們現在將軌跡確定為能指，將數字歸屬為所指的位置，那么缺失與特征的關系應被視為能指的邏輯。

Relation of Subject and Signifier

主體與能指的關系

In effect, what in Lacanian algebra is called the relation of the subject to the field of the Other (as the locus of truth) can be identified with the relation which the zero entertains with the identity of the unique as the support of truth. This relation, in so far as it is matrical, cannot be integrated into any definition of objectivity - this being the doctrine of Lacan. The engendering of the zero, from this not-identical with itself under which no thing of the world falls, illustrates this to you.

?

實際上，在拉康代數中被稱為主體與大他者場域（作為真理的場所）的關系可以等同于零與作為真理支撐的獨特性的同一性所具有的關系。這種關系，就其矩陣性而言，不能被整合到任何客觀性的定義中——這就是拉康的學說。零的產生（即來自于這個世界上沒有任何事物落入其下的與自身的不同）闡明了這一點。

What constitutes this relation as the matrix of the chain must be isolated in the implication which makes the determinant of the exclusion of the subject outside the field of the Other its representation in that field in the form of the one of the unique, one of distinctive unity, which is called "unary" by Lacan. In algebra, this exclusion is marked by the bar which strikes the S of the subject in from of the capital A, and which is displaced by the identity of the subject onto the A, according to the fundamental exchange of the logic of the signifier, a displacement whose effect is the emergence of signification signified to the subject. Untouched by the exchange of the bar, this exteriority of the subject to the Other is maintained, which institutes the unconscious.

將這種關系構成為鏈條矩陣的東西必須在蘊涵中被隔離，就是說這使得主體被排除在大他者領域之外的決定因素在該領域中以獨一且特別的統(tǒng)一體之一的形式表現出來，拉康稱之為“一元”。 在（拉康）代數中，根據能指邏輯的基本交換，這種排除的標志是從大寫字符 A 中擊中主體 S 的橫杠，并通過主體的身份將其置換到 A 上， 這種移置的效果是使得主體所指意義的出現。 不受橫杠交換的影響，主體對大他者的這種外在性得以維持，無意識從而建立了起來。

For: - if it is clear that the tripartition which divides (1) the signified-to-the-subject, (2) the signifying chain whose radical alterity in relation to the subject cuts off the subject from its field, and finally (3) the external field of this reject, cannot be covered by the linguistic dichotomy of signified and signifier; - if the consciousness of the subject is to be situated on the level of the effects of signification, governed, so much so that they could even be called its reflections, by the repetition of the signifier: - if repetition itself is produced by the vanishing of the subject and its passage as lack - then only the unconscious can name the progression which constitutes the chain in the order of thought.

因為：- 如果很明顯，三分法將分成 (1) 所指與主體，(2) 用其與主體相關的根本他異性將主體從其場域中切斷的能指鏈，以及最后 (3) 這個拒絕的外部場域，不能被所指和能指的語言二分法所涵蓋； - 如果主體的意識要被置于意指效果的水平上，并被能指的重復所支配，以至于它們甚至可以被稱為它的反映： - 如果重復本身是由主體的消失以及其作為缺失的通道產生的——那么只有無意識才能命名構成思想順序鏈條的進程。

On the level of this constitution, the definition of the subject comes down to the possibility of one signifier more.

在這一構成層面上，主體的定義可以歸結為超出一個能指的可能性。

Is it not ultimately to this function of excess that can be referred the power of thematisation, which Dedekind assigns to the subject in order to give to set theory its theorem of existence? The possibility of existence of an enumerable infinity can be explained by this, that "from the moment that one proposition is true, 1 can always produce a second, that is, that the first is true and so on to infinity".?[7]

難道最終不是這種過度的功能可以被稱為主題化的力量，戴德金將其指定給主體以便為集合論提供其存在定理嗎？ 可數無窮存在的可能性可以這樣解釋，即“從一個命題為真那一刻起，1總能產生第二個，即第一個為真，以此類推至無窮大”。 [7]

In order to ensure that this recourse to the subject as the founder of iteration is not a recourse to psychology, we simply substitute for thematisation the representation of the subject (as signifier) which excludes consciousness because it is not effected for someone, but, in the chain, in the field of truth, for the signifier which precedes it. When Lacan faces the definition of the sign as that which represents something for someone, with that of the signifier as that which represents the subject for another signifier, he is stressing that in so far as the signifying chain is concerned, it is on the level of its effects and not of its cause that consciousness is to be situated. The insertion of the subject into the chain is representation, necessarily correlative to an exclusion which is a vanishing.

為了確保這種求助于作為迭代創(chuàng)始人的主體不是求助于心理學，我們簡單地用主題化代替主體的表征（作為能指），它排除了意識，因為它不會對某人產生影響，而是在在鏈條上、在真理的領域對它之前的能指產生影響。 當拉康將標志定義成為某人代表某物，將能指定義成為另一個能指代表主體時，他是在強調，意識是被定位在能指鏈的影響而不是能指鏈的原因的水平上。主體對能指鏈的插入中是再現，必然與一個正在消失的排除相關。

If now we were to try and develop in time the relation which engenders and supports the signifying chain, we would have to take into account the fact that temporal succession is under the dependency of the linearity of the chain. The time of engendering can only be circular - which is why both these propositions are true at one and the same time, that subject is anterior to signifier and that signifier is anterior to subject - but only appears as such after the introduction of the signifier. The retroaction consists essentially of this: the birth of linear time. We must hold together the definitions which make the subject the effect of the signifier and the signifier the representative of the subject: it is a circular, though non-reciprocal, relation.

如果現在我們要嘗試在時間上發(fā)展產生和支撐能指鏈的關系，我們將不得不考慮這樣一個事實，即時間的連續(xù)性依賴于能指鏈的線性。產生的時間只能是循環(huán)的——這就是為什么這兩個命題同時為真，主體先于能指，能指先于主體——但只有在引入能指之后才出現?；厮葜饕ǎ壕€性時間的誕生。 我們必須把使主體成為能指的效果和使能指成為主體的代表的定義放在一起：它是一種循環(huán)的但非相應的關系。

By crossing logical discourse at its point of least resistance, that of its suture, you can see articulated the structure of the subject: as a "flickering in eclipses", like the movement which opens and closes the number, and delivers up the lack in the form of the 1 in order to abolish it in the successor.

通過在邏輯話語阻抗最小的地方，即它的縫合點，你可以看到清晰的主體結構：作為“日食中的閃爍”，就像打開和關閉數字的運動，并以一的形式提供了缺失，以便在后繼數中廢除它。

As for the + you have understood the unprecedented function which it takes on in the logic of the signifier (a sign, no longer of addition, but of that summation of the subject in the field of the Other, which calls for its annulment). It remains to disarticulate it in order to separate the unary trait of emergence, and the bar of the reject: thereby making manifest the division of the subject which is the other name for its alienation.

至于 + ，你已經理解了它在能指邏輯中所承擔的前所未有的功能（一個標志，不再是加法，而是主體在要求它被取消的大他者場域中的總和）。為了分離涌現的單一特征和拒絕的障礙，仍然需要拆散它：從而表明主體的分裂，這是其異化的另一個名稱。

It will be deduced from this that the signifying chain is structure of the structure.
由此可知，能指鏈是結構的結構。

If structural causality (causality in the structure in so far as the subject is implicated in it) is not an empty expression, it is from the minimal logic which I have developed here that it will find its status.
如果結構因果關系（就主體牽涉其中而言的結構中的因果關系）不是一個空洞的表達，那么它將從我在這里發(fā)展的最小邏輯中找到它的地位。

We leave for another time the construction of its concept.
我們下次再討論其概念的構建。
Notes:

[1]?Edmund Husserl,?L'origine de la géometrie, translation and introduction by Jacques Derrida, PUF, 1962.

[2]?German text with English translation published under the title?The Foundations of Arithmetic, Basil Blackwell, 1953.

[3]?Our reading will not concern itself with any of Frege'g various inflections of his basic purpose, and will therefore keep outside the thematisation of the difference of meaning and reference, as well as of the later definition of the concept in terms of predication, from which is deduced its non-saturation.

[4]?Which is why we must say identity and not equality.

[5]?I leave aside the commentary of paragraph 76 which gives the abstract definition of contiguity.

[6]?And, at another level, the impossibility of meta-language (cf by Jacques Lacan,?Cahiers pour 1'analyse, No I, 1966).

[7]?Dedekind, quoted by Cavailles (Philosophie mathémathique, p 124, Hermann, 1962).

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