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.

没有那些只有个人分析才能提供的关于分析的精确概念，没有权利涉及它。女士们先生们，毫无疑问，你们完全符合弗洛伊德在《（精神分析）新论》中的下的这个规矩。

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

 

因此，在涉及到你们的问题时（这是一个难题），我会有一个疑问。

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?

如果我要违反这个规矩不去谈论精神分析的话 - 那么，只想拿到资格证书的你却在这里听一个无法给你提供证书的人讲的话，是在这儿做什么呢？

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，如果我的主题不是精神分析 - 那么，你们这些为了熟悉与弗洛伊德领域相关问题而如此热诚地参加这里的活动的人，是在这儿干什么呢！

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.

而分析师们，女士们和先生们，你们在这里做什么呢？弗洛伊德明确警告过你们，不要依赖那些没有在你们的科学实践中得到承认的人，不要依赖那些所谓的权威，那些文科知识分子，他们只是来寻求庇护而已，甚至没有认识到你们的殷勤。即使掌管你们厨房的大厨可以玩笑般地让比最低级的厨房男孩还低的人拿到你们关心的锅，因为你们从中获取生计，但仍然不确定（我承认我自己也怀疑）你们是否愿意喝那样煮出来的汤。然而，你们还在这里。请允许我惊叹一下你们的在场，以及非常荣幸你们借给我你们可支配的最宝贵的器官——你们的耳朵的特权。

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

现在我必须试图向它（耳朵）证明，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.

我不会让你等太久。这个理由在这里，对于这个研讨会自学年开始以来一直让你们着迷听到的发展，这并不会让你们感到惊讶，那就是弗洛伊德领域无法被表示为一个封闭的表面。精神分析的开放不是自由主义的结果、也不是自命为它的守护者的心血来潮，甚至是盲目。而是因为如果不在内部并不使你被排除在外，那是因为在一个特定的，被排除在一个二维拓扑结构之外点上，两个表面会相互连接，周边或外缘会穿过界限。

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.

我能够认识并抓住这一点，这就将你们从我提出的难题中释放出来，并使你们今天有权听我讲话。女士们和先生们，这将使你能够理解你在我的事业中涉及到的程度以及它的成功结果对你的影响有多大。

 

Concept of the Logic of the Signifier

能指之逻辑的概念

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.

我试图通过整合散布在雅克·拉康的著作中的线索，来恢复所谓“能指的逻辑” - 它是一种普遍的逻辑，因为它的功能在所有知识领域中都是形式化的，包括精神分析领域，它在那里获得了特殊性并起支配作用；它是一种最小逻辑，因为它只给出了那些必要的部分，以确保它的进展仅限于线性运动，在其必要序列的每个点都均匀地生成。将这种逻辑称为“能指的逻辑”，避免了那种仅将其有效性限制在首次作为一种范畴出现的领域的局限性；修正它的语言变化，是为了为其引入到其他话语中铺平道路，一旦我们在这里理解了它的要点，我们就不会放弃将它引入到其他领域的努力。

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.

这种最小化处理的最大优势是概念使用的最大节约，但这也有可能会使你忽视它所实现的某些功能之间的联结是如此重要，以至于忽略它们会损害分析推理的正确性。

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.

通过考虑这种逻辑（能指的逻辑）和我会称之为“逻辑学家的逻辑”之间的关系，我们可以看出它的特殊性在于第一个处理了第二个的出现，并应被看作是逻辑的起源 - 换句话说，它不遵循逻辑法则，而是规定它们的管辖范围，它本身则超出了那个范围。

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.

这种考古学的维度可以通过从它的误认处返回自身的运动来最简洁地把握，最根本是因为最接近它的认识被影响了。

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.

这一步骤重复了德里达所展示的现象学的典范[1]，只有最草率的人会忽略了这个关键的区别，即这里的误认是以意义的产生为出发点，它不是一种遗忘，而是一种压抑。

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.

我选择使用“缝合”这个名称来指代它。缝合指的是主体与其话语链的关系；我们将看到，它在那里被描绘为缺失的元素，以代理的形式存在。因为虽然它缺失，但它并不纯粹地或简单的缺席。从广义上讲，缝合——缺失与结构的一般关系，它是其中的一个元素，因为它意味着一个可被填充（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.

本文的目的是阐述缝合的概念，尽管它并没有被雅克·拉康明确地命名为缝合，但在他的体系中一直存在。

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".

让我们非常清楚，我在这里讲话并不是作为哲学家或哲学家的学徒 - 如果哲学家就像海因里希·海涅在弗洛伊德引用的一句话中所描述的那样，“穿着他的睡帽和睡袍的破布，修补宇宙结构中的缺口”。但是注意不要觉得缝合的功能是哲学家特有的：特定于哲学家的是确定他所操作的领域作为“普遍结构”。重要的是，你们要意识到，逻辑学家和语言学家在其特定的层面上也进行缝合。同样，任何一个说“我”的人也是如此重要的缝合者。

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.

为了理解缝合，我们必须跨越话语所明确表达的东西，并从其意义中区分出其字符。本文涉及一封信 - 一封无法到达的信。如果意义随后消失，这并不会让人感到惊讶。

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.

本分析的主要线索会是戈特洛布·弗雷格在《算术基础》中的论证[2]，这里是至关重要的，因为它对皮亚诺公理中被认为是基础的那些术语提出了质疑 - 即零、数字和后继数[3]。这一对理论的质疑，通过从统一的公理中解脱出来，缝合，最后得出了这个。

The Zero and the One

“零和一”

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

 

下面就是以最一般的形式提出的问题；

 

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

 

在我们可以指定其级数的整个自然数序列中，它的作用是什么？

 

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

 

在确立它之前，我将立即给出答案：

 

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

 

在构成系列的过程中，

在级数的起源中，

在主体的功能中，误认在起作用。

 

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.

弗雷格的逻辑话语排除了经验主义理论认为的对事物到单元以及单元集到数字单元之间的过渡至关重要的功能，即支持抽象和统一操作的主体功能，对于任何知道这一点的人来说，这个命题肯定会表现为一个悖论。

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，对于个体和集合而言，这种确保的统一只有在数字作为其名称时才存在。这种意识形态的根源在于将主体视为虚构物的制造者，而不承认它是其产品的产物，这种意识形态将逻辑和心理话语结合在一起，并将政治话语置于关键位置，其在奥卡姆处被承认，又在洛克那儿被掩盖，再被（人们）误认为是正确的。

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.

 

因此，一个主体，由其作为政治属性的另一面定义，具有权力，具有闭合集合而不丢失任何可互换元素所必需的记忆能力，以及以归纳方式运作的重复能力。毫无疑问，正是这个主体，弗雷格从一开始就反对算术的经验主义基础，将其从数字概念出现的领域中排除出去。

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，如果认为主体在其最基本的功能上不可还原为心理学，则将其从数字领域中排除也是类似的重复。这就是我需要证明的。

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.

你可能已经知道，弗雷格的论述从包括概念、对象和数字三个基本概念以及两个关系构成的基本系统开始，即概念与对象之间的包含关系，以及我将称之为指定关系的概念与数字之间的关系。数字被指定给包含对象的概念。

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.

这个系统的逻辑特点在于每个概念只能通过它与所包含的对象之间的包含关系来定义和存在。同样地，一个对象只有在它属于一个概念的范畴时才存在，它的逻辑存在中没有其他的规定性，因此对象（客体）通过其时空定位将其意义从其差异带到事物的整体，再带到真实。

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,

 

从那里你可以看到为了使它作为对象出现而必须实现的事物的消失——就这个物它被记为一而言

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.

很明显，在该系统中起作用的、仅通过包含关系的规定而形成概念，是一个加倍的概念：概念与概念的同一性。

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.

这种由同一性引起的概念的加倍，在概念中引起了逻辑维度，因为它在实现物的消失的同时引起了可计数性的出现。

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，如果我将属于“阿伽门农和卡珊德拉的孩子”概念的东西分组，我需要召唤珀罗普斯和泰勒达姆斯以便将它们归入其中。只有当我运用“概念的同一性：阿伽门农和卡珊德拉的孩子”这个概念时，我才能给这个集合指派一个数字。通过这个概念的虚构效应，孩子们现在介入到彼此之间，每个孩子可以被视为应用于自身，这将其转化为一个单位，并赋予它作为可计数对象的地位。正是这个单一的、与被包含者的同一性相关的单元，是所有数字所共有的，因为它们首先被构成为单元。

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.

由此可以推导出数字的指定定义：根据弗雷格的说法，“指定给概念F的数字是与概念F相同的概念的外延”。弗雷格的三元系统其作用是，令事物只剩下与自身的同一性的支撑，因此成为可操作概念的对象，并由此获得可计数性。

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.

我刚刚阐述的过程使我得出以下命题，其相关性将在后面显现出来：可以称为概念统一的单位，只要它是由数字指定的，就从属于支持数字的区分单位。

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.

至于区分单位的位置，它的基础应该位于同一性的功能中，同一性赋予了世界上每个事物存在的属性，使其成为（逻辑）概念的对象。

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

在建构的这一阶段，你将意识到我即将提出的同一性定义的所有重要性。

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.

 

这个定义必须赋予数字概念真正的意义，而绝不能从中借用任何东西——这正是为了产生计数功能。

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.

这个定义是弗雷格系统的关键所在，他从莱布尼茨那里借鉴了这个定义。它包含在这个陈述中：eadem sunt quorum unum potest substitui alteri salva veritate。（它们是相同的，其中一个可以代替另一个而不保留真理。）那些可以相互替换而不丢失真理的事物是同一的。毫无疑问，你可以估计到这个陈述所产生的至关重要性：真理功能的出现。然而，它所假定的比它所表达的更为重要，即自我同一性。一个事物不能代替它自己，那么这把真理留在了什么地方呢？（那）绝对是它的颠覆。

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.

如果我们遵循莱布尼茨的论证，真理的失败仅是一瞬间的可能性，真理的失去发生在一个事物被另一个事物替代时，但它会立即在一种新的关系中重建：真理被恢复是因为被替换的事物与自己同一，可以成为判断的对象，并进入话语秩序中：与自身同一，它可以被清晰表达。

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

但是，如果一个事物不能与自己同一，就会颠覆真理领域，破坏它并废除它。

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.

你会理解到，如果要保持真理，自我同一性对于从事物到对象的转变至关重要。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。每个事物都与自己同一。

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.

现在让我们按照弗雷格的方案进行操作，走完他指导我们进行的三个阶段的流程。假设世上有一个事物X。假设有这个X的经验概念。在这个计划中找到一个位置的概念不是这个经验概念，而是将之加倍的概念，即“与X的概念同一”的概念。属于这个概念下的对象是X本身作为一个单元。在此，指定给 X 概念的数列的第三项将是数字 1。这意味着数字1对于世界上所有事物来说都是重复的。从这个意义上说，这个1只是构成数字本身的单元，而不是作为数字的个人身份的1，作为个人身份的1的意思是它在数字系列中有自己的特定位置和专用名称。

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，它的构建要求我们，为了转化它，我们要调用世界上的一个物体，而根据弗雷格的说法，这是不可能的：逻辑必须只通过自身得到维持。

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.

为了让数字从相同的1的重复到有序的后继中传递，为了让逻辑维度最终获得完全的自主性，而没有任何对真实的参考，零就必须出现。

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.

这种出现的获得是因为真理存在，零被指定到了“与自身不同一”的概念。事实上，假设存在一个“与自身不同一”的概念。由于这个概念是一个概念，因此它有一个外延，包含一个对象。哪个对象？无。由于真理存在，没有对象落入这个概念的被包含者的位置，限定其外延的数字是零。

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.

在零的产生过程中，我强调了它是由真理存在的命题所支持的。如果没有对象落入“与自身不同一”的概念下，那是因为真理必须被拯救。如果没有事物与自身不同一，那是因为与自身不同一与真理的维度相矛盾。对于它的概念，我们指定零。正是这个决定性的命题，即“与自身不同一”的概念通过被数字零所指定，缝合了逻辑话语。

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.

因为，在逻辑通过自身的自主构建中，为了排除任何对实在的参考，就必须在概念层面上唤起一个与自身不同一的对象，随后将其从真理维度中排除。这里我正在跨越弗雷格的文本进行分析。

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.

被零所标记的数字位置完成了对这个对象的排除。至于这个被包含者所标记的位置，在这个位置上对象是缺失的，没有任何东西可以被书写，如果必须绘制一个0，那仅仅是为了描绘一个空白，使缺失变得可见。

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

从零的缺失到零这个数字，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.

现在我们暂时搁置零的缺失，只考虑它的唤起和撤销的交替所产生的东西，即零的数字。

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.

零被理解为一个数字，将对象（客体）的缺失指定给包含概念，（其）会作为一个物，思维中的第一个非真实的物。

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.

如果我们从数字零构造概念，它所包含的唯一对象是数字零。指定给它的数字因此是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，弗雷格的系统通过这种元素循环来工作，每个位置都有其固定的元素，从数字零到其概念，从概念到其对象和数字，最终产生数字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，这个系统是由0计为1所构成的。0被计为1（尽管零的概念在现实中仅包含一片空白），这是数字序列的普遍支撑。

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.

正是这一点，弗雷格通过对继承者操作的分析证明了这一点，这个操作包括通过加上一个单元来获得后继的数字：n'是n的后继，等于n + 1，即...n...（n + 1）= n'...弗雷格展开n + 1，以便发现从n到其后继所涉及的内容。

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继承者的最一般公式，你就会理解这种产生的悖论：“被指定给以n结尾的自然数系列成员的概念的数字，在自然数系列中直接跟在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).

让我们以数字三为例。它将用来构成以三结尾的自然数系列成员的概念。我们发现被指定给这个概念的数字是四。这里就是n + 1的1来自哪里。数字3被指定给它的加倍概念，作为集合的统一名称：作为储备。在“以3结尾的自然数系列成员”的概念中，它是术语（在元素和最终元素的意义上）。

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.

在现实的秩序中，数字3包含3个对象。在数字的秩序中，即受真理约束的话语的秩序中，被计数的是数字：在数字3之前，有3个数字，因此它是第四个数字。

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.

在数字的秩序中，如果进行加法运算，则0会计为1。数字从储备的功能转变为术语的功能，意味着0参与求和。这就是后继的含义。在现实中纯粹的缺席通过数字的事实（通过真理的实例）被标记为0并计为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.

这就是为什么我们说，那个由真理唤起并拒绝的不同一于自身的对象，由话语（包含作为这样的）建立和废除 - 一言以蔽之，缝合。

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.

缺失作为0的出现，以及0作为1决定了后继的出现。假设有n；缺失被固定为1：n + 1；这个1被加上以给出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.

确实，如果数字n + 1不过是对零的计数，那么加号符号的功能就是多余的，我们必须恢复水平表征以生成垂直方向：1被视为真理领域中缺失出现的主要符号，加号符号表示跨越、违反，通过这种差异，零的缺失被表示为1，产生了n到n'的差异，而你已经看到这是一个数字名称的意义的产物。

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.

逻辑表示使这个三层结构崩溃。我所进行的操作展开了这个结构。如果你考虑这两个轴的对立，你就会理解逻辑缝合所涉及的问题，以及我提出的逻辑（能指的逻辑）与逻辑学家的逻辑的区别。

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

零是一个数字：这是保证逻辑维度封闭的命题。

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

我们的目的是在数字零中识别出缝合代替缺失。

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

在这里，记住伯特兰·罗素在他的工作中关于零的定位（内部？还是外部于数字系列？）所持续的犹豫。

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.

数字系列的生成中的重复是以此为支撑的，即零的缺失首先沿着垂直轴通过限制真理领域的障碍为了以1的形式被表示在那里，随后取消了在每个数字的名称中的含义，这些数字被卷入了连续进行的转喻链中。

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.

正如零作为矛盾对象的缺失必须与在数字系列中缝合这种缺失的东西区分开来一样，数字1作为一个数字的专用名称也应该与将不同于自身的零通过自身的同一性缝合在特征中的东西区分开来，这是真理领域话语的法则。需要理解的中心悖论（正如你马上会看到的，这是拉康所说的能指的悖论）是，同一个特征代表了不同的东西，从而推导出其加倍的不可能性，从这个不可能性中推导出重复的结构，作为同一的差异化的过程。

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?
现在，如果数字系列是对零的转喻，并从它的隐喻开始，如果数字系列中的0成员仅作为数字的代表位置来缝合缺失（绝对的零）的缺席，其根据表征和排斥的交替在转喻链条下方运动 - 那么在零与数字系列的恢复关系中，我们有什么理由不将其视为主体与能指链的最基本表达？

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.

逻辑话语召唤不同一于自身的不可能对象，然后将其拒绝为纯粹否定。逻辑召唤并拒绝它以构成它之所是，它召唤并拒绝希望对它一无所知。我们将这个对象称为主体，就其作用而言，它是在数字系列中运转的多余部分。

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

它从它在内部暗示的话语中被排除，这种排除就是缝合。

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.

如果我们现在将轨迹确定为能指，将数字归属为所指的位置，那么缺失与特征的关系应被视为能指的逻辑。

Relation of Subject and Signifier

主体与能指的关系

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.

 

实际上，在拉康代数中被称为主体与大他者场域（作为真理的场所）的关系可以等同于零与作为真理支撑的独特性的同一性所具有的关系。这种关系，就其矩阵性而言，不能被整合到任何客观性的定义中——这就是拉康的学说。零的产生（即来自于这个世界上没有任何事物落入其下的与自身的不同）阐明了这一点。

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.

将这种关系构成为链条矩阵的东西必须在蕴涵中被隔离，就是说这使得主体被排除在大他者领域之外的决定因素在该领域中以独一且特别的统一体之一的形式表现出来，拉康称之为“一元”。 在（拉康）代数中，根据能指逻辑的基本交换，这种排除的标志是从大写字符 A 中击中主体 S 的横杠，并通过主体的身份将其置换到 A 上， 这种移置的效果是使得主体所指意义的出现。 不受横杠交换的影响，主体对大他者的这种外在性得以维持，无意识从而建立了起来。

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.

因为：- 如果很明显，三分法将分成 (1) 所指与主体，(2) 用其与主体相关的根本他异性将主体从其场域中切断的能指链，以及最后 (3) 这个拒绝的外部场域，不能被所指和能指的语言二分法所涵盖； - 如果主体的意识要被置于意指效果的水平上，并被能指的重复所支配，以至于它们甚至可以被称为它的反映： - 如果重复本身是由主体的消失以及其作为缺失的通道产生的——那么只有无意识才能命名构成思想顺序链条的进程。

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

在这一构成层面上，主体的定义可以归结为超出一个能指的可能性。

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]

难道最终不是这种过度的功能可以被称为主题化的力量，戴德金将其指定给主体以便为集合论提供其存在定理吗？ 可数无穷存在的可能性可以这样解释，即“从一个命题为真那一刻起，1总能产生第二个，即第一个为真，以此类推至无穷大”。 [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.

为了确保这种求助于作为迭代创始人的主体不是求助于心理学，我们简单地用主题化代替主体的表征（作为能指），它排除了意识，因为它不会对某人产生影响，而是在在链条上、在真理的领域对它之前的能指产生影响。 当拉康将标志定义成为某人代表某物，将能指定义成为另一个能指代表主体时，他是在强调，意识是被定位在能指链的影响而不是能指链的原因的水平上。主体对能指链的插入中是再现，必然与一个正在消失的排除相关。

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.

如果现在我们要尝试在时间上发展产生和支撑能指链的关系，我们将不得不考虑这样一个事实，即时间的连续性依赖于能指链的线性。产生的时间只能是循环的——这就是为什么这两个命题同时为真，主体先于能指，能指先于主体——但只有在引入能指之后才出现。回溯主要包括：线性时间的诞生。 我们必须把使主体成为能指的效果和使能指成为主体的代表的定义放在一起：它是一种循环的但非相应的关系。

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.

通过在逻辑话语阻抗最小的地方，即它的缝合点，你可以看到清晰的主体结构：作为“日食中的闪烁”，就像打开和关闭数字的运动，并以一的形式提供了缺失，以便在后继数中废除它。

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 + ，你已经理解了它在能指逻辑中所承担的前所未有的功能（一个标志，不再是加法，而是主体在要求它被取消的大他者场域中的总和）。为了分离涌现的单一特征和拒绝的障碍，仍然需要拆散它：从而表明主体的分裂，这是其异化的另一个名称。

It will be deduced from this that the signifying chain is structure of the structure.
由此可知，能指链是结构的结构。

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.
如果结构因果关系（就主体牵涉其中而言的结构中的因果关系）不是一个空洞的表达，那么它将从我在这里发展的最小逻辑中找到它的地位。

We leave for another time the construction of its concept.
我们下次再讨论其概念的构建。
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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