Logic of phantasy 04 Jacques Lacan

Logic of phantasy 04
Jacques Lacan
雅克 拉岡

Lacan Seminar 14: The Logic of Fantasy 04

Seminar 2: Wednesday, November 23, 1966

(5) Mathematical usage which depends precisely on the fact that when we have somewhere – and not only, as you know, in an exercise of algebra – when we have posited somewhere a letter, capital A, we take it up, subsequently, as if it were still the same the second time that we make use of it. Do not raise this objection; today is not the day I am going to give you a class in mathematics.

(五)数学的用法主要是依靠这个事实,当我们在某个地方拥有, 不单是在代数的练习中,你们知道,而且在某个地方,我们提到一个大写字母A,我们随后接纳它,好似我们第二使用它时,它都会一成不变。

You should know, simply, that no correct statement about any use whatsoever of letters – even if it were, precisely, in what is closest to us today, for example, in the use of a Markov chain – would require of any teacher (and this is what Markov himself did) a stage, which is in a way propaedeutic, to make clear the impasse, the arbitrariness, what is absolutely unjustifiable (quite apparent moreover) in employing A the second time to represent the first A, as if it were still the same. It is a difficulty which is at the source of the mathematical use of so-called identity.


We do not have to deal with it explicitly here today, because we are not dealing with mathematics. I want simply to recall to you that the foundation, that the signifier is not grounded by signifying itself, is admitted by those very people who, on occasion, may make a use that is contradictory to this principle – at least in appearance. It would be easy to see the intermediary by which this is possible, but I do not have the time to go astray in this. I want simply to pursue – and without tiring you any more – my proposition which is then the following: what is the consequence in this Universe of discourse of this principle: that the signifier cannot signify itself?


What does this axiom specify in this Universe of discourse in so far as it is constituted, in short, by everything that can be said? What sort of specification is it and does the specification that this axiom determines, form part of the Universe of discourse? If it does not form part of it, this is undoubtedly a problem for us. What specifies, I repeat, the axiomatic statement that the signifier cannot signify itself, will have the consequence of specifying something which, as such, would not be in the Universe of discourse. Even though, precisely, we have admitted saying that it encompasses everything that can be said, into its ambit. Are we going to find ourselves in some diversion which would signify that what, thus, cannot form part of the Universe of discourse, cannot be said in some way or other?


And, of course, it is clear that since we are speaking about it, about what I am bringing to you, it is obviously not to tell you that it is the ineffable thematic regarding which you know that from pure consistency and without for all that belonging to the school of Mr. Wittgenstein, I consider as: that it is vain to speak.


(6) Before coming to such a formula, and you can see after all that I am not sparing you either bits relief or the impasse that it constitutes, since moreover we are going to have to come back to it – really do everything to open up the paths to what I am trying to get you to follow me in – let us take care to put to the test the following: that what specifies the axiom that the signifier cannot signify itself, remains part of the Universe of discourse.


What do we then have to posit? What is at stake in, what specifies the relation that I stated in the form that the signifier cannot signify itself – let us take arbitrarily the usage of a little sign which serves in this logic which is founded on writing, this Win which you will recognise the shape (these games are not perhaps purely accidental) of my diamond, in a way with its hat knocked off, that has been opened up like a little box, and which serves, this W, to designate, in the logic of sets, exclusion. In other words, what is designated by the Latin ora, which is expressed by an aut: one or the other. The signifier, in its repeated presentation, only functions qua functioning the first time or functioning the second. Between one and the other there is a radical gap, this is what is meant by: the signifier cannot signify itself.

那麽,我们要提出怎样的命题呢?什麽东西会岌岌可危?在「意符无法使自己被意符化」里,我所陈述的这个关系的明确细节是什麽?让我们随意地拿一个小符号的用法当例子,这个小符号可以运用在以书写为基础的逻辑里。在「赢」这个单字的字首W,你们认出我的方块鑽石的形状(我玩弄这个遊戏,不完全是巧合。)只是它的上一半被踢掉,它像一个小盒子被打开,这个W 的形状,在集合的逻辑里,指明的意义是:排除。换句话说,ora这个拉丁字,在法文是aut, 指明的是:一个或另外一个。这个意符,以重复地出现的方式,充当的功用仅仅是,作为第一次的功用,或第二次的功用。在一个或另外一个之间,有一道很大的鸿沟,那就是它的意思:意符无法使自己被意符化。代号就是:S W S

We suppose, as we have said, that what determines this axiom as a specification in the Universe of discourse is what we are going to designate by a signifier, B – an essential signifier which you will notice can be appropriated to something the axiom specifies: that it cannot, in a certain relation and from a certain relation, generate any meaning. B is very specifically the signifier which can be specified, without objection, by the fact that it marks, as I might say, this sterility. The signifier in itself being characterised precisely by the fact that there is nothing obligatory, that it is far from being in the first spurt that it generates a meaning. It is this that gives me the right to symbolise by the signifier B this feature: that the relation of the signifier to itself does not generate any meaning.


But let us start, to begin with, from the following which after all seems to be required: the fact is that something that I am in the process of stating to you forms part of the Universe of discourse. Let us see what results from that. That is why I make use for the moment – because after all it does not seem to me to be inappropriate – of my little diamond in order to say that B forms part of A, that it has relations with it whose richness I will certainly have to bring into play, for you, throughout this year, and whose complexity I indicated to you the last time, by decomposing this little sign in all the binary fashions in which it can be done.

但是首先让我们从以下的问题开始,畢竟那似乎是必要的条件,这个事实是,我目前正在跟你们陈述的某件事情,组成了真理论述的宇宙的某一部分。让我们瞧一瞧,那造成的结果是什麽。那就是为什麽,我现在会使用我那个小方块鑽石的符号(畢竟这样使用,对我而言,似乎並没有什麽不适当),为了要说,B的意符组成A的意符的一部分。B的意符跟A的意符,彼此关系的繁复,今年一整年,我确实还要跟你们一再演说。它们的复杂性,我上一次已经跟你们指明,我拆开这个小符号,以双边的关系,可以书写成公式如下:B A的念法是: B的意符大於或小於A的意符。

(7) It is a matter of knowing, then, whether there is not some contradiction resulting from it. Namely, whether from the very fact that we have written that the signifier cannot signify itself, we can write that this B, not signifies itself, but, forming part of the Universe of discourse, can be considered as something which, in the style which characterises what we have called a specification, can be written: B forms part of itself. It is clear that the question arises: does B form part of itself? In other words what the notion of specification grounds, namely, what we have learned to distinguish in several logical varieties, I mean that I hope that I hope that there are enough people here who know that the functioning of a set is not strictly speaking super-imposable on that of a class, but that in fact all of this at the origin, must be rooted in this principle of a specification.


Here, we find ourselves before something whose kinship in fact should sufficiently resonate in your ears with what I called the last time Russell’s paradox, in so far as to what I am stating, that here, in the terms which interest us, the function of sets – in so far as it does something that I, for my part, have not yet done, for I am not here to introduce it but to maintain you in a field which logically is on this hither side, but to introduce something that there is an opportunity to grasp in this connection: namely, what is grounded by the bringing into play of the apparatus described as set theory, which today is presented as something quite original, undoubtedly, for any mathematical statement, and for which logic is nothing but what mathematical symbolism can grasp – this function of sets will also be the principle, and this is what I put in question, of the whole foundation of logic.


If there is a logic of the phantasy, it is because it is more fundamental (principielle) than any logic which flows into the formalising defiles where it has revealed itself, as I have said, to be so fruitful in the modern epoch.


Let us try then to see what Russell’s paradox means, when it covers something which is not far from what is there on the board. Simply, it promotes as altogether enveloping this fact of a type of signifier, that it takes moreover to be a class. A strange error! … To say, for example, that the word “obsolete” represents a class in which it would itself be included, under the pretext that the word “obsolete” is obsolete, is undoubtedly a little conjuring trick, which has strictly no interest except to found, as a class, the signifiers which do not signify themselves. While precisely we posit as an axiom, here, that in no case can the signifier signify itself and that it is from there that one must start to sort oneself out, even if it were only to see that it is necessary to explain differently that the word “obsolete” can be qualified as obsolete. It is absolutely indispensable to bring into it what the division of the subject introduces.



Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: