Identification 127

Identification 127

Jacques Lacan
雅克 拉康

11.4.62 XVII 209

I pose the
following question to you: what happens if Euler, instead of
drawing this circle, draws my inverted eight the one that today I
have to talk to you about?


In appearance it is only a particular case of the circle with the
inside field that it defines and the possibility of having
another circle within. Simply the inside
circle touches – here
is what at first sight some people
may say to me – the inside circle
touches on the limit constituted by
the outside circle. Only it is all
the same not quite that, in this
sense that it is quite clear, in
the way I draw it, that the line
here of the outside circle
continues into the line of the
inside circle and finds itself


And so in order simply immediately to mark the
interest, the
import of this very simple shape, I will suggest to you that the
remarks that I introduced at a certain point of my seminar when I
introduced the function of the signifier consisted in the
following: reminding you of the paradox or the supposed one
introduced by the classification of sets – you remember – which
do not include themselves.

I remind you of the difficulty they introduce: should one or
should one not include these sets which do not include themselves
(10) in the set of sets which do not include themselves? You see
the difficulty here. If yes, then they include themselves in
this set of sets which do not include themselves. If not, we
find ourselves confronted with an analogous impasse.


This is easily resolved on this simple condition that one grasps
at least the following – it is the solution that moreover the
formalists, the logicians have given – that one cannot speak, let
us say in the same way, about sets which include themselves and
sets which do not include themselves. In other words that one
excludes them as such from the simple definition of sets, that
one poses when all is said and done that the sets which include
themselves cannot be posed as sets.

这很容易被解决,条件很简单:我们至少理解以下的东西—而且,这是形式主义者,逻辑专家曾经给予的解决—容我们用相同的方式说,我们无法谈论关于包含自己的那些集合,与那些没有包括自己的集合。换句话说,我们排除它们自身,从集合的这个简单的定义。当一切都说都做了,我们提出的这个定义, 包括它们自己的那些集合,无法被提出作为集合。

I mean that far from this
inside zone of objects as important in the construction of modern
logic as sets, far from an inside zone defined by this image of
the inverted eight by the overlapping or the redoubling in this
overlapping of a class, of a relation, of some proposition or
other by itself, by being raised to a second power, far from this
leaving as a well-known case the class, the proposition, the
relationship in a general fashion, the category inside itself in
a fashion that is in a way more weighty more accentuated, this
has the effect of reducing it to homogeneity with what is

11.4.62 XVII 210

How is this conceivable? For indeed one must all the same
clearly say that, if this is the way that the question is
presented, namely among all the sets, there is no a priori reason
not to make of a set which includes itself a set like the others.
You define as a set for example all the works that refer to the
(11) humanities, namely to the arts, to the sciences, to
ethnography. You make a list of them; the works produced on the
question of what one should class as humanities will form part of
the same catalogue, namely that what I have even defined just now
in articulating the title: works about the humanities, forms part
of what is to be catalogued.


How can we conceive that something which is thus posed as
redoubling itself in the dignity of a certain category can find
itself practically leading us to an antinomy, to a logical
impasse such that we are on the contrary constrained to reject
it? Here is something which is not as unimportant as you might
think because one has practically seen the best logicians see in
it a sort of failure, a stumbling block, a vacillating point of
the whole formalist edifice, and not without reason. Here is
something which nevertheless puts to intuition a sort of major
objection, inscribed, tangible, visible of itself in the very
form of these two circles which are presented, in the Eulerian
perspective, as included one in the other.


It is precisely on this point that we are going to see that the
use of the intuition of the representation of the torus is quite
usable. And given that you clearly sense, I imagine, what is
involved, namely a certain relationship of the signifier to
itself, as I told you, it is in the measure that the definition
of a set has got closer and closer to a purely signifying
articulation that it leads us to this impasse, it is the whole
question of the fact that it is a matter for us of putting in the
foreground that a signifier cannot signify itself. In fact it is
something excessively stupid and simple, this very essential
point that the signifier in so far as it can be used to signify
itself has to be posed as different to itself. This is what it
is a matter of symbolising in the first place because it is also
this that we are going to rediscover, up to a certain point of
extension which it is a matter of determining, in the whole
subjective structure up to and including desire.



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