Identification 126

Identification 126
Jacques Lacan
11.4.62 XVII 207

(7) There is another relationship illustrated by these
overlapping circles: it is that of intersection, symbolised by
this sign whose signification is completely different. The
field of intersection is included in the field of union.
In what is called Boolean algebra, it is shown that, up to a
certain point at least, this operation of union is analogous
enough to addition for it to be able to be symbolised by the sign
of addition (+). It is also shown that intersection is
structurally analogous enough to multiplication for it to be
symbolised by the sign of multiplication (X).

这些重叠的圆圈所说明的,还有另外一种关系:交会的关系,由这些符号象征的关系。这个符号的意义完全是不同的。交会的领域被包括在结合的领域。在所谓的布林代数。它显示出来,至少直到某个点,结合的这个运作足够类同于“增加”,为了让它被“加 法+”的这个符号所象征。它也显示,交换在结构上足够类同于“乘法X”,为了让它被“乘法X”这个符号所象征。

I assure you that I am giving here an ultra-rapid extract
designed to lead you where I have to lead you and I apologise of
course to those for whom these things present themselves in all
their complexity for the elisions that all of this involves.


Because we must go further and on the precise point that I have
to introduce, what interests us, is something which up to De
Morgan – and one can only be astonished at such an omission – had
not been properly speaking highlighted as precisely one of these
functions which flow from, which ought to flow from an altogether
rigorous usage of logic, it is precisely this field constituted
by the extraction, in the relationship between these two circles
of the zone of intersection.

因为我们必须更加深入。在我必须选择的准确点。让我感到興趣的东西,恰当而言,是某件一直到德 莫根都没有准确地被强调—对于这个省略,我们仅能惋叹—作为流露出了的这些的功能之一,应该从逻辑的非常严谨的用法流露出来的东西。确实就是这个领域,由这个摘要所形成,在这两个圆圈之间的关系,交会的地区的这两个圆圈之间的关系。

And to consider what the product is, when two circles cut, at the
level of a field described in this way, namely the union minus
the intersection. This is what is called the symmetric


This symmetric difference is what is going to retain our
(8) attention, what for us – you will see why – is of the
greatest interest. The term symmetric difference is here an
appellation that I would simply ask you to take for its
additional usage. This was what it was called. Do not try
therefore to give a grammatically analysable meaning to this
so-called symmetry.


The symmetric difference, this is what that
means, that means: these fields, in the two Eulerian circles, in
so far as they define as such an exclusive “or”. With respect to
two different fields, the symmetric difference marks the field
as it is constructed if you give to the “or”, not the alternative
sense, but one which implies the possibility of a local identity
between the two terms; and the usual usage of the term “or” meansthat in fact the term “or” applies here very well to the field of union. If a thing is A or B, this is how the field of its extension can be drawn, namely in the first form that these two
fields are discovered. If on the contrary A or B is exclusive this
is how we can symbolise it, namely that the field of intersection is excluded.

这个均称的差异,这就是它的意思。它意味着:这些领域,在这两个尤勒的圆圈。因为它们定义一个排除的“或者”,作为自身。关于这两个不同的差异,这个均称的差异标示这个领域,因为它被建构,假如你们给予这个“或者”,不是替代的意涵,而是这个意涵暗示着这个可能性,在这两个术语之间的局部的认同的可能性。“或者”这个术语的通常用法意味着,实际上,“或者”这个术语在此应用得非常恰当,对于结合的领域。假如一件东西是A 或B,这就是它的延伸到领域如何被获得。假如相反地,A或B是互相排除,这就是我们用来象征它的方式。换句话说,交会的领域被排除。

This should lead us back to a reflection about what is
intuitively supposed by the usage of a circle as a basis, as a
support for what is formalised in function of a limit. This is
very sufficiently defined in the fact that on a commonly used
plane, which does not mean a natural plane, a plane that can be fabricated, a plane which has completely entered into our universe of implements, namely a sheet of paper, we live much more in the company of sheets of paper than in the company of tori. There must be reasons for that but after all reasons which are not evident. Why after all does man not fabricate more tori?


Moreover for centuries, what we nowadays have in the form of sheets were rolls which must have been more familiar with the notion of volume in epochs other than our own.


Finally there is certainly a reason why this plane surface is something which
(9) suffices for us and more exactly that we satisfy ourselves
with it. These reasons must be somewhere. And – I indicated it
earlier – one cannot give too much importance to the fact that,
contrary to all the efforts of physicists and philosophers to
persuade us of the contrary, the field of vision whatever is said
about it is essentially two-dimensional:



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