From an other to the Other 42

From an other to the Other 42

Jacques Lacan
雅克 拉康
8.1.69 VI 9
The progress of this logical practice has allowed to be assured, but
only thanks to the use of formalisation processes, namely, by putting
into two columns, as I might say, what is stated from the first discourse
of mathematics, and this other discourse subjected to this double
condition of getting rid of equivocation and of being reduced to a pure


It is starting from there and only starting from there, namely,
from something that distinguishes the first discourse, the one in which
mathematics has boldly made all this progress and without having, a
curious thing, to correct it epoch by epoch, in a way that ruins the
acquisitions generally accepted in preceding epochs, in opposition to
this discourse pinpointed on this, occasion, and very wrongly in my
view, by the term of meta-language —


the use of this formal language
(77) called, for its part, no less wrongly, language – because it is from
something that a practice isolates as a closed field in what is quite
simply language, the language in which mathematical discourse could
not properly speaking be stated.


It is starting from there, I am saying,
that Godel shows that in this apparently most certain system of the
mathematical domain, that of arithmetical discourse, the very supposed
7 . . . . consistency of discourse implies what limits it, namely,
incompleteness. Namely, that by starting even from the hypothesis of
consistency, there will appear somewhere a formula, and it is enough
for there to be one for there to be many others, to which it cannot, by
the very paths of the accepted proof qua law of the system, be
answered yes or no. The first phase, the first theorem


The second phase, the second theorem Here I must abbreviate. Not
simply can the system, I mean the arithmetical system, not therefore
assure its consistency except by making of it its very incompleteness,
but it cannot, I am saying in the very hypothesis grounded on its
consistency, demonstrate this consistency within itself.


I took a little trouble to get across here something that is not assuredly
properly speaking our field, I mean the psychoanalytic field, if it is
defined by some olfactory apprehension or other. But let us not forget
that at the moment of telling you that it is not properly speaking about
what the sentence implied that I am finishing with another subject, you
see clearly where I land, on this vital point. Namely, that it is
unthinkable to operate in the psychoanalytic field, without giving its
correct status to what is involved in the subject.


8.1.69 VI 10

What do we find in the experience of this mathematical logic? What,
if not precisely this residue where the presence of the subject is
designated? At least is this not what a mathematician himself,
certainly one of the greatest, Von Neuman, seems to imply in making
this rather imprudent reflection that the limitations, I mean the
logically tenable ones, it is not a matter of any antinomy, of any of
these classical mind games that allow it to be grasped that the term
obsolete, for example, is an obsolete term

这个数学的逻辑的经验,我们发现什么呢?它难道不就是这个残渣,在那里,主体的存在被指明?至少,这难道不是数学家自己似乎在暗示的东西?他确实是其中一位最伟大的数学家,范 纽曼。当他从事这个相当不谨慎的反思。这些限制2,我指的是逻辑上自圆其说的限制,那并不是任何对立的问题,任何这些古典心灵遊戏的问题,这些心灵遊戏让它能够被理解,譬如,过时的这个术语是一个过时的术语。

And that starting from there
we are going to be able to speculate on the predicates that are applied
to themselves and those that are not so applied, with all that this
involves as a paradox. That is not what is at stake. What is at stake is
something that constructs a limit that uncovers nothing, no doubt, that
mathematical discourse has itself not discovered since it is on this field
of discovery that it tests out a method that allows it to question it about
something that is all the same essential.

从那里开始,我们将能够推理,根据这个陈述, 被运用到它们自己的陈述,以及那些没有那么被运用的陈述与这个牵涉作为悖论的一切东西。那并不是岌岌可危的东西。岌岌可危的东西是某件建构限制的东西。无可置疑,这个限制并没有揭露任何东西,数学的辞说它自己还没有发现的东西,因为在这个发现的领域,它测试一个方法。这个方法让它质疑它,关于某件东西,仍然是基本的东西。

Namely, up to what point can
it account for itself up to what point can its coincidence with its own
domain be affected if these terms had a sense, while it is the very
domain in which the notion of content had properly speaking been
(78) emptied. To say with Von Neuman that after all this is all very
fine because it bears witness to the fact that mathematicians have still a
reason to be there, since it is with what presents itself there in its
necessity, its proper ananke, its necessities of detour, that they will
indeed have their role. It is because something is missing that the
desire of the mathematician is going to come into play.

换句话说,直到什么时刻,它才能够说明它自己,直到什么时刻,它跟它自己的领域的巧合才能够被影响,假如这些术语具有意义。虽然,这就是这个领域,内容的观念恰当而言已经被掏空。就范 纽曼而言,毕竟,这是非常精致的,因为它见证到这个事实,数学家依旧有理由在那里。因为使用呈现它自己在那里的东西,在它的必要性,它的恰当的ananke,它的迂回的必要性,它的专门术语“必阿南刻(必然性ananke)”,它们确实拥有它们的角色。因为某件东西是失落,数学家的欲望将会运作。


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