Identification 65

Identification 65

Jacques Lacan
雅克 拉康

28.2.62 XI 127

It is for that reason that it is not at all indifferent to show
where there passes in effective the frontier of what is effective
in experience despite all the theoretical purifications and the
moral rectifications.


It is quite clear in any case that there
is no way of admitting Kant1s “Transcendental aesthetic” as
tenable despite what I called the unsurpassable character of the
service that he renders us in his critique, and I hope to make
you sense it precisely from what I am going to show you it would
be well to substitute for it.


Because precisely if it would be
well to substitute something for it and if this functions while
preserving something of the structure that he articulated, this
is what proves that he at least glimpsed, that he profoundly
glimpsed this very thing.


Thus it is that the Kantian aesthetic
is absolutely not tenable, for the simple reason that for him it
is fundamentally supported by a mathematical argumentation which
belongs to what one could call the geometrizing epoch of
mathematics. It is in so far as Euclidian geometry is
uncontested at the time Kant was pursuing his meditation, that it
is sustainable for him that there are in the spatio-temporal
order certain intuitive facts.


One has only to bend down, to
open his text, to collect examples of what may appear now
(10) immediately refutable to a student averagely advanced in a
mathematical initiation, when he gives us as an example of a fact
which does not even need to be demonstrated, that only one
straight line can pass between two points.


Everyone knows, in so
far as the mind has in sum adapted itself rather easily to the
imagination, to the pure intuition of a curved space through the
metaphor of this sphere, that through two points, there can pass
many more than one straight line, and even an infinity of
straight lines.


When he gives us in this table of nichts, of
nothings, as example of the Leere Gegenstand ohne Begriff: of the
empty object without a concept, the following example which is
rather extraordinary: the illustration of a rectilinear figure
which would only have two sides, here is something which might
seem to Kant – and no doubt not to everyone at his epoch – as the
very example of the inexistent object and what is more the
unthinkable one;

当他给予我们,用nichts的这个表格,空无的表格,作为leere Gegenstand ohne Begriff的例子:没有观念的空洞的客体。以下的例子相当特殊:直线图形的说明,仅有两个边。在此是某件对于康德—无可置疑,对于他的时代的每个人就不见得—似乎可作为不存在的客体的例子,而且是匪夷所思的例子。

but the least usage I would say even of the
quite elementary experience of a geometer, the investigation of
the trace described by a point linked to the circumference of a
circle, what is called a Pascalian cycloid, will show you that a
rectilinear figure, in so far as it properly puts in question the
permanence of the contact between two lines and two sides is
something which is truly primordial, essential to any kind of
geometrical comprehension, that there is well and truly here a
conceptual articulation and even a quite definable object.


Moreover, even with this affirmation that nothing except the
synthetic judgement is fruitful, it may still, after the whole
effort of logicising mathematics, be considered as subject to
(11) reason.


The so-called unfruitfulness of the a priori
analytic judgement, namely of what we will call quite simply the
purely combinatory usage of elements extracted from the primary
position of a certain number of definitions, that this
combinatory usage has in itself its own fecundity, this is what
the most recent, the most advanced critique of the foundations of
arithmetic, for example, can certainly demonstrate.


That there
is in the final analysis, in the field of mathematical creation,
a necessarily undemonstrable residue, this is what no doubt the
same logicising exploration seems to have led us to (Godel’s
theorem) with a rigour unrefuted up to now, but it remains
nonetheless that it is by way of formal demonstration that this
certainty can be acquired and, when I say formal, I mean by the
most expressly formalist procedures of logicising combination.


What does that mean? Is it that for all that this pure
intuition, as for Kant at the end of a critical progress
concerning the required forms of science, that this pure
intuition teaches us nothing? It undoubtedly teaches us to
discern its consistency with and also its possible disjunction
from precisely the synthetic exercise of the unifying function of
the term of unity qua constitutive in every categorical formation
and, once the ambiguities of this function of unity have been
shown, of showing us to what choice, to what reversal we are led
under the influence of diverse experiences.



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