Sur les traces de Lévi-Strauss, Lacan et Foucault, filant comme le sable au vent marin...
23 Janvier 2021
THE SUBJECT AS MATTER OF THE SPEECH
- Resumption of an old project by Descartes and Leibnitz: to regulate one's thinking with a method.
- ENTROPOLOGY is taken from Lévi-Strauss in "Tristes Tropiques": how to consider an exchange between two interlocutors as an upgrade of their information systems, in the sens that one would have a thermodynamic balance (cold water+hot water=warm water) (cf.: Huyguens pendulums).
LESSON 1 : Imaginary Levels
A Sujet is a being of language (Lacan among others)
I started from this base to explore the language of category theory in mathmatics.
After this first exploration, I revisited what I had learned from physics to arrive at the idea that our Imaginary can be brought back to 5 different levels, bounded by the Real and the Symbolic, what I represent thus (my own place as the "bearer of the discourse" being spotted by the symbol 𓂀 to the extreme right, closing he statement) :
☯[∃] [⚤] [#] [♲] [∅]☯𓂀
Definition of glyphs used :
Both levels [∃] and [∅] are the boundary of an Imaginary, which is essentially articulated between [⚤], [#] and [♲].
LESSON 2 : The postures of the Subject
Exemple with these pendulums.
The Subject is always in motion in is Imagination, and thought is movement.
We find Spinoza, and his 3 types of understanding :
From this point of view, fixed attitudes are seen as dysfunctions in relation to a "normal" functioning of the subject:
In short, the postures of the Subject in his own Imaginary are as follows :
☯ [∃]𓁝I𓁜[⚤]𓁝I𓁜[#]𓁝I𓁜[♲]𓁝I𓁜[∅] ☯
Some writting conventions, in order to situate our concepts before discussing them:
LESSON 3 : Repetition automation
The fundamental point is that each level [⚤], [#] & [♲] defined a specific diachronic principle :
1/ In [⚤], the concepts of successor⚤ ou ⇅ , or order⚤, or causality⚤ are used to identify the jumps [∃] [⚤]𓁜.
Freud's repetition automatism is expressed temporally.
2/ In [#] the concepts of alterity# or orthogonality# or ⊥ are used to characterize the jumps [⚤] [#]𓁜.
The repetition automatism destroys the previous notion of order⚤, to give representations of the object by its surface#, in an increasingly complex space: from R (with still de notion of order) repetition# leads to R2 (where it disappears), R3,...R∞.
3/ In [♲] is expressed the concept of equivalence♲ or ⇆ allowing to compare what at the lower levels is dissimilar. The object is no longer represented by a surface but by a volume♲ or quantity♲ that is measured♲. Both equivalence and conservation relate to comparisons of these measures. (Example : a Picasso table worth 20.000 tons of green lemons). We come to the following diagram :
THE AUTHOR OF THE SPEECH
By hypothesis :
This can be done by indicating as an index of 𓂀 the diachronic concept used by the author in his speach:
The same author being able to express several speeches about the same object (in this case a Subject as "Other" of himself), one can draw up a table where each line would correspond to a particlar level of the speech.
An indication of the depth of the discours, would then be the line level of the table.
Example : the description of the difference of positions of the Subejct around the Imaginary level [#] (mirror stage) :
|niveau de 𓂀||les discours de 𓂀 sur 𓁝I𓁜|
The fundamental difference between the author 𓂀 and the Subject 𓁝I𓁜 is that :
1/ Closing of the discourse in [♲]⇆𓂀:
1.1/ Once the author identifies with the Subject on the highest degree of rationality of his Imaginary, in other words, after having expressed: (𓁝⇆𓁜)⇆𓂀, he can no longer add anything and by hypothesis ((𓁝⇆𓁜)⇆𓂀⇆((𓁝⇆𓁜)⇆𓂀)⇆𓂀)⇆𓂀, so there is no discourse in the form of "Russian dolls" developping to infinity.
1.2/ We can represent the speach space in [#]⊥𓂀 by two orthogonal axes :
The discours in [♲]⇆𓂀 is a tantanum to noting a redoubled equivalence :
Which is as folding our space delimited by these 4 points :
like closing an hancherchief by tying its 4 corners. In topology it is called "projective space", with here our author/ Subject in place of the projection point.
1.3 Emmy Noether Triptych :
2/ Spatial representation in [#]⊥𓂀 :
The author 𓂀 and the Subject 𓁝I𓁜 can share a common understanding of the concept of orthogonality#, which makes it possible to conceive for each of them a different geometry respecting the same concept#, and in particular to:
The only concept we share is the idea of orthogonality# !
It's a good thing, since this concept of orthogonality# can be deduced, as we have seen, with Bachmann'geometry, to a principle of symmetry♲ of level [♲]!
3/ Temporal Representation in [⚤]⇅𓂀:
By definition, the Subject in ex ante position 𓁝 has no temporal reference (since precisely he is not in [∃] [⚤]𓁜 position), so there are only two times :
Example : the time measured by a station chief on the plateform and a passenger in the moving car :
1/ Having in mind that "I am another", we form the hypothesis that the Imaginary structure of the author 𓂀 of the discourse is similar♲ to that of the Subject 𓁝I𓁜 of which he speaks.
☯[∃] [⚤] [#] [♲] [∅]☯
2/ When the concepts of similarity♲, orthogonality# and successor⚤ are common at the respective levels [♲], [#] and [⚤] of the Subject 𓁝I𓁜 (in the speech) and the author 𓂀, closing the speech (note: think of the Brouwer fixed point theorem which explains the need for [∅]), then
|𓂀/𓁜||☯[∃] [⚤] [#] [♲] [∅]☯|
|[♲]||(𓁝⇆𓁜)⇆𓂀 QUANTA & RELATIVITY|
Return to the identity of the Subject:
When the Author speaks about himself, he identifies each of the levels of his Imagination, which can be represented by identity Id.
I am another (𓁝⇆𓁜)⇆𓂀
Our Subject becoming self-aware at the mirror stage is represented by a symmetry♲ around this diagonal, like the fold of the Subject folding back upon itself.
THE 3 DISCOURSES OF LACAN, LÉVI-STRAUSS AND DESCARTES
Lacan indicates a transcendent approach, which must be completed by an immanent process of symetrization by steps, implemented by the Subject to structure his Imaginary in synchronic levels, stopping at the awareness of his own consistency, in terms of volume retention♲.
The transcendent process corresponding to this permanence♲ of the Subject is seen by Lacan as a decoherence from the Other. This process not being closed in the Imaginary of the Subject (i.e.: 𓁝☯) remains for him, irrational !
Canonical form of the myths of Lévi-Strauss:
When an object cannot be reduced to a dichotomous criterion (the object is (white or black)⚤ it must be concluded that the criteria chosen to describe it are foreign to each other (pottery⊥jealousy)# and that the object must be spotted as a product# of these two concepts# : the woman# is (potter; jealous)#.
What Lévi-Strauss points out in this process is the way to progress from a level [⚤] to a level [#] through a process developped in mythical thought, and which he defines by the canonical form of myths.
Example : Among the Jivagos, the woman has for totem the nighthawk, symbol of jealousy and chaos, but she is also a potter and shows meticulousness in the choice of pottery ground and the care that she puts to follow the rites of manufacture. The woman is at the same time nighthawk and no-nighthawk, which shocks the Cartesian logic of our good Jivaros !
The mythical process thus consists in sacrificing the disturbing concept (here the nighthawk) ceasing as well as being in contradiction with the observation (the woman is potter), to become an element of her définition as cartesian product : woman=(jealous; potter).
Nothing has changed untill today, and we find the same process to define "a" as a2=2 or "i" as i2=-1.
The myth does not solve the contradiction that appears in a dialectic way (nighthawk/ oven-bird) by staying at the level [⚤], but indeed by a "diachronic jump" at level [#] regulated by a principle in [♲]𓁝☯.
Complementarity of the two processes :
Now, we have just seen this last immanent process as the reverse of the mirror stage described by Lacan! We are just going through the same sequence in two different directions :
When the storyteller 𓂀 expresses himself in the form of a process, (𓁝[#]⏩[#]𓁜)⇅𓂀, he remains outside the audience ([#]𓁜⏩[#]𓁝[♲])𓂀 and thus, marks his own permanence (𓁝⇆𓁜)⇆𓂀, as a teacher giving a lesson, and it is here that he becomes the Other of the Subject to which he is intriged, at the Symbolic level (𓁝☯)𓂀.
Descartes' cogito :
Descartes becomes aware in [⚤]𓂀 of two postures:
Which cover two movements, namely :
In this scheme, the coming and going of through [∃]⇅[⚤], allows two observations, according to the point which one takes at origin :
Discussion: The sequence of the 2 disocourses recalls a fundamental distinction between identity / Idempotence, specific to topology# and is expressed particularly well in category theory.
The thesis that can be argued is that Descartes brings back in [∃][⚤] an immanent experience of the mirror lived by the child in [⚤][#].
His hope to base his method just on an immanent process would be doomed from the outset to failure on several levels :
The 3 discourses : ☯([∃]𓁝⇅𓁜([⚤](𓁝⇅𓁜)[#]𓁝⊥𓁜)[♲]𓁝I⇆𓁜[∅]☯)𓂀
- What about Noether's one ?
- It covers the entire Imaginary field of the author 𓂀 as of the Subject 𓁝|𓁜 and is expessed by [♲]𓂀, this is what we checked at each jump [∃]/[⚤], [⚤]/[#] and [#]/[♲], until it desappears in the last jump [♲]/[∅]!
I hope that I responded to an attack launched by Derrida to the structuralists, at a congress in Cerisy : "how do you structure the genesis of your structures?"
We can distinguish three stages of our European evolution :
I would like to find the three modes of understanding of Spinoza :