AGAINST THE PATHOS OF THE COLD EQUATIONS: the ideology of mathematical reductionism

My specific argument against Badiou’s foundational treatment of mathematics goes one step further than general arguments against the validity of scientism and foundationalism that Badiou himself lays out convincingly.

Badiou’s philosophy is profoundly split between a specifically mathematical exploration that does not, and cannot, have the philosophical consequences that he wants and a more general metaphorical extrapolation of concepts he has derived from his reflection on the mathematics. Badiou declares that mathematics is ontology but the burden of proof is on him.

In the specifics of the working out of his system he will derive certain concepts from the mathematics. For example in his reflexion on omega, the first infinite ordinal, he extracts a typology of infinities: the infinite as point, as place, as horizon, and as repetition. He then turns to poetry to “explore the labyrinth of the different forms taken by the couple finite/infinite”, admitting explicitly that this turn is metaphorical.

The mathematics is a very interesting theoretical tool that is well worth working out, but that has only suggestive value, heuristic rather than apodictic force.

Badiou has aptly remarked that the contemporary transcendental is a mixture of “crass positivism” (his expression) and vacuous moralism. I think that the nadir of this mix in theoretical circles is the rise of mathematical reductionism, an ideology which combines the speculative privileging of mathematics and a sort of hard-nosed pathos reminiscent of what in science fiction used to be called the “cold equations”.

People whose philosophical penetration does not go beyond a glib juggling with jargon but who have some mastery of theoretically fashionable sectors of mathematics pop up and descry, or so they think, their own image writ large in Badiou’s philosophy. Formerly this combination of bland moralism and crass positivism was embodied in an obsession with physics as foundational. We can see relics of this in Laruelle’s appeal to a vague “quantum thought” of his own imagination, that would be better described as a quantum Stimmung.

The advantage of mathematics as de-realised foundational discipline is that any tie with actual scientific theories and empirical evidence. Mathematical reductionism irepresents an attempt at an ontology compatible with any scientific discovery while yet maintaining an aura of scientificity. I do not think that Badiou himself fully falls into this trap, but he is not fully free from it either.

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LA VOIE DU BONHEUR: Milarépa le Candide Noétique

Milarépa, né Mila Thöpaga, est un grand “saint” tibétain dont la vie s’est déroulée il y a environ 1000 ans. Son père, un riche commerçant, est mort quand Thöpaga était enfant, en confiant ses enfants et son épouse aux bons soins de son frère, qui s’est approprié leur héritage et les a réduit à l’état de serviteurs appauvris.

Mû par le ressentiment et empli de la soif de vengeance, Thöpaga est parti pour apprendre la sorcellerie auprès d’un grand maître et en revenant il s’est servi de la magie noire pour se venger contre son oncle bête et méchant, violent, cupide, cruel et tyrannique. Ensuite, accablé de pitié et de regrets, Thöpaga recherche un maître spirituel qui peut lui montrer comment se libérer de ses remords et de sa tristesse, pour vivre la vie bonne et atteindre le bonheur.

L’histoire est une des plus célèbres du Tibet et de la littérature spirituelle mondiale. Le film raconte de façon sobre cette première partie de la vie de celui qui va devenir un des grands maîtres spirituels non seulement des tibétains mais du monde entier. Une seconde partie est prévue, qui raconterait la lente purgation de toute cette souffrance, le passage de la négativité  à la positivité, et la transformation spirituelle de Thöpaga de sorcier repenti en yogi illuminé. Même si cette seconde partie n’a pas encore été tournée on connaît la fin, ceci n’est pas un film à suspense. Pour le définir je dirais que c’est un film de “voyance”, au sens que nous devons le voir non seulement avec les yeux physiques mais aussi avec les yeux de l’esprit.

Deux Lectures: Il existe deux façons de comprendre la vie de Milarépa.

En tant que récit biographique l’histoire de Milarépa est spécifique à un lieu et à une époque: elle a un intérêt historique et sociologique, et une valeur inspirationnelle.

En tant que leçon de vie universelle elle est générique, et s’adresse à tout le monde: elle exprime un drame intérieur, où tous les personnages correspondent à des éléments de notre propre personnalité.

Lecture Extérieure et Exotisme: Cette histoire se déroule il y a longtemps dans un pays lointain. Lue à la lettre elle nous informe sur la biographie d’un saint et sur les conditions de vie dans un pays exotique, mais elle ne nous apprend pas grand-chose sur notre vie.

Le film véhicule quelques sentiments pieux qu’il est toujours bon à rappeler: les valeurs de la compassion, la foi, la persistance, la volonté de surmonter notre passé, la cultivation des pensées et des affects positifs, le pouvoir transformateur des épreuves de la vie. Mais nous, spectateurs occidentaux, ne pouvons pas partager la cosmologie de ces tibétains, nous ne croyons pas à la sorcellerie, ni à la réincarnation.

C’est la nécessité de se méfier de l’exotisme qui pourrait être l’un des enseignements le plus puissant du film. La sorcellerie, même si elle a une place dans leur culture, est un art mineur, un reste des religions chamaniques pré-bouddhistes. C’ est une pratique exotique pour les tibétains eux-mêmes, tout comme le yoga pour nous. La ligne de démarcation entre les deux est mince et perméable. Dans le film, le même maître qui enseigne la sorcellerie à Thöpaga lui conseille de suivre le chemin du bouddha.

Pour nous, la leçon serait que n’importe quelle pratique, y compris une pratique spirituelle comme le yoga ou la méditation, ne devrait pas être abordée comme une pratique exotique où on imite un modèle extérieur et étranger à notre enracinement culturel et existentiel. Ce serait une forme de “pensée magique” de pratiquer aveuglément des rituels cultuels, adopter des comportements d’un autre monde, s’exprimer dans des phrases stéréotypées dont on ne maitrise pas le sens profond mais qu’on plaque sur n’importe quelle situation qui semble s’y prêter, sans discernement – tout cela représente plutôt une fuite de la vie, une aliénation, de la volonté de puissance, ou du narcissisme.

Lecture Intérieure et Domestique: Tous les personnages et les situations de l’histoire correspondent à des éléments de notre propre personnalité, à des écueils sur le chemin vers le bonheur ou à des forces favorisant l’éveil à la vraie vie. Nous avons en nous tous les défauts de l’oncle: méchanceté, bêtise, cupidité, violence, cruauté, tyrannie, égoïsme. Nous avons tendance à instrumentaliser tout le monde qu’on rencontre et tous les enseignements qu’on reçoit à notre propre gain et à notre gloire.

L’ennemi est intérieur et ça ne sert à rien de le projeter à l’extérieur, et de faire dépendre notre bonheur à la bonne volonté de quelqu’un d’autre que nous-mêmes. L’oncle c’est l’image de la vie projetée, avare et cupide lui-même il accuse les autres, y compris ceux qu’il a spoliés, de ses propres défauts. Cette projection n’est pas sans conséquences pour les autres, et c’est déjà une forme de sorcellerie néfaste, que de faire endosser par les autres la culpabilité et les châtiments découlant de nos propres actes.

Du Sorcier au Yogi: Il n’y a pas de suspense, nous connaissons la fin de l’histoire, même si pour l’instant nous devons nous satisfaire d’un film qui ne raconte que la première moitié de la biographie de Thöpaga, qui devient “Milarépa”, le célèbre yogi et poète. Loin de nuire à la compréhension, cette incomplétude renforce la double vision que nous devons avoir de ce personnage que nous voyons devant nous. Il souffre, son esprit se remplit d’amertume et de ressentiment, il se durcit contre toute compassion pour ses ennemis et il se venge.

Cependant, on sait que ce personnage entouré de souffrance et rempli de négativité sera un des plus grands sages de l’histoire de l’humanité. On voit déjà les prémices de son éveil futur: sa sincérité, sa spontanéité, son amour familial (au point de vouloir endosser tout le karma négatif de sa mère), son ouverture, sa puissance de concentration, son dévouement. On voit tout ceci, mais aussi on le “noétise”, c’est à dire qu’on l’assimile comme une allégorie du chemin spirituel, de la voie du bonheur.

Le secret de la transformation n’est pas une surprise, c’est archi-connu, mais pas archi-pratiqué. Il faut bien sûr la maîtrise de l’esprit, la conscience, mais ce n’est pas suffisant. Le sorcier a déjà maîtrisé son esprit, il doit rester conscient et concentré pour réaliser ses exploits. Mais cette conscience est parcellaire, parce qu’il n’est pas conscient de son but et de ses actes, sortis de leur contexte plus grand. Il n’est pas conscient des conséquences pour les autres et pour lui-même, il n’est pas conscient du karma.

Ce qui lui manque, c’est la compassion. Sans compassion notre plus grande conscience contient toujours une grande partie d’inconscience. On n’est pas conscient que les défauts qu’on voit et les fautes qu’on punit sont les nôtres aussi, que nous contenons l’ombre en nous et que nous pratiquons la magie noire sans le savoir.

C’est en prenant conscience de cette leçon que Mila Thöpaga (Mila ,”la bonne nouvelle”) commence à réaliser son potentiel, à devenir Milarépa (Mila, “qui porte la robe de coton des ascètes”).

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BADIOU CRITIC OF DELEUZE: absolute place

The problem that Badiou raises with Deleuze’s philosophy is one of place and not of sense. Badiou has already said (in METAPHYSICS OF REAL HAPPINESS) that for him “sense” in Deleuze corresponds to “truth” in his own system.Badiou argues that Deleuze posits an “absolute place” that is both unifying and totalizing.

We have seen that in WHAT IS PHILOSOPHY? Deleuze and Guattari talk of a plane that is a “reservoir”, “reserve” or “absolute horizon”.

Previously, in RHIZOME they criticised the notion of the Eternal Return as introducing a “supplementary”, or transcendent, dimension, implicitly criticising Deleuze’s earlier philosophy expressed in DIFFERENCE AND REPETITION.

The hunt for transcendences is unceasing, so it is a continuation of the same process when Badiou uncovers and rejects a subjacent unifying and totalising instance in the notion of the plane of immanence. This is an onto-theological element, turning immanence into the Presence of a plane.

I think that this needs further argument, but I certainly do not belong to the “Deleuze can do no wrong” school that will just paste on any ad hoc explanation that comes to mind to cover over any serious objection.

My hypothesis is that Badiou is involved in a slow becoming-Deleuzian. Unfortunately we will never see the possible fourth volume in his BEING AND EVENT series, which could be called: “ONTOLOGY OF PLURALISM: Deleuze as Educator”.

In considering Badiou’s critique of Deleuze one should in a first approach forget about the mathematics. Badiou explicates mathematics (specifically set theory) as foundational for ontology (this is his scientism) but his actual use of it is metaphorical. The main question is: is Deleuze misreading himself when he critiques the eternal return?

IBadiou captures very well the moment of totalisation in Deleuze and Guattari’s thought that can be criticised, as does Laruelle. This is Latour’s critique too. Unfortunately, Badiou regresses from this insight into a real problem in Deleuze’s system with his foundational use of maths.

But we cannot remain fixated on one phase of the historical process. Deleuze died 22 years ago, when he was 70. Badiou is writing today, he is 80, and he is still evolving. Despite his wrong-headedness and his “weirdness”, he is a more legitimate inheritor of Deleuze than the Anglophone business machine academics who dominate the discussion of Deleuze in English.

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Badiou’s THE IMMANENCE OF TRUTHS: Prologue (against Deleuze)

Badiou’s Prologue is entitled: Formal Presentation of the Absolute Place (or Location).

Note: I am continuing my commentary on the Table of Contents to Badiou’s forthcoming book THE IMMANENCE OF TRUTHS, trying to anticipate some part of its content based on his prior published works and on his unpublished seminars.

This is an intriguing title as in his previous work Badiou has always ruled out the existence of such an “absolute place”. In his SECOND MANIFESTO FOR PHILOSOPHY he argues that the idea of a total multiplicity, or multiplicity of all multiplicities, is incoherent and thus is devoid of being.

There is not the localizing being of worlds and the localized being of objects. Nor is there the Universe as the absolute place of all there is (SECOND MANIFESTO, 30-31).

This non-existence of an absolute place is also a crucial part of his presentation of his difference with Deleuze. In his seminar on Politics Badiou contrasts his own thinking of the Void with Deleuze and Guattari’s thought of Chaos:

In any case, if the key concept is chaos then I stipulate philosophically that chaos does not exist, for beneath this unthinkable “there is”, outside of sense, unattainable, hides the figure of presence. Deleuze and Guattari try to maintain such a figure simply unbound to any allegiance to sense.

Let us examine their definition of chaos: “Chaos is defined not so much by its disorder
as by the infinite speed with which every form taking shape in it vanishes. It is a void that is not a nothingness but a virtual, containing all possible particles and drawing out all possible forms, which spring up only to disappear immediately, without consistency or reference, without consequence” (page 118, with a note citing Prigogine and Stengers Entre le temps et l’éternité).

Infinite speed of births and disappearances, which define chaos as a place of the virtual, i.e. as “a void that is not a nothingness”, chaos is presented as the absolute reservoir of possibles in an incessant movement of births and disappearances. Constant infinitesimal upsurge of all possibilities, chaos refers to an absolute place of all possibles, i.e. to a pure natural “there is” as absolute system of all virtualities deprived of any being. In contrast, although it is called a void by Deleuze and Guattari, I oppose to their definition of chaos, the residue, in my opinion non-existent, of a figure of presence, my own definition of the sutured being of the void. It is a questiion here of a fundamental philosophical choice, marked by a very sharp distinction between chaos and the void (from the seminar Politics, academic year 1991-1992, course three entitled Deleuze 2).

The problem with Deleuze and Guattari’s plane of immanence, according to Badiou, is that it re-institutes a transcendence, in the form of a transcendent presence or absolute place, a totality of all possibles.

However, this thesis of the non-existence of an absolute place can be seen to be in tension with another thesis that Badiou develops in the Introduction to THE IMMANENCE OF TRUTHS, that of the “absolute ontological referent”, which he explains in the short text Toward A New Thinking of the Absolute.

Badiou’s objection to the concept of an absolute place is that it implicitly re-institutes a form of onto-theology. It posits as coherent the idea of a totality of all beings, which it treats as a presence, and so is yet another figure of transcendence. In the article “Toward a New Thinking of the Absolute” Badiou’s own version of the absolute ontological referent frees it from these residues of transcendence.

This absolute ontological referent is “V” the Universe of sets.

We shall conventionally call V, the letter V, which can be said to formalize the Vacuum, the great void, the place (truly inconsistent since non-multiple) of everything that can be constructed by means of axioms. What is metaphorically “in V” is what can respond to the axiomatic injunction of set theory. This means that V is in reality only the set of propositions that can be proved from the axioms of the theory. It is a being of language exclusively. It is customary to call such beings of language “classes.” We shall therefore say that V is the class of sets, but bear in mind that this is a theoretical entity that is unrepresentable, or without a referent, since it is precisely the place of the absolute referent.

V, the Universe of sets, a place that is inconsistent, a being exclusively of language (and so not a presence). It is the “place of the absolute referent”. The universe V is not thinkable as a coherent idea, but is only definable axiomatically. It is a “rational fiction in which all sets are thinkable”, but is not itself thinkable.

In conclusion, I do not endorse Badiou’s solution without seeing further arguments. For me it is even more onto-theological. But I do think he is on to something. In WHAT IS PHILOSOPHY? Deleuze and Guattari write:

“Concepts are events, but the plane is the horizon of events, the reservoir or reserve of purely conceptual events: not the relative horizon that functions as a limit, which changes with an observer and encloses observable states of affairs, but the absolute horizon, independent of any observer, which makes the event as concept independent of a visible state of affairs in which it is brought about” (page 36).

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Badiou’s “THE IMMANENCE OF TRUTHS”: Introduction (sketch)

We have enough material available to anticipate the general outlines of many sections of Badiou’s forthcoming book. I will try to give some sense and content to the chapter titles

1) Speculative strategy (source: seminar IMMANENCE OF TRUTHS, December 12, 2012)

Badiou’s strategy involves beginning with a critique of the dominant ideology of modern society, which is no longer based on a finitude of stability and repetition but on a new form of finitude, one of movement and innovation. The critique of the dogma of human finitude will lead him to elaborate a new theory of the infinite.

Badiou criticises the postmodern as an attempt to make one’s peace with the finitude of capitalist circulation, to inhabit it playfully and cynically, i.e. to accept it as a given albeit without being duped by it.

He accuses Lyotard’s post-modernism of being a form of pessimism and resignation, of accepting that there is no exit from the finitude of the modern world. According to Badiou, Lyotard is right to give up the notion of waiting for a better world tomorrow, but he is wrong to conflate the grand narrative with messianism and prophetic expectations.

Against this postmodern “pessimism over finitude” Badiou insists that we need a grand narrative without the messianic wait. We can have a grand narrative based on openness rather than on waiting. We need to find elements of the infinite inside the finite world we live in and “release” them:

To release the infinite is to live in the world in such a way that the present is so intense that there is no need to wait for tomorrow; in reality tomorrow must be there.

There must be points of infinite intensity already there, points of infinity immanent to the world of mediocre intensities:

2) Immanence, finitude, infinite (source: Argument Seminar 2012-2013)

For Badiou in LOGICS OF WORLDS a truth is, in a given particular world, an immanent exception. In THE IMMANENCE OF TRUTHS Badiou returns to the notion of immanence, and by a reversal of perspective examines

“not only what a truth is from the point of view of the world where it arises, but what the world becomes when it it is perceived and thought from the point of view of the truth”.

To pursue this thought of immanence Badiou will have to destroy the dominant thesis of the obligatory  finitude of existential or cognitive experiences.

“The affirmation that the finite, strictly speaking, does not exist, and that the dogma of “human finitude” is an imposture, is the beginning of all liberation”.

Thus Badiou’s “reversal of perspective” involves thinking finitude as illusory appearance on the basis of the infinite real.

3) The absolute ontological referent (source: Toward A New Thinking of the Absolute)

According to Badiou any contemporary materialism must assume an “absolute ontology”, i.e. it presupposes the existence of a universe of reference, a place of the thinking of being qua being, with four characteristics, or principles:

1. Immobility: while making the thinking of movement, and indeed all rational thought possible, it remains absolutely foreign to that category.

2. Non-composition, or intelligibility on the basis of nothing. It is not composed of other entities. It is non-atomic.

3. Non-empiricity or axiomatic prescription: it can only be described or thought formally, by means of axioms, or principles. There can be no experience of it or any construction of it that depends on an experience. It is radically non-empirical.

4. Maximality: any intellectual entity whose existence can be inferred without contradiction from the axioms prescribing its existence exists also by that very fact.

For Badiou V, the universe corresponding to the axioms of set theory, obeys the four principles and thus is the absolute ontological referent.

4) The two possible readings of this book

We can only speculate here. However, Badiou has often stated that his philosophy can be approached ontologically (in terms of its conceptual systematicity and demonstrativity) or phenomenologically (in terms of its examples drawn from the four truth procedures: art, science, politics, and love, these being the conditions of philosophy. As the table of contents shows there is an alternation between systematic chapters (marked with the prefix “C”) and sequels (“S”) to many (but not all) of these chapters, containing examples drawn from one of the four truth procedures.

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Badiou’s THE IMMANENCE OF TRUTHS: contents

Thanks to François Nicolas we have a working idea of Badiou’s forthcoming book, the third volume of “BEING AND EVENT” entitled THE IMMANENCE OF TRUTHS. My translation:

A. General Introduction

  1. Speculative Strategy
  2. Immanence, finitude, infinity
  3. The absolute ontological referent
  4. The two possible readings of this book

B. Prologue. Formal Presentation of the absolute location

C. Section I. The classical forms of finitude

C1. Destinies of finitude

S1. Modern finitude on trial: René Char

C2. The four types of finitude

S2. The localisation of the infinite in Victor Hugo

C3. The operators of finitude: 1. Identity

S3. Impersonality according to Emily Dickinson

C4. The operators of finitude: 2. Repetition

S4. Paul Celan: the work and the ordeal of masked repetitions

C5. The operators of finitude: 3. Evil

S5. Mandelstam in Voronezh: Make no concession to Evil. Neither plaint nor fear

C6. The operators of finitude: 4. Necessity and God

S6. The poems of Alberto Caiero. Bare being. Neither God, nor interpretation, nor necessity

C7. The operators of finitude. 5.Death

S7. A poem by Brecht. The unknown: death and identity, or life and universality

D. Section II. Modernity of finitude: covering

C8. Phenomenology of covering

S8. Uncovering of the covering of an infinite

C9: Ontology of covering

S9. Formal presentation of the constructible universe

C10. A crucial choice: constructible or generic

S10. Gödel or Cohen

E. Section III. Sovereignty of the infinite

C11. The four modes of access to the infinite

C12.Inaccessible infinites

S12.The matheme of the inaccessible

C13.Infinites of resistance to division

S13.Matheme of partitions: compact and Ramsey infinites

C14. The infinite by immanent magnitude of its parts

F. SECTION IV: Adjacent to the absolute

C15. On what conditions can classes express the absolute location?

S15. Technical conditions for classes to resemble V

[Note: “V” or the von Neumann universe is the class of hereditary well-founded sets]

C16. Closer and closer to the absolute?

S16. Elementary embedding, critical point, complete cardinal

C17. Explicit relation between the absolute location and one of its immanent attributes

S17. Construction of an internal model of V by ultrapower

G. Section V. Conditions for a defeat of covering

C18. Limits of modern finitude under the condition of an infinite. Scott’s Theorem.

S18. Infinites in the finite, infinites outside any finite. Demonstration of Scott’s theorem.

C19. Ontological conditions of any creative initiative. Jensen’s Theorem.

S19. Jensen’s Theorem. Apparent simplicity and real confusion of finitude

H. Section VI. Parmenides’ Revenge

C20. The hierarchy of infinites

S20. Differences, orders and limits in the realm of infinites

C21. End without end

S21. Kunen’s Theorem, and beyond

I. Section VII. Works according to the object: science, art

C22. General theory of works-in-truth

S22.Plato, Descartes, Hegel

C23. Power of the form: the arts

S23. Can the arts be classified?: Hegel and the cinema

C24.Power of the letter: the sciences

S24. Husserl: “our mother the Earth is immobile”

J. Section VIII. Works according to becoming: love, politics

C25. The scene of the Two

S25.Kierkegaard, Auguste Comte, Régine, and Clotilde de Vaux

C26. The two ways, the two classes, and the two lines

S26. For a cultural revolution of politics

K. General Conclusion: Immanent infinity of true life

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“PENSER DANS UN MONDE MAUVAIS” paradoxe gnostique ou constat immanent

“Penser dans un monde mauvais”, le titre est pessimiste, il contient une tension presque contradictoire. Si le monde est totalement mauvais comment peut-on arriver à penser dans un tel monde?

Le titre contient un paradoxe, le monde n’est pas simplement et monotonement mauvais. On dirait presque du Cioran, le constat gnostique répétitif de la “mauvaiseté” du monde, la lucidité du désespoir, la sagesse monotone du renoncement.

Je ne veux pas retourner au dogme optimiste d’un monde totalement bon, ni au dogme hédoniste d’un monde globalement satisfaisant (ce que Badiou appelle le monde “atone” du “matérialisme démocratique). Le constat pluraliste reconnaît cette omniprésence du pouvoir, mais ce n’est pas le dernier mot. Il y a d’autres niveau et d’autres tons. Dans ces mondes atones penser fait exception. Selon Badiou le monde atone nous convoque à “vivre sans Idée”. Mais nous vivons toujours dans beaucoup de mondes, et la foi dialectique nous dit que la pensée est toujours possible:

Tout animal humain peut se dire qu’il est exclu que partout et toujours il ne rencontre qu’atonie…Incessamment, dans quelque monde accessible, quelque chose advient” (LOGIQUES DES MONDES, 536).

Pour Geoffroy de Lagasnerie aussi la pensée ne se confond pas avec une simple lucidité passive. Il reprend à son compte les indications de Michel Foucault décrivant l’acte de la pensée. Penser c’est passer à l’acte dans un monde de passivité, c’est transformer le champ des possibles et se transformer soi-même.

Deleuze aussi parle du constat d’immanence, du monde comme champ de démolition, de la perception aiguë de l’injustice du monde. Mais les choses ne s’arrêtent pas là. Selon sa foi pluraliste il est toujours possible de tracer des lignes de fuite, qui sont aussi des lignes de création. Deleuze parle de croire au monde, d’avoir confiance en ses possibilités. S’il y a rupture entre la pensée et le “mauvais monde” il faut se détourner de ce monde mauvais et trouver des raisons de croire au monde et de continuer à penser.

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