- General Introduction
- Speculative Strategy
- Immanence, finitude, infinity
- The absolute ontological referent
- The two possible readings of this book
- Prologue. Formal Presentation of the absolute location
- 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
- 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
- Section III. Sovereignty of the infinite
C11. The four modes of access to the infinite
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
- 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
- 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
- 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
- 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”
- 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
- General Conclusion: Immanent infinity of true life
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:
- Immobility: while making the thinking of movement, and indeed all rational thought possible, it remains absolutely foreign to that category.
- Non-composition, or intelligibility on the basis of nothing. It is not composed of other entities. It is non-atomic.
- 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.
- 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.
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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