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.