Badiou explicitly calls his research in view of writing a third book to complete the system begun with BEING AND EVENT and continued with LOGICS OF WORLDS an « inquiry« . The first two books constituted an « analytic« , but the third book requires a « conversion ». He is no longer deducing the conditions of possibility of truths from the point of view of their being (ontology) or of their appearing in a world (phenomenology). He is concerned in this third stage of his with exploring what a world is when examined from the point of view of a truth. Given his emphasis that a truth is a practice we can perhaps call this a pragmatic conversion, but Badiou himself does not use this term.
Badiou begins his three and a half year seminar devoted to the immanence of truths with a summary of his concept of truth, listing six characteristics of truths. This is what he calls in the second class the « material » of the inquiry :
« 1. By « truth » I understand a construction, a process, a creation, and thus not something that has to do with the exactitude of a judgement ».
Immanence of truth: a truth is not reducible to a judgement, and it cannot be analysed as the correspondence of a proposition and the real. A judgement can be veridical, but this is the derivative effect of a truth procedure, and belongs to constituted knowledge, not to a constitutive truth. For a materialist, truth is a part of the world, immanent to the real, not corresponding to the real but transforming it.
« 2. This process includes an element of risk, an element irreducible to the figures of necessity of the world inside which there is this process ».
Truth as exception: the origin of a truth is an « event », a figure of chance, an encounter, an indetermination, a break in the necessities of the world in which it is constructed. This cut is the source of its possible universality. Immanent in the world a truth is not reducible to the world, is not absorbed by the world, not limited to the world from which it draws its materials.
« 3. The process of construction of a truth is also and at the same time construction of a subject of truth, which is the principle of orientation of the construction ».
Active obedience: the subject is not reducible to the somatic or psychological individual nor to a social group or institution. The subject is both active and passive: the local point of a truth procedure’s construction and its principle of orientation. The subject both obeys and decides.
« 4. What this process constructs is universal. The universal is not reducible to a logical category, it is not the universality of a judgement (it is not the universal quantifier ».
Universality means that a truth is potentially intelligible and practicable in different worlds than the one it originated in. Badiou adduces the example of Sophocles’ tragedies, whose materials belong to a defunct world, but as universal work of art can be understood by us, and continued, enriched, and transformed for contemporary use. This amounts to a pragmatic criterion of universality, close to Deleuze’s notion of the « untimely », but as remarked above Badiou does not call it so. In the second class he cites diverse examples: Euclid’s Elements, Spartacus’ revolt, Sophocles’s plays, the love of Héloïse and Abelard. He remarks « It traverses the centuries and everyone understands. »
« 5. A truth process is an infinite process. It makes no sense to talk about its completion or its closure ».
Openness: a truth is infinite, perpetually open to re-interpretation and to re-deployment in different worlds. It contains no intrinsic finitude. One of the criteria of universality of a truth is its openness, its incompleteness. A truth can always be « resurrected »: giving rise to new conclusions, re-understood and re-used in new ways. As an open process a truth can always be continued (Latour would say « reprised »)..
« 6. There are essentially four types of truth procedures: science (which makes truth from the relation possible between writing and the real), art (which makes truth from the border between form and non-form, politics (which makes truth from the collective capacity, from what the collective itself is able to do), and love (which makes truth from difference as such, in the mediation of sexed positions ».
Pluralism: there is a double pluralism of truths. Truth is not a singular concept, there is a constitutive plurality truths. Further, there are different categories of truths.
Badiou resumes these six characteristics in a single definition:
« A truth is a process, risky as to its possibility, subjective in its duration, particular in its materials, universal in its address or result, infinite in its being, and deployed according to four distinct types of processes ».
He proposes to condense this definition even further:
« a truth is an immanent exception to the world where it arises ».
A truth is produced in immanence to the world, in the world and from the materials of the world, and also, due to its potential universality, it is an exception to the world.
Note: Badiou begins the first class of his first seminar (2012-2013) with this explication of his concept of truth, and repeats it in virtually the same terms in the second class. I have translated the six characteristics from the version he gives in the first class, and in the explanations appended for each one I have combined the explanations from both the first and the second class, sticking very close to Badiou’s actual words.
Each year of his seminar is preceded by an « argument » stating the problematic and the programme of the coming year. I have translated these arguments here. In particular one can find the argument for the seminar of the academic year 2012-2013, which I have been discussing here.