Badiou and A Typology of Truths

One of the most common objections to Badiou is that his listing of the four truth procedures (science, love, art, politics) is arbitrary; why are there only these four? The reproach tends to come from one of two directions: either readers perceive no rigorous method proposed by Badiou in this enumeration, or they think that the arbitrariness of the four types follows from Badiou’s own concept of the radically subjective nature of truths.

The result in both cases is to reduce Badiou’s enumeration to a mere personal proclivity, which often accompanies other claims about Badiou’s supposed authoritarian posturing. However, rigorous philosophical method involves transcending ad hominem attacks and instead focusing on precise conceptual distinctions that are charitably drawn from the text itself.

The two lines of criticism mentioned above can be repudiated by demarcating specifically the manner in which Badiou’s theory of truth develops at the dual level of empirical specificity and conceptual generality. I propose a schematization of Badiou’s theory which he himself does not offer, but for which ample support can be found in First Manifesto For Philosophy, Being and Event, and Logics of Worlds.

There are three “levels” in Badiou’s thinking of truth, moving from the most general notion of truth to the most specific.

These are:

The concept of Truth (or Truth in general)
The typology of truths (math, love, art, politics)
Specific truths/truth procedures (Cantorian set theory, the Bolshevik Revolution, serialist music etc.)

The Concept of Truth or Truth in General

Badiou’s theory of Truth in general is most clearly explicated in First Manifesto For Philosophy. For Badiou, the concept of Truth is constructed in the unique space that is philosophy. The concept of Truth is not in itself material, but rather a discursive, general concept abstracted from existent truths. This is part of the sense in which truths “condition” philosophy, as Badiou says. Philosophy needs truths in order to determine what is most common to Truth, in the same way that one can only form a concept of “car” through the observation and analysis of real cars.

However, not all conditions are equal. As Badiou explains in Being and Event, he essentially agrees with Heidegger that philosophy must be assigned its destination only on the basis of the ontological question, the question of Being. Given that Badiou, as is well known, equates math with ontology, this means that philosophy will have a privileged relation to mathematics as one of its conditions. What are the motivations for this move?

Let’s think about the impetus that runs through all of Badiou’s philosophy: the critique of relativism and his defense of universal truth. Now if Being and Event has a kind of culminating point it is the utilization of Cohen’s theory of generic sets. If mathematics is ontology, and Cohen’s theory formalizes the indiscernible universality that belongs to any truth, then math assures that Truth has an ontological form. Thus, it is at least possible that Truth is not a fiction. Math assures that there is a consistent, ontological form of Truth. Truth, affirmed as ontologically possible, then is to be conceptually and discursively “filled in” by the philosophical analysis of the specific truth procedures that would locally instantiate this form.

The Typology of truths/Specific truth procedures

How do we move from the concept of Truth in general to the typology of the various kinds of truths? In order to explicate this move we have to already jump to the idea of the most specific truth procedures themselves. Our knowledge of specific truth procedures is radically empirical. This is straightforwardly Badiou’s concept of the Event. Truths happen, as real occurrences in history. As such, that there is this or that truth exists is an empirical matter. There is no deduction of the existence of a truth, and this is in part why truths are subjective decisions and are “axiomatic.”

Does that mean there is no criteria as to what can count as a truth? No. The rejection of this point is what allows Badiou to elaborate a theory of truths as subjective decisions and to construct a systematic theory of the essence of Truth.

Again, we must refer to philosophy’s ontological assignment. For Badiou, mathematics formalizes and develops the ontological notion that Being is pure multiplicity and the one is not. However, outside of the purely ontological presentation of multiplicity, a dialectical contradiction between the one and the multiple can arise according to local conditions: this what he calls the Event. Breaking the logical/linguistic unity of the oneness of the situation, the Event serves as the condition of there arising in said situation an indiscernible multiple, non-reducible to the language of the situation: i.e what would count, ontologically, as a truth. Thus, the Event is the condition for the local deployment of a particular truth which would instantiate the ontological form of Truth in general.

The possibility of truths thus rests on the existence of this dialectical contradiction between the one and the multiple, as well as the material consequences of the Event (the way the truth actually begins to change the situation in a readable way). This is the objective criteria as to whether or not something can be a truth.

So why love, art, math, politics?

Let us note the following.

1) The four categories are only adduced, and can only be adduced, because events of the corresponding character have actually taken place. That is, if no love events had taken place, if no revolutionary art or politics, or no mathematical breakthroughs had ever happened, the adduction of these four categories would be impossible.

2) Each category is meant to point out qualitative similarities between various truth procedures which are brought together using the conceptual means provided by philosophy in its development of Truth in general. Thus, love will correspond to the Two of the Event, art the relation between the one and the multiple (as staged in sensual form), math the thinking of the multiple-void itself, and politics the subtraction from the one (qua state apparatus).