What is a Contradiction? Badiou’s Theory of the Subject

In a previous post on Badiou’s Theory of the Subject, I described how the subject disappears under the chain of the signifiers, and how the masses inhabit the dimension of the Lacanian real. In this post, I’m going to dig deeper into Badiou’s text by looking at his wrestling with the concept of contradiction and dialectic. The text opens with a discussion of dialectics, for which he defines as one of the four modes of philosophy.

Let me sketch out the four modes briefly, but its important to note that these paradigms change for Badiou throughout his career in philosophy. For example, his new book on the 20th century has radically altered this layout, but these remain interesting and helpful models nonetheless.

The four modes of philosophy are:

Materialist: privileges being over thinking.

Idealist: privileges thinking over being.

Dialectician: turns contradiction into the law of being

Metaphysician: turns identity into the law of being.

Yet, there is a single contradiction throughout these modes: that between being-in-itself and thinking. Philosophers have grappled with this contradiction historically by presenting five primary theses, from Berkley, Kant, Hegel, and then Marx, who is actually split in two versions of materialism. It’s also important to know Badiou’s allegiance to Marxism, as well as his willingness to surpass its laws and structures.


Thesis 1: Berkley’s metaphysical idealism – thinking has no sensible outside. All thought remains in the imaginary. Truth = coherence. This paradigm forecloses the dimension of the real.

Thesis 2: Kant’s transcendental metaphysics: the being of knowledge is excluded. Being-in-itself possesses the force of law for the transcendental subject.

Thesis 3: Hegel’s dialectic: argued that the interior produces its own exteriority. The local exteriorization is never anything but the effect of a global interiorization.

For Hegel, absolute knowledge is that moment of discourse when in a perfect non-contradiction up to and including the fact that it includes itself and explains itself. All truth in the Hegelian sphere is integral. In its Lacanian version, we find that error is the agent of truth. If Hegel makes a passage out of the local, he seeks to secure something in the whole, for which Badiou argues we must move beyond (Pg, 121).

Thesis 4: the materialist who posits truth in the realm of the imaginary. We escape truth by going beyond repetition.

Thesis 5: the materialist dialectic who argues that we must differentiate thought from sensible being. What is already there in the process of knowledge is taken from being, and not from an idea. There is a subjective essence of the true: it is never reached except by twisted pathways.

This inventory gives us four names for truth: coherence, repetition, totality, and torsion.

In this post, I want to develop a better idea of how Badious wrestles with contradiction in his development of the theory of the subject.

What is a contradiction?

1. First and foremost, it is a difference. Weak differences are that of places – and strong differences happen when one true discourse destroys another false discourse.

2. Difference is implicated qua correlation, the two are differentiated via this is the unity of the opposites that posits the one of the movement of the two, and the one of their effective divergence. Struggle then is defined as a correlation that ruins the One. The current class struggle (post May 68) is a weak struggle/contradiction, and is therefore not deducible from the weak correlation.

3. A contradiction is not the equilibrium of the two but is the law of their inequality. One term fixes the place, and one term is subjugated. The essence-in-becoming of the asymmetry is the inversion, not the invariance, of position. It is the advent, centered on the outplace, of a splace overthrown.

There are three components to a contradiction: difference, correlation, and position. We can inscribe in a dialectical bipolarity whether the contradiction is weak (structural), or strong (historical). As Badiou says, “every real dialectical process entangles a structural contradiction and a historical contradiction, affecting the same terms” (Pg, 25). The anchor point of the historical is the structural, which is the nodal point for the question of the subject.

A capitalist society is characterized by the contradiction between productive forces and social relations of production, and the contradiction results in the antagonism amongst social classes. Yet, Badiou claims, we need a Marxism beyond the contradiction of Bourgeoisie and Proletariat – i.e. beyond the law of contradiction.

Building on the master dialectician and poet Mallarme, where we find a trinity of dialectical machines: vanishing term, splitting, causality of lack — anxiety, Badiou posits that a dialectical sequence approaches its closure when the practical process carries its theory in its own wake, when it possesses in itself the active clarity of its temporal trace (Pg, 19). This concept of a “temporal trace” can be taken in two senses:

1. All that is needed is for one of the contradictions, the outplace, or splace to become the bearer of the intelligibility of the preceding sequence.

2. Everything exists based on what is lacking from it, and the logical deduction from this is that the same applies to the cause. It is only by abolishing a first causality that you give consistency to the concept of causality itself (Pg, 82).

It is the “lack of lack” (what Lacan refers to as anxiety) that brings Badiou’s work in alignment with Heidegger’s philosophy of dasein. The lack of lack is what leads to poetic emergence, to chance, and to the real. Because the real for Badiou is ‘self-inclusion by way of being an element of itself’ – the negation of negation becomes a crucial part of the subject’s position. Badiou defines negation of negation through Mallarme’s idea that, “chance having been denied the first time, the second negation produces the idea of chance itself.” As Hegel says, “the infinite emerges from chance, which you have denied”

The negation of negation for Badiou involves the real, having been denied, and then in its denial, it produces the idea of the real for which it inhabits. Put another way; chance having been denied the first time, the second negation produces the idea of chance itself.

As Hegel says, “the infinite emerges from chance, which you have denied,” and it is the “lack of lack that leads to poetic emergence.” The forced exception leads to the subject, which is a bifurcated subject. Without the gap there would only be the monotonous and infinite efficacy of the grinding of being under the law of an absence (Pg, 89).

Badiou’s point is to “remit the real to the oblivion of its oblivion from where its causal force is purified in the lack: in the alignment of the true onto the whole. This type of work requires moderation” (Pg, 143).

What we are left with is ethics – I think part of the reason why the subject is rooted in this lack of lack and anxiety is because it is a subject that made clearer. As Lacan says of anxiety – it never deceives. The subject must assume their own lack in the real, for which Badiou asks: what is the difference between psychoanalysis and the political reeducation project? Both seek to totalize the symptom, because no subject preexists anxiety or lives beyond superego.

Yet the work of staying true to the dialectic may prove too much for modern man. As Lacan commented:

“Do we extend our analytical intervention to the point of becoming one of those fundamental dialogues on justice and courage in the grand dialectical tradition? It is not easy to answer, because in truth, modern man has become singularly unused to broaching these grand themes. He prefers to resolve things in terms of conduct, of adaptation, of group morale and other twaddle” (Lacan 1954).

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