Badiou, Meillasoux and Zizek: Formalizing the Event
The following attempts to locate the logical points of difference in Badiou, Meillasoux and Zizek’s ontological formalizations of the Event. The Event as treated will also be designated by two other names: “pure multiplicity” or “pure/radical contingency.” The justification for treating “multiplicity” and “contingency” here as synonymous will be grounded in the fact that, for all three thinkers, the One and the Law will be essentially be synonyms in such a way that their opposites, multiplicity and contingency, will be as well.
Such brings us immediately to the question of the relationship between Badiou’s pure multiplicity and Meillasoux’s radical contingency. In fact, a difference between the two terms does immediately seem to present itself, in so far as for Badiou, pure multiplicity will merely be the form of any being in so far as it is a being – that is, multiplicity itself as the generic structure of beings – while for Meillasoux, contingency will be a kind of ontically creatively void, where anything can come into existence or go out of existence at any moment for no reason whatsoever. In other words, the difference between multiplicity and contingency here presents itself as the ontological difference: the difference between Being, as a mere structural form of beings, and beings at the level of actual ontic occurences.
However, in addition to noting that Meillasoux’s radical contingency is also the most generic principle of beings in general that can be posited (thus granting it also an ontological status) we should note that for Badiou, multiplicity also can have an ontically creative function, i.e in what he calls, in the strict Badiousian sense, the Event.
If Being as void for Badiou excludes the event (as self-belonging multiples are prohibited by mathematics) there is still the possibility of the event arising as a local contradiction between a situation and its particular void. In other words, Being can move from form of multiplicity to contingent ontic creativity if multiplicity is localized in a situation – what Badiou calls “the evental site” – thus linking multiplicity and contingency.
However, the key to the possibility of the evental site is the existence of what Badiou calls the state. The evental site is the part of the situation which escapes the doubling effect of the state, and the state is the set-theoretical function that re-counts the original situation (every multiple whose multiples are in turn also part of the situation) in order to secure the hold of the One. The evental site is what exists in a situation, without its multiples in turn existing in the situation, such that it escapes this redoubling function of the state.
If for Meillasoux Being is irreducibly ontically creative, while for Badiou Being excludes the event unless it is localized in the evental site, this can only be for the simple fact that for Meillasoux there is no State of the situation.
Consider the way Meillasoux distinguishes his radical contingency from probabilistic occurrence. In After Finitude, Meillasoux explains that contingency is different from probability because probability requires a set of possible occurences. However, at the level of the universe itself, there cannot be a total set of possibilities. Meillasoux invokes the set theory which, following Russell’s paradox, demonstrates that there cannot be a set of all sets, a total overarching set. There can be probabilistic occurences within particular physical laws, but there is nothing to guarantee these laws themselves cannot vanish at any moment, since there is no ultimate Law to regulate and sustain their existence.
Yet Badiou agrees, also using set theory, that there is no totalization of the universe. The difference is that Badiou takes seriously the power-set axiom, the set-theoretical transcription of the fact that every situation has its state. So why can’t events just randomly happen at any time for Badiou (that is without taking into account the necessity of the structural perquisite of an evental site)? Because every situation always has some state above it which is holding said situation in its place. There is always relative stability, even if there is no total one.
Let us now examine the difference between Badiou and Zizek in formalizing the Event. The key move for Zizek, as outlined in Less Than Nothing: Hegel and the Shadow of Dialectical Materialism, will be to assert the speculative identity of the Lacanian barred subject and object petit a. What this ultimately amounts to is thinking the contradiction wherby the merely formal subject coincides with the missing object of the subject’s desire. Form lacking object and object lacking form become identical.
The key is to understand how we are here within the conceptual constellation of Kantian epistemology (elaborated more in the previous post). For Kant, the transcendental subject is a mere form without content, the fact that things always-already are structured. Just like Badiou’s One, it is always only “a mere operation,” not a positive entity. However, the Kantian subject rests on the existence of what Kant called “the object = x” whose Lacanian translation is the object petit a. In order for the transcendental subject to operate it must relate to a missing object which will stand in for any object at all, which is why Kant also calls the object = x, “the concept of an object in general.” It is the universal object, which is also why it itself can never be given in experience, in the here and now as this or that particular thing.
Zizek has expressed his disagreement with Badiou concerning the one and the multiple by saying that for him, the pure multiplicity of Being must be thought as internal to the non-being of the one. This is the difference between Badiou’s subtraction and Zizek’s dialectical negation. Whereas for both thinkers the one is not, for Badiou the subtractive process of mathematics splits Being from the one and thinks it as independent from non-being.
Yet for Badiou, this contradiction of the One in its non-being and Being is to be thought in his version of the Event, that is, in the local contradiction between the evental site and the state, as already examined. The state, which tries to secure the One, in certain situations misses the void which has snuck its way into the evental site. When the multiplicity of the evental site is then introduced directly into the situation, a contradiction results whereby something new can happen – ontic contingency.
For Zizek, the Event is internal to Being, because the contradiction between state and lack (that which escapes the state) is the very contradiction between form and content which is the speculative identity of Being itself. The barred subject, mere form, is at the same time to be thought of as a content, the object petit a, which is the content that lacks a form, never given in a direct apprehension. I.e the content without form, the multiple without-one, can only be secured if we see the very non-being of the one – the merely formal character of the subject – as the very multiple-content. What escapes the state's count is the state itself.
Yet, for Meillasoux, like Zizek, the Event is also internal to Being, because Being's singular principle is the radical contingency of occurrences, the ever-present possibility of something new. However, for Meillasoux the state does not exist, where it does for Zizek, the Event being the very presupposition of the state in its self-contradiction.
I.e at the level of ontology:
The difference between Badiou and Meillasoux is that for Meillasoux there is no state of the situation.
The difference between Badiou and Zizek is that for Zizek the Event, as contradiction between the one and the multiple, is internal to Being itself.
The difference between Zizek and Meillasoux is that, for Meillasoux, there is no state of the situation.