Tag Archives: Badiou

Russell’s Paradox – A proposal for a better explanation.

I think I finally have a good way of explaining Russel’s paradox.

Think of the box that holds all of the boxes.

This box is the biggest possible box. This seems to work.

The definition of a box is to contain something smaller than itself.

What if instead of the word box, I replace it with its definition:  Something that holds things smaller than itself. If we want to have THE thing which holds ALL things smaller than its, then it would have to be smaller than itself and bigger than itself at the same time. As in, The Biggest Box, as that which can hold/contain things, must hold itself, but since this is impossible we cannot conclude that this Biggest box exists. There are only some Boxes.

Or, think of The Container that contains All the containers. If ALL the containers are contained in this One Container, then this container should also be contained in this One Container. This One Container that supposedly contains All containers can no longer said to be a container. By its definition/property (containment) then becomes contradictory.  How can a container contain itself? It cannot. Can’t we just change the name to, say, The ONE?

No. that is, not if we are trying to provide the foundation for what exists based on containment (set), which is a collection of objects determined by a property. The sole “being” of the set is determined by how the objects relate to each other in the set.

It’s tempting to give a Wittgensteinian answer: “When we try to determine what things are based on their definition and not by their use, we run into all sorts of funny trouble.” This would not hold up for a number of reasons. First, though sets are defined by their composition, “use” is not excluded and is in fact an essential part in identifying a set. A set is determined by a property, which is chosen based on its use. Badiou’s “Count-as-one” is essentially the same as Wittgenstein’s “use”  or “game.” Second, if a being is determined by its use, what would it look like to determine “all that exists” by its “use”? We would have to remain silent on this question, or have many different definitions. Third, if we are looking to define beings with use, then we would have to determine how we use, use, in order to make any attempt to define “all that exists.” Finally, for those that are skeptical in applying set-theory to ontology, and therefore skeptical about rejecting The One, the being that contains all beings, one would have to demonstrate an alternate formulation of differentiating between beings, that is, the one and the multiple.

If The One is defined as that which contains everything, then it is contradictory and another way of making distinctions between beings must be proposed, that is, an alternative ontology.

What do you think?

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Badiou and Phenomenology — a few words

I am currently working on the second installment of “Ontology — Badiou and Merleau-Ponty — Part II.” It’s proving to be an extremely fruitful endeavor. I hope it will also be fruitful for you, my dear reader. And though Part II is not quite finished (I apologize for the delay),  I wanted to share a few quotations with you by Alain Badiou in hopes that it my elucidate this project between the Logician of Worlds and the Phenomenologist of this world.

“The poem is not the guardian of being, as Heidegger thought, but the exposure to language of the resources of appearing. Further, this exposure itself is not yet the thinking of appearing, which, as we will see, takes the form of logic [a formal theory of relations] alone.” Second Manifesto for Philosophy (29).

“The difference between being and appearing is much rather that which distinguishes mathematics (as ontology) from logic (as phenomenology) — each of these two disciplines being just as formalized and rigorous as the other.” Second Manifesto for Philosophy (36).

“When I recognize that  multiple which belongs to the situation (which is counted as one there) is connected — or not — to the name of the event I perform the minimal gesture of fidelity: the observation of a connection (or non-connection). The actual meaning of this gesture — which provides the foundation of being for the entire process constituted by a fidelity — naturally depends on the name of the event (which is itself a multiple), on the operator of faithful connection, on the multiple therein encountered, and finally on the situation and the position of its evental-site, etc. There are infinite nuances in the phenomenology of the procedure of fidelity. But my goal is not a phenomenology, it is a Greater Logic (to remain wihtin Hegelian terminology). I will thus place myself in the following abstract connection and non-connection. This abstraction is legitimate since ultimately — as phenomenology  shows (and such is the sense of the words ‘conversion’, ‘rallying’, ‘grace’, ‘conviction’, ‘enthusiasm’, ‘persuasion’, ‘admiration’ … according to the type of event) a multiple either is or is not within the field of effects entailed by the introduction into circulation of a supernumerary name.” Being and Event (329).

The quotations above point towards a project concerned with the workings, structure, and organization of terms. The intimate relationship that these terms have with a subject, or subjects, is not what is of primary importance. What is of primary importance is whether or not a term is eventually rejected or incorporated into a situation. In other words, the (sometimes long) process of discerning whether or not a term is necessary to complete a goal is not Badiou’s objective. Badiou’s objective is to name the fact that this judgement, this exclusion and inclusion of terms, must occur in order to realize one’s commitment to a grander idea.

Badiou — where is agency?

It’s ironic that Badiou criticizes Delueze for having a subject with no agency when Being and Event is written almost entirely in the passive voice. Furthermore, he seems to be doing more phenomenology than he would like to admit. He describes the event, but, paradoxically, by describing the event and it’s conditions, he may be inadvertently giving those subjects, who read his book and would like an event, the poison and not the cure.

For Badiou, it would appear that event has far more agency than the subject; the subject only carries out what the event has prescribed. Now, given this, is a subject’s awareness of evental conditions something that hinders or facilitates an event? I can see a few options.

  1. Badiou might say that the event is so powerful that it won’t matter whether a subject is ready or not.
  2. The awareness of these conditions facilitate the event because one can try and organize multiples accordingly.
  3. Trying to calculate and manipulate multiples is antithetical to the production of an event because an event cannot be calculated. For instance, I’m told that there are many revolutionaries who try to calculate the perfect time for an event, but because they are so intentional in their readyness for the event, they are never sure whether “this is it!” until the revolution had already taken place. To put it differently, those who were grabbed by an event were not thinking “make an event happen” but “make X happen.”
  4. Badiou might say that these calculative revolutionaries might have just had the wrong calculative apparatus.
  5. On 219, Badiou praises Pascal for saying that the “miracles (events beyond proof)” are what founds a subject’s belief.  Badiou condemns, in the name of Pascal, those nihilist libertines/pessimistic French Moralists who try and produce a Christian subject — that is, produce an event in a subject — by presenting a chaotic and desolate picture of the world. The subject has two choices: ultimate despair (atheism) or life (Christianity). In this sense, a subject can try and push themselves to an extreme, engaging in self-destructive activities until they are either pushed over the edge or until they experience an event. One could almost say that this is the real meaning of “the cast of the die” in  Mallarmé’s poem. If one wants to push it further, one could say that participating in “only a little bit of self-destructive behavior” is only carried out because the subject wants to feel like they have control over their mortality: “I can push myself off the edge if I want to. See! Look at me! I’ve done this little bit of self-destructive behavior.” Once this activity is completed, they go back to their normal lives, and occasionally flirt with their mortality. But it there is never a true interaction with death and finitude. One might say that because they are not faithful enough to their nihilistic event (say, a day or two of utter despair which resulted from a few unfortunate encounters, death of a loved one, etc.) their fidelity is only spontaneous. In this sense, to provoke a conversion via nihilism is always a failed enterprise because an event names something positive and self-referential, which does not exist because one sees the evil in the alternative.
    Anyone have thoughts on whether a subject has more agency than an event, if so, in what way?

A subject is formed by something that does not exist

As some of you know, I’m in a reading group that centers on the work of Zizek, Lacan, and Badiou. Lately, the project has taken on a new life. We are currently working towards the possible publication of a reader’s guide to Badiou’s extremely intimidating Magnum Opus: Being and Event. In it, Badiou claims that mathematics is ontology. In other words, our discourse about the world requires us to make distinctions between beings, and since mathematics is the most rigorous method for making distinctions, the next step is to claim that mathematics is the study of being.

This has led me towards a few thoughts.

If Mathematics is ontology, then Being can, to a large extent, also be predicted. It is calculable. This leads Badiou to ask “how is a subject possible within a universe that is radically predictable?” It turns out that events alone are what constitute a subject. The subject’s allegiance to an event is what constitutes a subject. The event re-aligns the subject’s framework for interacting with the world because we interact with beings in our world according to a certain importance, according to a relationship to something else (like an event). So, being able to truly say that I love someone, commits me to a lifestyle and manner of interacting with people that orients my entire existence. Thus, how I distinguish and interact with beings is re-oriented. In Badiou speak, how I count things is re-oriented. But Badiou uses the passive voice almost entirely throughout his work. Which leads us to ask “Who is doing the counting?” The answer seems to be: the event is doing the counting. Therefore, a subject is constituted on the basis of how faithful s/he is to the event’s count/the organization of beings.

However, events only appear for a short while, like the vanishing isle on the back of a giant turtle which never appears in the same place twice. And it is only after the island/event has disappeared that one can recognize it as such. In this sense, events don’t actually exist because one can never name an event as such, only after the fact. This means that events don’t actually exist. Thus leading to a troubling conclusion: if events don’t exist, then, at bottom, are subjects formed by something that does not exist?

Now, is counting (set theory), even if it is guided by an event, really the fundamental movement of ontology?

Heidegger claimed that once a specific being was looked at in a calculative manner, the being is gone. It is no longer possible to see it in terms of our condition, in terms of Da-sein.  By privileging the calculative analysis (the count), the many colors of Being are white washed into a single tone. The sole criteria for determining the worth, or meaning of beings is reduced to a calculation, a mode of thought that only views a beings as resources to be mined and placed in an network of utility. Is it possible, as Badiou claims, for calculative thought to be reconciled with a phenomenological hermeneutic? How does one balance these two modes of analysis?

Context as Necessity

Often reading textbooks on Art History, philosophy, or even Music, a great deal of context is given. The work in question has to be situated. It comes from somewhere.

But I get the sense that when the climate of the times is described, the author implicitly suggests that the work wasn’t anything really special, or genius. One can easily trace its origins to the current ideas circulating.

When one presents a work like this, we cease to really see its transforming power. We cease to see it as a work of genius. And, I think, there are geniuses. When one reads a biography of the artist/philosopher in question, the transforming power of the work is almost always raised to a much higher degree because the work in question is seen in detail. When I look at it as one instance of one person’s work, as a sign of the times, I’m not really looking at the work as it was presented in its own context.

I can’t help hear Badiou’s voice in my head: an event is an ontological decision. One of his examples is the French Revolution. Once it is infinitely picked apart, no one can name it as unified event anymore, and if no one can name it as an evental site, it no longer holds any trans-formative power.

In sum, the way one views an artwork is a decision. I can decide to see Schoenberg as a consequence of the steady increase of the use of dissonance. Indeed, he seemed to say as much. But. One hundred years after Schoenberg, people often see his late work as the cut-off of what constitutes good classical music (Bach, Beethoven, Brahms, Mahler, then it ends…). And I can also say: “Ya, he wasn’t so great. You can easily see where he comes from. Sooner or later someone would have done what he did.” Here, (bad?) historical context is used as a weapon against the naming of a revolutionary work.

Be wary of textbooks and biographies that use context. Tracking the influence of a work is a difficult business, even if it is within context. So, “Context”, then, can be used either for the discrediting of a revolutionary work, or it can be used to show just how revolutionary the work really is.

Distinction: Badiou and Heidegger

Is the most rigorous form of making distinctions located in mathematics? Badiou seems to think so. How is it that there is a world that can guide our making of distinctions? What are the conditions for us saying that something can exist in the first place? These are Heidegger’s questions.

In other words, if Badiou is right, then is math, and should math be, primary in our distinction making? Another way to look at the question would be to turn to art. How is it that a style emerges from an artist that is somehow distinct from the rest of the canon? Can mathematics help us here?