The appearing of Heidegger’s beings in Badiou’s set theory.

Color shines and wants only to shine. When we analyze it in rational terms by measuring its wavelengths, it is gone. It shows itself only when it remains undisclosed and unexplained. Earth thus shatters every attempt to penetrate it. It causes every merely calculating importunity upon it to turn into a destruction. This destruction may herald itself and the appearance of mastery and of progress in the form of the technical-scientific objectifivation of nature, but this mastery nevertheless remains an impotence of will. The earth appears openly cleared as itself only when it is perceived and preserved as that which is essentially undisclosable, that which is shrinks from every disclosure and constantly keeps itself closed up.

[Die Farbe leuchtet auf und will nur leuchten. Wenn wir sei verständig messend in Schwingungszahlen zerlegen, ist sie fort. Sie zeigt sich nur, wenn sie neentborgen und unerklärt bleibt. Die Erde läßt so jedes Eindringen in sie an ihr selbst zerschellen. Sie läßt jede nur rechnerische Zudringlichkeit in eine Zerstörung umschlage. Mag diese den Schein einer Herrschaft und des Fortschritts vor sich hertragen in der Gestalt der technischwissenschaftlichen Vergegenständlichen der Natur, diese Herrschaft bleibt doch eine Ohnmacht des wollens. Offen gelichtet als sie selbst erscheint die erde nur, wo sie die wesenhaft Unerschließbare gewahrt und bewahrt wird, die vor jeder Erschließung zurürckweicht und d. h. ständig sich verschlossen halt.]

Here we see Heidegger making a statement about how the earth truly reveals itself. It reveals itself only when it is presented as undisclosed and uncalculated. When a painting or waterfall is reduced to wavelengths, it ceases to work upon one’s everyday experience of beings. It becomes one set of wavelengths among many, and no wavelength more important than the other, except as it pertains to the domination of nature. If all things are reduced to objective particles, then they cease to work upon our experience as they should, that is, as beings revealed. Beings revealed are those that work upon our view of things and give things their shine, like a Greek temple which reveals beings as they are and how they relate to us and to the temple, and vice versa. In contrast, the kind of calculation that he is talking about is one that seeks to dominate nature. It seeks to bend things to the human’s will to power. “Do I want this? Yes, then I will do it since all things are, are a bunch of particles and have no importance beyond that.Thus, I see all things as particles, as resources, waiting to be gotten by me.” — instead of beings that shine.

Let’s turn to Badiou. Badiou recognizes, and he thinks most agree with him, that Heidegger is the last recognized philosopher. Furthermore, Badiou is constantly in dialogue with him and grapples with his thought almost at every turn. Badiou also incorporates mathematics (the most rigorous form of making distinctions/calculations) into his own ontology (Being and Event) – something that has never been done before. at least with such rigor, that is. The result is often one that is less than inspiring. Often, when one reads Badiou, one gets an overwhelming sense of a cold calculative disposition towards the world (see Clayton Crockett’s critique — a rather superficial one, I think). But this is a gross misreading of Badiou. It misses Badiou’s constant praise of the poetic and the phenomenal. It would not be too brutal a statement, or proposal, to say that Badiou is a staunch Heideggerarian who has been able to incorporate a productive understanding of calculation.

I propose that Heidegger is misusing the term “calculation.” Or rather, he is giving it a bad name. What Heidegger is talking about is not really so much calculation as such. He is attacking a particular way of viewing beings. A particular kind of calculation. No doubt painters can be said to be calculating as they paint, or composers as they compose, or writers as they write. Each of them must focus in on certain aspects of composition at certain times of importance. They can organize material according to large structures, or small ones depending on how they are calculating, or in set theory/Badiou language: “how they are counting.”

Set theory does not calculate beings in the pejorative sense that Heidegger is addressing, but, in fact, it simply organizes them. It never presumes to reduce anything to a number. Things (or sets) gain their existence by being in a relationship with other things. In other words, set theory functions according to axioms and not according to defining, at bottom, what a being is. Set theory is a system of relations. It is not ‘out to dominate nature.’

So, is Badiou’s use of set theory too calculative, too nature-dominating? I propose that it is not. I propose that it merely organizes beings in terms of importance. And, is this not what art is? Is this not what Heidegger demands of the artist – to organize beings according to what is important?


About JoeL

I completed a Master of Music degree from McGill University. I am currently working towards an Artist Diploma also at McGill. I like to do philosophy as a hobby.

6 thoughts on “The appearing of Heidegger’s beings in Badiou’s set theory.

  1. Let me suggest that a key term for phenomenology in the context of what you’re writing about here is “seeing.” Badiou’s preferred term, it seems, is “calculating.” Does this difference in term preference make any difference? Are you saying that if we understand it broadly enough that “calculating” is another way, perhaps even a better way, of talking about the different ways of seeing. Does it matter that many painters, poets, etc. would be loathe to describe their inspiration in terms of calculation (perhaps you’d disagree with this premise)? Is there a difference here between the rules of music and perhaps specifically improvisation and counterpoint (two of your primary disciplines) and putting brush to canvas or words to page in a needlessly inefficient but powerful poetic way?


    1. When one does math, one “does calculations.” And since Badiou uses math so much, he can be said to calculate ontology. But he also “sees” as well. A central concept for Badiou is “presentation” “What presents itself is presentation” And the structure of this presentation, “what we see” can be formalized with math, that is, with set theory and its rigorous calculative apparatus. What I’m trying to answer in this post is this question: is it possible to say that, at bottom, the structure of presentation (beings as they appear) is mathematics, or are the two irreconcilable? And my point is that set-theory does not reduce beings to a point. Set theory is axiomatic, it formalizes relations between beings. The composition of beings determines their identities. And since their composition can change, beings are not reducible in set-theory and thus with Badiou. This is also the question I was trying to get at in this post


  2. I am both excited and made uneasy with this discussion. It sounds like you are positing a kind of relational ontology via set theory for all beings; in this case I give two thumbs up and say “tell me more…” Mostly because, for Christians, I think there is something helpful in grounding worship in a doctrine of the trinity that holds one’s being in a full relationality – this is something I’m working on.

    But as I begin to trace and complicate this discussion I become uneasy. Speaking about a kind of base, however relational or axiomatic it may be, tends towards both an essentialism and representation; an essentialism in the claiming of a base; a representation in saying that X is, at its most base not X but XmathsX. Does the claim that set theory is at the base disempower X? Or, does Badiou’s claim of X’s dynamic composition eliminate the possibility of X’s disempowerment?


  3. [Sometimes a painting of rabbits is a painting of rabbits. Grey is grey and pink is pink. Right now I am working on a small painting that has about 7 different rabbits on it and they are all pink or grey. I don’t think this painting “shines” but perhaps viewers besides the artist are better suited to make that judgement. I also don’t know where the mathematics are in the piece. When I’m done I’ll send it to you and you can judge it on its shininess and axiomatic potentiality. It might be fun?]

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  4. Great questions Lisa. I will try and do another post based on those ideas since “representation” is treated very precisely in Badiou’s work. “Speaking about a kind of base, however relational or axiomatic it may be, tends towards both an essentialism and representation.” I think the opposite is true. A rabbit is a rabbit because it’s easily identifiable as rabbit. I “count” it as a rabbit. Yet the rabbit is a multiplicity of things: legs, ears, fur, etc. These multiple parts are included in the name “rabbit.” We do not have to make a choice what a rabbit, at bottom, or at base IS. It is a rabbit insofar as fulfills our current and local criteria for what constitutes a rabbit. We get into trouble when we try and provide a universal definition for what a rabbit, essentially IS. This is the difficulty that Plato had: how can we have so many varieties of horses? well, probably there is one Idea of a horse somewhere. Does that help a little? like I say, I will try and do more posts about Badiou. it’s difficult to give easy summaries because all of his terms relate to one another somehow. But the deeper you get, the easier it is to get a grasp on what he’s doing. It’s really brilliant.


  5. Another thing that my help is to think of Badiou as a strange Wittgensteinian. The backbone of Badiou’s work “the count-as-one” is not really any different than aWittgenstein’s “language games.” I say this is rabbit because that is how I use the word rabbit. Obviously Badiou has problems with Wittgenstein (Badiou has problems with everyone, basically), but he does draw a lot from his work.


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