Whn Badiou asserts that mathematics is Ontology what does he mean by Ontology?

Question

Badious oeuvre can be succintly phrased in his slogan: mathematic is ontology.

Mathematics I understand. So the question really is the other part of his slogan. I take his 'is' to be normal and ordinary english verb fulfiling its notoriously ambiguous function. So what does he mean by Ontology? Is it say the same Ontology that Heidegger expounds on in his Being and Time. Is it process and active rather than static and stable? Whereas time is a contiuum, Badiou in his book prefers the event - a punctuation in time. Is this significant?

Answer 1

I might well be wrong, but what I understand, Badiou sees mathematics as our way of getting at things-in-themselves, as opposed to philosophy and the natural sciences, which have to deal with everything mediated by sense perception, with all the epistemic obstacles inherent to that (things-for-us).

I'd also point out that that statement does not sum up Badiou's oeuvre; it's important, but there are a lot of other very important axioms and assertions in there too (theory of the subject, etc).

As a sidenote. Looking down the list of questions, it seems that the vast majority of the questions (and presumably the contributors) fall with the analytical/anglo tradition. Are you the sole continental voice on here Mozibur? :) (I would be happy to help balance things a bit!)

Answer 2

As I read Badiou, he means the statement in a strongest sense possible: mathematics is simply what exists. The Event is an illegal intercession on ontology that violates the axiom of regularity (or foundation) by belonging to itself. As for his concept of time, you're not alone in finding it to be unclear. His Being and Event was criticized as being too static -- a shortcoming he attempted to redress in Logics of Worlds, which deals with appearance (in the sense of becoming) in addition to being.