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March 09, 2006
Maybe Being is a Mess
Taking into account the importance of historicity (evental history of mathematics) Badiou's minimal claim is only that set theory is the most powerful tool we have at our disposal now for describing things in so far as they are, regardless of what they are, and therefore constitutes our epoch's access to being; which is a claim that's both clear and eminently contestable, mathematically and philosophically. It seems to really depend (like Heidegger's decision - but with very different commitments, of course) upon a prior decision as to what ontology needs to encompass.
What is questionable is the claim that by adopting set theory we remain philosophically uncommitted (just as – to continue the analogy à gauche suggests – phenomenology affects to be free of all intellectual commitments) since the decision is historically-mathematically sanctioned. B. suggests that the decision, far from being arbitrary, has in some sense been made for us by the history of mathematics.
On the other hand, it seems more or less that it is the elegance and simplicity of set theory which commends it to the philosopher. But who is to say that being is simple or elegant? Isn't this precisely an unwarranted intuitive demand on the universe? What about Quantum Mechanics? String theory? even, on Badiou's own territory, the prime number distribution, the Riemann hypothesis. [[Questions that Badiou doesn't usually get asked, but which we hope to get an answer to when B returns from the States, in an interview in upcoming collapse 1)]].
I would guess that even mathematicians themselves would regard it as a somewhat tendentious decision to regard all other approaches as negligible and actually reducible to axiomatised set theory. I think (again, just a guess) most mathematicians are, pragmatically speaking, methodological and (implicitly) ontological pluralists. But then, Badiou dismisses 'working mathematicians' from the ranks of the ontologically-enlightened as easily as he dismisses complex numbers and quaternions from ontology itself[in Number and Numbers -]...)
Looking at the background that is laid out in Number and Numbers Badiou seems to stake a lot on a particular type of linear order whose characteristics have more to do with anthropological counting systems than with the realities that are being revealed to us at the cutting edge of science and mathematics. So is Badiou's claim that 'ontology=mathematics' is a claim about discourse not about reality all too near the mark...?
What in fact comes first is a set of demands, a politics of being, the real decision, which a suitable ontology will come elegantly, inevitably, to support (again, like Heidegger...?).
Posted by robin at March 9, 2006 08:09 AM