"The ideal of the open must be opposed to the scientific ideal. Adorno is one of those who went in for the ideal of the open, along with Bergson, Heidegger and Deleuze, among others, all of whom were opposed to the supposedly closed nature of the scientific ideal, to be understood as conveying the idea that the negation of negation is an affirmation, and consequently closes negation. The aim of the ideal of the open, on the contrary, is the idea of a negation such that even negation does not eliminate it: even if negation were to be negated, in other words, it would not be eliminated, and the open would be maintained. The open is the fact of replacing form with formal transformation. The informal, from this perspective, is the possibility of confronting formlessness in a context that would ensure that any form exists only in order to be immediately transformed and that this transformation must itself be erratic, or have no form whatsoever."

— Badiou, *Five Lessons On Wagner*, “Adorno’s *Negative Dialectics*.”

This is actually a pretty brilliant insight, and its making me totally revise my opinion on Badiou—I don’t know if his thought re: mathematics is more complex than I originally thought or if he’s just doing a very faithful exposition of Adorno, but the claim that only for a mathematical consciousness does the negation of negation make a stable, positive affirmation is *really *good (and totally contradicts what I thought I had understood about Badiou’s mathematical realism).