Thinking further re. the Nirenbergs' critique of Badiou which I referred to last post, it strikes me that the oddest part is their casting of his equation mathematics = ontology as politically motivated, as trying to furnish an iron foundation for a 21st-century marxism--their analogy is to Engels' Dialectics of Nature. This seems to me to get Badiou wrong in a subtle but important way. Badiou is up-front with his motives. Whenever he talks about the lamentable philosophical effects of neglecting the matheme, it is always with reference to what he calls Romanticism. Romanticism, in turn, is that school which makes definitive the thematization of finitude. Badiou's re-casting of set theory as ontology is a move intended to laicize and banalize infinity once and for all, to render it incapable of lending comfort to the obscurantism of crypto-theology; and, let's be clear, for Badiou there is no other kind.
Can we really be surprised at so-&so's Rabbinic Judaism, or so-&so's conversion to Islam, or another's thinly veiled Christian devotion, when nothing is said that does not boil down to this: that we are 'consigned to finitude' and 'essentially mortal'?...The truth is that this disentwining [between mathematics and philosophy] renders the Nietzschean proclamation of the death of God ineffectual. Atheists, we lack the wherewithal to be so, so long as the theme of finitude governs our thinking....The only way to situate ourselves within a radical desecration is to return infinity to a neutral banality, to inscribe eternity uniquely in the matheme, and to abandon conjointly historicism and finitude. (Conditions, pp98-99)
One could cite any number of other passages, but let this suffice. Badiou's casting of mathematics as ontology or vice-versa is simply a radical secularizing move, to deprive "Being" of any lingering penumbra of holiness The "Question of Being" is, in this way, to be answered. This is what Badiou means by "Heidegger as commonplace." (It's also, incidentally, one of the essential connections between Badiou and Meillassoux.)
Now obviously I don't see things this way. There is (or can be) a finitism without pathos. (And forcing the banalization of infinity as he does obliges Badiou to read Cantor quite against Cantor's own sense of himself.) Spelling this out would be another and much longer post. But while Badiou's politics are not beside the point, they don't motivate the project in the same way. Yes, Badiou's critique is heir to Marx. But as we know, Marx himself insisted that "the prerequisite of all critique is the critique of religion." In this, at least, I am on Badiou's side, by the way.