Paul Livingston of the Philosophy Department at the University of New Mexico has a book coming out with Routledge this summer entitled The Politics of Logic: Badiou, Wittgenstein and the Consequences of Formalism. Sample chapters are available here. This passage from Chapter 1 gives a sense of the stakes involved:
This is the question of the formalization of formalism itself, of the reflection of formal-symbolic structures within themselves, and thus of the possibility of these structures coming to comprehend and articulate their own internal constitution and limits.
Within the analytic tradition, this question is posed and pursued within the ill-defined field sometimes called "metalogic." Its results are recognized as profound, but their larger significance has, so far at least, been difficult to place. In particular, despite the largely negative significance usually ascribed to them, the transformative results of Russell, Gödel, and Tarski, for instance, have in fact fundamentally articulated what we can expect from a critical reflection on the nature of language and our human access to it.
On the "continental" side, as well, such transformative critical meta-reflection has resulted from the massive mid-century project of structuralism as soon as "post-structuralist" philosophers subjected it to internal critique on its own terms.
One of my chief goals in the present work is thus to argue that these two strands of reflection on language – metalogical analysis on the "analytic" side, and post-structuralism in a deconstructive mode on the "continental" - can be allied, and thus can both be useful sources of critical reflection on the political implications of formalism as such. Their combination can yield, in particular, a formally clarified understanding of the constitution and structure of political communities, as well as of their possibilities of alteration and internal dynamics of change.
I'm very much looking forward to reading this when it comes out. I taught a course on Badiou in Fall 2009 and while it was very rewarding for me, and I can honestly say I greatly admire Being and Event, I couldn't quite buy the linkage of formalism and politics, despite the valiant efforts contained in Peter Hallward's excellent Badiou: A Subject to Truth. To put it in kind of a jokey way (but not too jokey!), Badiou keeps saying you have to choose, so if I have to choose, I'll choose Deleuze, life, affect, biology, and so on, all the things that Badiou wants to leave behind. So I'm hoping that reading Livingston's book will make me choose again, and in a even more informed way this time. I still think I'll make the same choice, but I think it will be a more informed choice, if you see what I'm saying.