So long as academic presses continue to jail our books behind prices like this, I consider anyone who's not making their work available online to be a fool. Paul Livingston, who is not a fool, has just released his excellent book, The Politics of Logic, to you, dear readers. [UPDATE: THE MANUSCRIPT IS NO LONGER AVAILABLE AT THIS URL. PAUL CAN, HOWEVER, BE REACHED HERE.] The book is a fascinating piece of work, which conscripts the conceptual achievements of analytic philosophy -- and, in particular, of that artery of analytic philosophy that has developed a sustained and brilliant reflection on the aporias of structure and language -- to the ends of compiling and illuminating an "orientation of thought" that can compete with Badiou on Badiou's own territory -- what Livingston dubs the "paradoxico-critical orientation". The main gist is something like this: what Gödel's incompleteness theorems throw into dramatic relief is not a simple obligation to accept incompleteness (of any formal system capable of expressing arithmetic, etc.), but the need to make a decision between inconsistency and incompleteness. Badiou's conditioning of his philosophy by mathematics, and principally by the metamathematical and foundational results of Gödel, Skolem, Cohen and others, elides this decision, and so passes over the possibility of the capacity for a rigorous -- and "complete" -- but essentially inconsistent discipline of formal thought to condition philosophy. Against Badiou's vision of the absolutely multiple, Livingston aims to deploy a vision of the paradoxical one, while retaining the ideal of conceiving radical situational change through the lens of formal thought. To this end, the book interweaves a sympathetic and subtle, but at bottom antagonistic reading of Badiou's work with a meditation on the foundations of mathematics and logic, and an invigorating synthesis of Wittgenstein and Agamben, Gödel and Derrida, and others.
Now go and read it [LINK BROKEN] for free.