University of Cardiff, Wales
Abstract. Alain Badiou is a highly original,
indeed decidedly iconoclastic thinker
whose work has ranged widely over areas of equal
concern to philosophers in the ‘continental’ and mainstream analytic
traditions. These areas include ontology, epistemology, ethics, politics,
and – above all – philosophy of mathematics. It is unfortunate, and
symptomatic of prevailing attitudes, that his work has so far received
minimal attention from commentators in the analytic line of descent.
Here I try to help the process of reception along by describing Badiou’s
remarkably ambitious approach to issues of mathematical (more
specifically: of set-theoretical) ontology, and by explaining just where
his project stands in relation to some major issues within current
analytic debate. Chief among them are: the issue between realists and
anti-realists – along with various avowed middle-ground or compromise
solutions – and those oddly
tenacious problems-from-Wittgenstein (e.g.,
concerning what it means to follow a rule) that have so preoccupied
philosophers over the past decade. In particular I stress the unusual,
indeed unique combination in his thought of high formal rigour and
conceptual clarity allied to a speculative scope and inventiveness which
tend to make those other discussions appear somewhat self-absorbed and
parochial. Most importantly, Badiou engages these issues at a level of
creative as well as of technical or analytic grasp, which puts his
thinking closely in touch with the way that set theory has itself
evolved through a constant process of – in Badiou’s phrase – ‘turning
paradoxes into concepts.’ I also discuss his strong and principled
rejection of the ‘linguistic turn’ in its manifold (analytic and
continental) variants, and his idea of the ‘event’ as that which
inherently eludes or surpasses the conceptual resources of any received
ontology, whether in mathematics and the natural sciences or in the
history of
genuinely epochal changes in politics and ethics.
All in all, I put the case for Badiou as a thinker of the first
importance not only for the impressive range, depth and originality of
his work, but also because it points to an escape-route from some of the
more cramped or windowless quarters of present-day philosophic thought.
