An interesting, quick read, not what one often expects when cracking open a volume by Badiou. I think that its light approach is what threw me off here; indeed, the lengthy translator’s introduction—which is longer and denser than Badiou’s own text—had me expecting Badiou at the height of his syntactical and enigmatic powers.While the premise of this is intriguing, the format of it may be problematic: originally delivered as a seminar, Badiou lays out his main argument—one that is not too hard to disprove, namely, that Wittgenstein was an antiphilosopher—in his own preface. The rest feels like a rumination on the first opening pages, often extended into repetitive logic. Again, this would work better in a seminar format in order to repeat points to the listeners, but I feel that this failed to be edited properly to work in book format.Badiou takes Lacan’s term “antiphilosopher” and extends its conceptual use: “I take them to be awakeners who force the other philosophers not to forget two points.” These two points are, in essence, that the antiphilosopher must force the philosopher not to forget that his or her truths are bearing witness to their own time only, and secondly, that the philosopher situates his voice in the place of a kind of Lacanian Master discourse.What was most interesting about this point was how Badiou juxtaposes the more ontologically-oriented philosophers with those who are more bodily-oriented—here, he juxtaposes Nietzsche with Wittgenstein, and also seems to suggest that one should read an Althusser/Lacan pairing in the same fashion.Also of interest is how Badiou situates philosophy’s quest for truth in a more mathematical approach to experience and knowing, a figuring of “what there is,” whereas “the antiphilosophical act consists in letting what there is show itself... If Wittgenstein’s antiphilosophical act can legitimately be declared archiaesthetic, it is because this ‘letting-be’ has the nonpropositional form of pure showing, of clarity...”Again, the main issue I have seems to be the medium here, and also that Badiou’s seminar assumes that the listeners (readers?) are familiar with seminal concepts in both Wittgenstein’s and Nietzche’s oeuvres. Recommended for fans of philosophy, Badiou completists, and those who may need to brush up on their Wittgenstein.