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Alain Badiou takes on the standard bearer of the “linguistic turn” in modern philosophy, and anatomizes the “anti-philosophy” of Ludwig Wittgenstein, in his Tractatus Logico-Philosophicus. Addressing the crucial moment where Wittgenstein argues that much has to be passed over in silence—showing what cannot be said, after accepting the limits of language and meaning—Badiou argues that this mystical act reduces logic to rhetoric, truth to an effect of language games, and philosophy to a series of esoteric aphorisms. in the course of his interrogation of Wittgenstein’s anti-philosophy, Badiou sets out and refines his own definitions of the universal truths that condition philosophy. Bruno Bosteels’ introduction shows that this encounter with Wittgenstein is central to Badiou’s overall project—and that a continuing dialogue with the exemplar of anti-philosophy is crucial for contemporary philosophy.