In close parallel to the thinking of Friedrich Nietzsche, but also in clear contrast to it, Alain Badiou explores the figure of antiphilosophy in Ludwig Wittgenstein. As a gesture that must be continuously exhibited as an "existential singularity," in absolute solitude, antiphilosophy proves to be a counterfigure to the regulated anonymity of science. For the antiphilosopher always personally steps onto the public stage of his thinking, which, without examples or guarantees, possesses only itself and its effects as confirmation of its truth. Along the demarcation line of thinking and non-thinking, Badiou traces the characteristic relationship of the antiphilosopher to non-meaning in order to address the problem of logic and its ontological foundation. Ultimately, it raises the fundamental question of whether mathematics constitutes a form of thinking.