The focus of this article is Levinas's "Exercises on 'The Madness of the Day'" in Proper Names and Blanchot's story, which is the subject of Levinas's reading. With reference to some of the writings by each of the authors, the problem of testimony and its limits is posed, in particular in relation to testifying to death or madness. What are Levinas's reading and Blanchot's story about? What differences in perspective can be emphasized? In what sense, in both approaches, is the point of the story elusive?