“Le non-comprendre fut mon aiguillon” – “Not-understanding was always my spur” wrote Valéry at the end of his life. This paper tries to follow, through a number of texts, in particular from the Cahiers / Notebooks, the concept of not-understanding, its status, meaning and function in Valéry’s work. The idea includes that of relationships to others and takes on the form of a not-understanding-myself which opens it up to the dimension of a community of understanding. This aspect of Valéry’s thinking thus joins up with some of the major post-war political reflections, in particular Hannah Arendt’s, on the benefits drawn from certain “lack in the intelligence” of things.