In On Certainty, Wittgenstein formulates several criticisms against skepticism about our knowledge of the external world. My goal is to show that Wittgenstein does not here offer a convincing answer to the skeptical problem. First, I will present a strong version of the problem, understanding it as a paradoxical argument. In the second part, I will introduce and raise problems for two pragmatic responses against skepticism that appear in On Certainty. Finally, I will present some of Wittgenstein’s logical criticisms against (...) skepticism, which may initially be considered strong, because they seem to refute some skeptical assumptions. They concern Wittgenstein’s ideas that it is logically impossible to doubt and to be mistaken about Moorean propositions, and that these propositions don’t have a truth-value. But even these, I intend to show, do not really challenge skepticism, for they are not well grounded. (shrink)