Abstract: Hume consciously reflects on the nature of scepticism in Treatise 1.4.7 (“Conclusion of this Book”) and Section 12 of his first Enquiry (“Of the Academical or Sceptical Philosophy”). I argue that we should read Hume as espousing a ‘residual’ form of scepticism in these sections. This means that Hume’s final, moderate sceptical position is a product of entertaining extreme sceptical worries but finding that they are impermanent. Recognition of this is important in its own right, as T 1.4.7 and EHU 12 are puzzling and central texts. But I also argue that this residual scepticism is informative for the debate over reading Hume on induction specifically. It turns out that the now popular approach of reading Hume as not an inductive sceptic is going to struggle accounting for Hume’s residual scepticism, because it cannot explain the relationship between his extreme doubts and his final position.