The Pyrrhonian sceptic who doubts everything is not simply wrong. Their arguments cannot be answered — the problem of induction has no rational solution, the external world cannot be proven by reason, our most fundamental beliefs rest on habit rather than demonstration. As a theoretical position, Pyrrhonism is genuinely difficult to refute. But it is also liveable: nature overrules it every time the sceptic eats breakfast.
Mitigated scepticism takes the lesson of excessive scepticism — that reason has strict limits — and draws a practical conclusion: confine enquiry to the domain where it can actually deliver results. Do not expect reason to answer questions about God, the soul, or ultimate causes. Do expect it to illuminate mathematics, logic, and the careful study of experience. Humility about the former is the precondition of progress in the latter.
Mitigated scepticism is not intellectual paralysis. It directs attention toward the only objects amenable to careful study: the workings of the human mind and the patterns of experience. This is exactly what Hume calls "the science of man" — the empirical study of how we actually think, feel, reason, and believe. The demolition of metaphysics clears the ground for a genuine human science.
Section XII, "Of the Academical or Sceptical Philosophy," closes the Enquiry. Hume distinguishes three grades of scepticism: antecedent (Cartesian doubt before enquiry), consequent (arising from enquiry), and excessive Pyrrhonian doubt. His own position is the moderate consequent scepticism he calls mitigated.