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Hume’s “Of scepticism with regard to reason” opens with an argument that is supposed to show how “all knowledge degenerates into probability” (T 1.4.1.1; SBN 180). While compelling with respect to demonstrative knowledge, commentators disagree over whether the argument plausibly extends to intuitive knowledge. This disagreement, I contend, is the result of mistakenly treating intuitions as a uniform class. Distinguishing what I call (i) philosophical intuitions from (ii) vulgar intuitions allows us to see why only the latter are subject to degeneration. That the former survive degeneration, however, is no objection to Hume’s argument. Demonstrative knowledge is possible in principle because philosophical intuitions are certain. Accepting this much at the outset, Hume calls on recollected errors to show how, in practice, all knowledge degenerates to probability.