Support is canvassed for a novel solution to the sceptical problem regarding our knowledge of the external world. Key to this solution is the claim that what initially looks like a single problem is in fact two logically distinct problems. In particular, there are two putative sceptical paradoxes in play here, which each trade on distinctive epistemological theses. It is argued that the ideal solution to radical scepticism would thus be a biscopic proposal-viz., a two-pronged, integrated, undercutting treatment of both putative sceptical paradoxes. A particular biscopic proposal is then explored which brings together two apparently opposing anti-sceptical theses: he Wittgensteinian account of the structure of rational evaluation and epistemological disjunctivism. It is argued that each proposal enables us to gain a purchase on one, but only one, aspect of the two-sided sceptical problem. Furthermore, it is argued that these proposals are not only compatible positions, but also mutually supporting and advanced in the same undercutting spirit. A potential cure is thus offered for epistemic angst.