Starting from an overview of approaches to naturalized epistemology, the paper shows, firstly, that Quine's programme yields a sceptical paradox. This means that Quine's attempt to defeat scepticism itself yields a rather strong argument for scepticism and thus against his own programme of naturalized epistemology. Secondly, it is shown that this paradox can be solved by an approach called reflexive-heuristic naturalism. Finally, the paper also raises some fundamental problems which the solution proposed has to leave open.