Abstract We start with Fodor’s critique of cognitive science in [8]: he argues that much mental activity cannot be handled by the current methods of cognitive science because it is nonmonotonic and, therefore, is global in nature, is not context-free, and is thus not capable of being formalised by a Turing-like mental architecture. We look at the use of non-monotonic logic in the Artificial Intelligence community, particularly with the discussion of the so-called “frame problem”. The mainstream approach to the frame problem is, we argue, probably susceptible to Fodor’s critique: however, there is an alternative approach, due to McCain and Turner, which is, when suitably reformulated, not susceptible. In the course of our argument, we give a proof theory for the McCain-Turner system, and show that it satisfies cut elimination. We have two substantive conclusions: firstly, that Fodor’s argument depends on assumptions about logical form which not all non-monotonic theories satisfy; and, secondly, that metatheory plays an important role