Evolutionary psychology is widely understood as involving an integration of evolutionary theory and cognitive psychology, in which the former promises to revolutionise the latter. In this paper, I suggest some reasons to doubt that the assumptions of evolutionary theory and of cognitive psychology are as directly compatible as is widely assumed. These reasons relate to three different problems of specifying adaptive functions as the basis for characterising cognitive mechanisms: the disjunction problem, the grain problem and the environment problem. Each of (...) these problems can be understood as arising from incommensurate characterisations of the nature and role of 'the environment' in the two approaches. Purported solutions to the problems appear to require detailed information concerning the EEA (environment of evolutionary adaptedness), with the disjunction problem placing the lowest requirement, the environment problem placing the highest requirement, and the grain problem placing an intermediate one. In each case, such information is not likely to be forthcoming, because it may require iterating through successively more distant EEA's with no principled stopping point. This produces a dilemma for evolutionary psychology - either to solve these apparently insoluble problems, or to attempt to avoid them but in doing so forego detailed evolutionary constraints on cognition. (shrink)