Much of the contemporary research in cognitive psychology presupposes an information processing or computational model of human cognitive processes. On this view cognitive states are characterized as relations to internally inscribed representations. Jerry Fodor and Zenon Pylyshyn have argued that those representations have a combinatorial syntax and a compositional semantics, and Fodor has argued that the individuation of representations according to semantic type corresponds, roughly, to individuation according to syntactic type. I investigate whether this computational model requires us to appeal, directly or indirectly, to the semantic properties of representations when we explain cognitive behavior. I first discuss the requirements of scientific explanation in general, and the constraints of materialism and physicalism in particular. Then I outline how it is possible for semantic entities to be involved in cognitive explanations, and how Fodor and Pylyshyn think they are involved in explanations on the computational model. I consider whether, given the computational model, references to representations are necessary to explain cognitive processes or whether references to representations can be eliminated in favor or references to uninterpreted formulae. Finally I criticize the argument, suggested by both Fodor and Pylyshyn, that it is our ability to respond to nonnomic or nonprojectable properties of stimuli that requires explanation in terms of the semantic properties of representations