Cognitivism in psychology and philosophy is roughly the position that intelligent behavior can (only) be explained by appeal to internal “cognitive processes,” that is, rational thought in a very broad sense. Sections 1 to 5 attempt to explicate in detail the nature of the scientific enterprise that this intuition has inspired. That enterprise is distinctive in at least three ways: It relies on a style of explanation which is different from that of mathematical physics, in such a way that it is not basically concerned with quantitative equational laws; the states and processes with which it deals are “interpreted,” in the sense that they are regarded as meaningful or representational; and it is not committed to reductionism, but is open to reduction in a form different from that encountered in other sciences. Spelling these points out makes it clear that the Cognitivist study of the mind can be rigorous and empirical, despite its unprecedented theoretical form. The philosophical explication has another advantage as well: It provides a much needed framework for articulating questions about whether the Cognitivist approach is right or wrong. The last three sections take that advantage of the account, and address several such questions, pro and con.