Many advocates of a cognitive approach to science, a form of naturalism, claim that it possesses normative dimensions or yields normative insights. I critically examine such claims, focusing on P. M. Churchland's radical neurocomputational approach. I point out that his approach cannot provide an epistomic, but only a pragmatic, distinction between good and bad explanations and that particular claims of his-e. g., that simplicity is an epistemic virtue because “simple networks generalize better”-are hardly tenable. Before discussing such normative issues, I give a general and critical account of his views on scientific and other forms of cognition. I submit that his choice of neuroscientific and connectionist ideas is an a priori normative answer to the circularity problem, facing naturalistic approaches; that his elaboration of these ideas tends to transcend his eliminative materialism and, in fact, involves a dualism of neural mechanisms and learning algorithms.