The term "recursion" is used in at least four distinct theoretical senses within cognitive science. Some of these senses in turn relate to the different levels of analysis described by David Marr some 20 years ago; namely, the underlying competence capacity (the "computational" level), the performance operations used in real-time processing (the "algorithmic" level), and the neural implementation (the "hardware" level). It is demonstrated here that the current focus of the artificial grammar learning literature on recursion blurs the different levels, resulting in three main corollaries: (1) the literature cannot tell us anything about the first level, as the explanation for the role of recursion therein lies elsewhere; (2) it has not studied the possible recursive processing of artificial strings properly, as studies have so far focused on the correct processing of the internal hierarchy of recursive structures, but none have attempted to probe the underlying processing operations; and (3) as a consequence, much cannot in fact be known about the neural basis of recursion. It is furthermore argued that, in general, these studies can actually tell us very little about the language faculty, and some programmatic remarks are described and defended towards a more coherent study. (Contains 2 figures, 1 table and 16 footnotes.)