Theories that explain versus theories that describe: the case of constraint satisfaction

Theories, by which I mean formal theories rendered in mathematical or computational formalisms, are commonly understood as describing the data on human cognition, or as implementing a computational (in the sense of Marr) specification of cognition. Beyond these functions, we also desire theories that explain the phenomena of cognition. Three scenarios where a new theory seems to explain cognition are: (1) the development of a new mechanism that captures empirical anomalies beyond the reach of existing theories; (2) the proposal of a new theory that provides a unified account of domains previously thought to be independent; and (3) the importation of a new formalism into cognitive science that supports theories that seem to effortlessly account for large swaths of cognition. In these scenarios, a new theory explains in part by offering a new perspective on cognition, one that directly captures phenomena without much need for tedious, low-level calculation. We illustrate these claims by considering the case of constraint satisfaction theories of cognition in some depth.