Brain damage may doubly dissociate cognitive modules, but the practice of revealing dissociations is predicated on modularity being true (T. Shallice, 1988). This article questions the utility of assuming modularity, as it examines a paradigmatic double dissociation of reading modules. Reading modules illustrate two general problems. First, modularity fails to converge on a fixed set of exclusionary criteria that define pure cases. As a consequence, competing modular theories force perennial quests for purer cases, which simply perpetuates growth in the list of exclusionary criteria. The first problem leads, in part, to the second problem. Modularity fails to converge on a fixed set of pure cases. The second failure perpetuates unending fractionation into more modules. © 2001 Cognitive Science Society, Inc. All rights reserved.