Two-by-two grids are a popular means of exposition of management thought. In this note such grids are identified with Carroll diagrams, developed by the Oxford mathematician and logician Charles Dodgson. Using this insight, the nature of the conceptual tool frequently used by management authors is reflected upon. Two-by-two grids are a clear means of exposition and can be a valuable vehicle for identifying hitherto neglected aspects of a management issue, but there is also a risk that, in their relatively parsimonious treatment of management topics, they fail to capture important features of practice. Two particular areas of risk are identified and discussed.