More than thirty years ago, Alfonso Caramazza laid out assumptions for drawing inferences about the undamaged cognitive system from individuals with brain damage. Since then, these assumptions have been challenged including the transparency or subtractivity assumption, that the cognitive system does not reorganize following brain damage. It has been repeatedly demonstrated that brains are highly plastic. However, there is no clear connection between brain plasticity and cognitive reorganization. Brain plasticity research does not require a rethinking of the core logic of cognitive neuropsychology. Differences in task-based activation between damaged and undamaged brains provide little insight into the cognitive architectures of brain-damaged patients. Theory and methods are needed to understand cognitive neuroplasticity, or how neural reorganization that follows brain damage relates to reorganization of functions. We discuss alternative types of cognitive neuroplasticity that may occur in damaged brains and consider how they impact the basic logic of cognitive neuropsychology.