The growing literature reporting results of cognitive-neural mappings has increased calls for an adequate organizing ontology, or taxonomy, of these mappings. This enterprise is non-trivial, as relevant dimensions that might contribute to such an ontology are not yet agreed upon. We propose that any candidate dimensions should be evaluated on their ability to explain observed differences in functional neuroimaging activation patterns. In this study, we use a large sample of task-based functional magnetic resonance imaging (task-fMRI) results and a data-driven strategy to identify these dimensions. First, using a data-driven dimension reduction approach and multivariate distance matrix regression (MDMR), we quantify the variance among activation maps that is explained by existing ontological dimensions. We find that ‘task paradigm’ categories explain more variance among task-activation maps than other dimensions, including latent cognitive categories. Surprisingly, ‘study ID’, or the study from which each activation map was reported, explained close to 50% of the variance in activation patterns. Using a clustering approach that allows for overlapping clusters, we derived data-driven latent activation states, associated with re-occurring configurations of the canonical frontoparietal, salience, sensory-motor, and default mode network activation patterns. Importantly, with only four data-driven latent dimensions, one can explain greater variance among activation maps than all conventional ontological dimensions combined. These latent dimensions may inform a data-driven cognitive ontology, and suggest that current descriptions of cognitive processes and the tasks used to elicit them do not accurately reflect activation patterns commonly observed in the human brain.