The central task of cognitive neuroscience to map cognitive capacities to neural mechanisms faces three interlocking conceptual problems that together frame the problem of cognitive ontology. First, they must establish which tasks elicit which cognitive capacities, and specifically when different tasks elicit the same capacity. To address this operationalization problem, scientists often assess whether the tasks engage the same neural mechanisms. But to determine whether mechanisms are of the same or different kinds, we need to solve the abstraction problem by (...) determining which mechanistic differences are and are not relevant, and also the boundary problem by distinguishing the mechanism from its background conditions. Solving these problems, in turn, requires understanding how cognitive capacities are elicited in tasks. These three problems, which have been noted and discussed elsewhere in the literature, together form a ‘cycle of kinds’ that frames the central problem-space of cognitive ontology. We describe this cycle to clarify the intellectual challenges facing the cognitive ontologist and to reveal the kind of iterative process by which ontological revision in cognitive neuroscience is likely to unfold. (shrink)