Neuroscience and psychology have recently turned their attention to the study of the subpersonal underpinnings of moral judgment. In this article we critically examine an influential strand of research originating in Greene's neuroimaging studies of ‘utilitarian’ and ‘non-utilitarian’ moral judgement. We argue that given that the explananda of this research are specific personal-level states—moral judgments with certain propositional contents—its methodology has to be sensitive to criteria for ascribing states with such contents to subjects. We argue that current research has often failed to meet this constraint by failing to correctly ‘fix’ key aspects of moral judgment, criticism we support by detailed examples from the scientific literature.