Traditionally, identity and supervenience have been proposed in philosophy of mind as metaphysical accounts of how mental activities (fully understood, as they might be at the end of science) relate to brain processes. Kievet et al. suggest that to be relevant to cognitive neuroscience, these philosophical positions must make empirically testable claims and be evaluated accordingly – they cannot sit on the sidelines, awaiting the hypothetical completion of cognitive neuroscience. We agree with the authors on the importance of rendering these positions relevant to ongoing science. We disagree, however, with their proposal that a metaphysical relationship (identity or supervenience) should “serve as a means to conceptually organize and guide the analysis of neurological and behavioral data” (p. 7). Instead, we advance a different view of the goals of cognitive neuroscience and of the proper means of relating metaphysics and explanation. Our central objection to the psychometric approach deployed by Kievet et al. is that the formal models only account for correlations between variables (measurements) and do not aid in explaining phenomena. Cognitive neuroscience is concerned with the latter. We develop this point in section 2 in which we present what we find to be problematic in their proposed models. In section 3 we advance an account of what is required to explain phenomena: (a) providing an adequate description of a phenomenon; and (b) characterizing the mechanism responsible for it. In doing so we will characterize a version of the identity theory, heuristic identity theory (HIT) which figures centrally in developing such explanations and illustrate its role in what we take to...