Cognitive neuroscience involves the simultaneous analysis of behavioral and neurological data. Common practice in cognitive neuroscience, however, is to limit analyses to the inspection of descriptive measures of association (e.g., correlation coefficients). This practice, often combined with little more than an implicit theoretical stance, fails to address the relationship between neurological and behavioral measures explicitly. This article argues that the reduction problem, in essence, is a measurement problem. As such, it should be solved by using psychometric techniques and models. We show that two influential philosophical theories on this relationship, identity theory and supervenience theory, can be easily translated into psychometric models. Upon such translation, they make explicit hypotheses based on sound theoretical and statistical foundations, which renders them empirically testable. We examine these models, show how they can elucidate our conceptual framework, and examine how they may be used to study foundational questions in cognitive neuroscience. We illustrate these principles by applying them to the relation between personality test scores, intelligence tests, and neurological measures.