This article clarifies what a neuroscience challenge to criminal justice must look like by sketching the basic structure of the argument, gradually filling out the details and illustrating the conditions that must be met for the challenge to work. In the process of doing so it explores influential work by Joshua Greene and Jonathan Cohen, and Stephen Morse respectively, arguing that the former should not be understood to present a version of the challenge, and that the latter's argument against the (...) challenge is unpersuasive. This analysis allows the article to flesh out the challenge, and demonstrate why it is currently non-completeable. However, the paper argues that contrary to what is often assumed the burden of proof falls on the defenders of criminal justice, and that they will find meeting it a monumental task. (shrink)