Philosophy is rife with intractable moral dilemmas. We propose that these debates often exist because competing psychological systems yield different answers to the same problem. Consequently, philosophical debate points to the natural fault lines between dissociable psychological mechanisms, and as such provides a useful guide for cognitive neuroscience. We present two case studies from recent research into moral judgment: dilemmas concerning whether to harm a person in order to save several others, and whether to punish individuals for harms caused accidentally. Finally, we analyze two features of mental conflict that apparently contribute to philosophical discord: the insistence that one answer to a problem must be correct (“non-negotiability”) and the absence of an independent means of determining the correct answer (“non-adjudicability”).