The experimental turn in philosophy has reached several sub-fields including ethics, epistemology, and metaphysics. This paper is among the first to apply experimental techniques to questions in the philosophy of law. Specifically, we examine Lon Fuller's procedural natural law theory. Fuller famously claimed that legal systems necessarily observe eight principles he called "the inner morality of law." We evaluate Fuller's claim by surveying both ordinary people and legal experts about their intuitions about legal systems. We conclude that, at best, we should be skeptical of Fuller's inner morality of law in light of the experimental data.