Abstract This chapter is the third of three case studies demonstrating the potential impacts of methodological naturalism. It focuses on an extra-empirical principle that says that we should avoid a certain kind of excess structure in our theories, and shows how that principle plays a key role in justifying the acceptance of special relativity over alternative theories that are also compatible with the data. It has often been observed that this kind of extra-empirical principle can be used to rule out theories of time that posit a fundamental distinction between the present, on the one hand, and the past and the future, on the other. This chapter argues that the very same extra-empirical principle would also apply in a surprising way to debates about the nature of possibility. It would lead to the rejection of views that posit a fundamental distinction between what is actual and what is merely possible.