 J.J.C. Smart provided an influential, tentative description of the reduction relation according to which an entity x reduces to an entity y only if x does not exist ‘over and above’ y (Smart 1959: 143). Smart frames the question as one of existence, an ontological question: What really exists? How many basic kinds of things exist? Approaching the issue from a different slant, the philosophical notion of ‘reduction’ might be cashed out in terms of an explanatory relation. If x reduces to y, then it can in a relevantly strong sense be explained in terms of y. Take an example from Ernest Nagel. Describing the possible reduction of headaches, he writes that when