Reduction as an a posteriori Relation

Reduction between theories in physics is often approached as an a priori relation in the sense that reduction is often taken to depend only on a comparison of the mathematical structures of two theories. I argue that such purely formal approaches fail to capture one crucial sense of reduction, whereby one theory encompasses the set of real behaviours that are well modelled by the other. Reduction in this sense depends not only on the mathematical structures of the theories but also on empirical facts about where the theories succeed at describing real systems, and is therefore an a posteriori relation. I discuss several detailed implications of this claim for the methodology of inter-theory and inter-model reduction in physics. 1Introduction 2Reduction as Domain Subsumption 3A Formal Approach to Reduction in Physics 4An Empirical Approach to Reduction in Physics 4.1A potential concern 4.2A local, empirical, model-based strategy for reduction in physics 5Conclusion Appendix.