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. 1   Introduction 2   Reduction as Domain Subsumption 3   A Formal Approach to Reduction in Physics 4   An Empirical Approach to Reduction in Physics    4.1   A potential concern    4.2   A local, empirical, model-based strategy for reduction in physics 5   Conclusion Appendix [ABSTRACT FROM AUTHOR]