Translation, reduction and equivalence

Contemporary epistemology and philosophy of science devote a central place to questions of the following sort: When are two conceptual frameworks equivalent? Under what conditions is one scientific theory reducible to another? This essay attempts to reach a clearer grasp of these issues by providing a logical analysis of intertheory translation and reduction. Taking first order logic as a starting point, several classical theorems on definability and interpolation are generalised so as to obtain a model-theoretic characterisation of some basic types of reductive relations between theories. This account is later extended by adopting a very general and powerful semantical framework inspired by abstract logic. In this setting it is shown how a richer class of intertheoretic relations can be defined, and how the structuralist approach to reduction, developed by Sneed and Stegmüller, can be critically evaluated.