There is a divide between two broad approaches to the nature of theoretical equivalence in physics, to what we mean when we say that two physical theories are fully equivalent, mere notational variants. On one side is a formal approach, according to which formal criteria play a pivotal role in questions concerning the equivalence of theories. On the other side is a resistance to formal approaches, to the point of regarding formal criteria as essentially or ultimately irrelevant to these questions. Without arguing for any particular account of theoretical equivalence or any one formal criterion, I defend the basic thought that theories’ formal or mathematical or structural features, as well as formal relationships between these features of potentially different theories, can bear true physical significance. I then show how this paves the way for a middle way on theoretical equivalence—an account according to which formal criteria of some kind are necessary (but not sufficient) for theoretical equivalence in physics.
Jill North (Thu,) studied this question.