On the Structure and Equivalence of Theories

Abstract

There is sometimes a sense in which two theories are equivalence. This dissertation examines the methods of answering questions of equivalence and inequivalence of theories that are currently on the table. In the first part (Chapters 2 and 3), I consider a recent suggestion that questions of theoretical equivalence can be settled by comparing the "amount of structure" that theories posit. In the second part (Chapters 4 and 5), I reconsider an older idea that questions of equivalence can be settled by evaluating whether or not the theories are "intertranslatable." I demonstrate how all of these different standards of equivalence are related in terms of their logical strength, and in addition, I evaluate them on their own merits. In Chapter 6, I turn to a particular case study from physics; I use the tools developed in the previous chapters to judge whether the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I conclude by mentioning some of the general philosophical payoffs that this investigation of equivalence yields.