Sophistication about Symmetries

Suppose that one thinks that certain symmetries of a theory reveal ‘surplus structure’. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory that traffics only in structures invariant under the relevant symmetry. In this article, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms. 1. Introduction2. Symmetry3. Reduction4. Sophistication5. Equivalence6. ConclusionAppendix