Representational conventions and invariant structure

Abstract: In the philosophical literature, symmetries of physical theories are most often interpreted within the general doctrine called 'Sophistication'. Roughly speaking, it says that models related by symmetries can peacefully co-exist while representing the same physical possibility. But this interpretation still leaves open two main worries about Sophistication: (a) it allows the individuation of what I call 'structure-tokens' to remain intractable and thus of limited use, which is why practising physicists frequently invoke 'relational, symmetry-invariant observables'; and (b) it leaves us with no formal framework for expressing counterfactual statements about the world. Here, I will show that a new Desideratum to be satisfied by theories with symmetries answers these worries. The new Desideratum is that the theory admits what I will call representational conventions for its structure-tokens.