  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.
