Invariance, intrinsicality and perspicuity

It is now standard to interpret symmetry-related models of physical theories as representing the same state affairs. Recently, a debate has sprung up around question when this interpretational move warranted. In particular, Møller-Nielsen (Philos Sci 84(5):1253–1264, 2017) argued that one only allowed physically equivalent characterisation their common content. I disambiguate two versions claim. On first, perspicuous interpretation required: an account models’ ontology. second, stricter, version claim, formalism required in addition: whose mathematical structures ‘intrinsically’ represent world, sense Field (Science without numbers: defence nominalism, Princeton University Press, Princeton, 1980). Using Dewar’s (Br J Philos 70(2):485–521, 2019) distinction between internal and external sophistication case study, argue second requirement decisive. This clarifies conditions under which it warranted equivalent.