On essential structures and symmetries

The main goal of the paper is to revisit the concept of a symmetry for relational structures in light of the ontological position dubbed “essentialist structuralism”. It is argued that the standard definition of the notion of a symmetry commits us to the existence of non-qualitative, haecceitistic differences between possible worlds. An alternative notion of symmetry is developed, based on the distinction between essential and contingent structures. It is claimed that this new concept is better suited for the doctrine of structuralism, and moreover it offers a new perspective on some well-known problems in the foundation of physical theories, such as the problem of permutation invariance in quantum mechanics and diffeomorphism invariance in general relativity.