We characterise and critically evaluate five formulations of the thesis that the structure of spacetime is conventional, rather than empirically determined. The proliferation of formulations comes from considering generalisation first, via a more liberal Carnapian understanding of the conventionalism argument in terms of universal effects, rather than Reichenbachian universal forces, and second, via a more liberal understanding of the modal context of the empirical underdetermination, that is as underdetermination between observers rather than models. Whilst three of the five formulations of conventionalism will be found to fail, two are found to open up new interesting problems for researchers in the foundations of general relativity. In all five cases, our analysis will explore interplay between geometric identities, symmetry, conformal structure, and the dynamical content of physical theories. The conventionalism dialectic is thus deployed towards as a tool of explication, clarification, and exploration.

We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this underdetermination occurs. Three of the five formulations of conventionalism will be found to fail. Two are found to open up new interesting problems for researchers in the foundations of general relativity. In all five cases, our analysis explores the interplay between geometric identities, symmetry, conformal structure, and the dynamical content of physical theories with the conventionalism dialectic deployed as a tool of explication, clarification, and exploration.