Mandersian Relationism: Space, Modality, and Equivalence

Modal relationism is the view that our best physical theories can dispense with substantival space or spacetime in favor of possible configurations of particles. Kenneth Manders argues that the substantivalist conception is equivalent to this Leibnizian conception of space. To do so, Manders provides a translation $f$ from the Newtonian theory ${T_N}$ into the Leibnizian modal relationist account ${T_L}$ . In this article, we show that the translation does not establish equivalence because there is no translation $g:{T_L} \mapsto {T_N}$ that preserves theoremhood. This seems to show that the modal relationist theory ${T_L}$ is less parsimonious than its substantivalist rival.