Structuralism and the Individuation of Causal Set Elements in Causal Set Theory

It has been suggested that causal set theory is particularly accommodating to a structuralist interpretation. In this paper, we will evaluate this claim, focusing on a recent version of structuralism proposed by Wüthrich (2012, 2024). We show that structuralism of this variety conflicts with the standard dynamics of causal set theory, and that removing this conflict may require reworking the dynamics. We also show that a structuralist interpretation along these lines requires metaphysically privileging the dynamical aspect of the theory. We consider three potential ways forward for a structuralist, but suggest that matters are difficult: two of these likely require reworking CST and one invokes controversial metaphysical assumptions.