On the Non-identity Causal Theory of Spacetime from Causal Set Theory

The aim to provide a causal theory of spacetime is not new. The overall program, however, was largely deemed unsuccessful, chiefly due to criticism voiced by Smart (Monist 53:385-395, 1969), Nerlich (Br J Philos Sci 33(4):361-388, 1982) and Earman (Synthese 24:74-86, 1972). Recently, Baron and Le Bihan (Noûs 58:202-224, 2023) have argued that developments in contemporary physics should make us reconsider this verdict. More precisely, they argue the emergence of spacetime from causal set theory (CST), where "the metric structure of spacetime can be recovered from its causal structure" (Baron and Le Bihan 2023, 2), "suggests a very natural way to reformulate the causal theory of spacetime" (ibid., 9)-an account which they end up dubbing the non-identity causal theory. This paper questions the success of Baron and Le Bihan's non-identity theory. It is shown that (1) the specific grounding Baron and Le Bihan propose for timelike and spacelike relations is not plausible even when charitably reconstructed; and (2) that a causal theory of spacetime based on general relativity is just as successful for establishing a non-identity theory as a theory based on CST. In short then, we argue that the causal theory of spacetime proposed by Baron and Le Bihan is supported just as well (or badly) by the physics that already took centre stage in the original discussions of the causal theory of spacetime.