On the Modal Aspects of Causal Sets

Abstract

The possibility question concerns the status of possibilities: do they form an irreducible category of the external reality, or are they merely features of our cognitive framework? If fundamental physics is ever to shed light on this issue, it must be done by some future theory that unifies insights of general relativity and quantum mechanics. The paper investigates one programme of this kind, namely the causal sets programme, as it apparently considers alternative developments of a given system. To evaluate this claim, we prove some algebraic facts about the sequential growth of causal sets. These facts tell against alternative developments, given that causal sets are understood as particular events. We thus interpret causal sets as multi-realisable objects, like states. This interpretation, however, is undermined by an argument for the probabilistic constraint of general covariance, as it says that multiple paths along which a causal set is produced are not physically different.