En Route to Reduction: Lorentzian Manifolds and Causal Sets

This Chapter presents aspects of causal set theory (a research programme in quantum gravity) as being en route to achieving a reduction of Lorentzian geometry to causal sets. The Chapter takes reduction in philosophers’ sense and argues that the prospects are good for there being a reduction of the type envisaged by Nagel. There is also discussion of the prospects for the stronger functionalist variant of Nagelian reduction, that was formulated by Lewis. One main theme will be causal set theory’s use of a physical scale (viz. the Planck scale) to formulate how it recovers a Lorentzian manifold. This use illustrates various philosophical topics relevant to reduction, such as limiting relations between theories, and the role of analogy. The Chapter also emphasises causal set theory’s probabilistic method, viz. Poisson sprinkling: which is used both for formulating the reduction and for exploring its prospects.