Is a past-finite causal order the inner basis of spacetime?

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The causal set -- mathematically a finitary partial order -- is a candidate discrete substratum for spacetime. I will introduce this idea and describe some aspects of causal set kinematics, dynamics, and phenomenology, including, as time permits, a notion of fractal dimension, a (classical) dynamics of stochastic growth, and an idea for explaining some of the puzzling large numbers of cosmology. I will also mention some general insights that have emerged from the study of causal sets, the most recent one concerning the role of intermediate length-scales in discrete spacetime theories.