Localizing the Singular Structure of Spacetime

I argue that the singular structure of spacetime is best conceptualized as an extrinsic, non-local, but localizable, property of spacetime regions (of any size), and that there is no unique, best definition of a singular region of spacetime. There is, however, a schema that any adequate definition instantiates. Moreover, the question of what kind of incomplete curves witness singular structure is intimately connected to the question of what kind of curves represent possible trajectories of observers in 'physically reasonable' motion.