 While path incompleteness seems to capture an important aspect of the intuitive picture of singular structure, it completely ignores another seemingly integral aspect of it: curvature pathology. If there are incomplete paths in a spacetime, it seems that there should be a reason that the path cannot go further. The most obvious candidate explanation of this sort is that something going wrong with the dynamical structure of the geometry of spacetime, which is to say, with the curvature of the spacetime. This suggestion is bolstered by the fact that local measures of curvature do in fact blow up as one approaches the singularity of a standard black hole or the Big Bang singularity. There is, however, one problem with this line of thought: no species of curvature pathology we know how to define is either necessary or sufficient for the existence of incomplete paths. (For a discussion of foundational problems attendant on attempts to define singularities based on curvature pathology, see Curiel 1999; for a recent survey of technical issues, see Joshi 2014.) 