 While the point of this project may seem at bottom identical to the path-incompleteness account discussed in  section 1.1,  insofar as singular structure will be defined by the presence of incomplete, inextendible paths, there is a crucial conceptual and logical difference between the two. Here, the existence of the incomplete path does not constitute the singular structure, but rather serves only as a marker for the presence of singular structure in the sense of missing points: the incomplete path is incomplete because it “runs into a hole” in the spacetime that, were it filled, would allow the path to be continued; this hole is the singular structure, and the points constructed to fill it constitute its locus. Indeed, every known boundary construction relies on the existence of incomplete paths to “probe” the spacetime, as it were, looking for “places” where boundary points should be appended to the spacetime; the characterization of singular structure by incomplete paths seems, therefore, logically, perhaps even conceptually, prior to that by boundary points, at least, again, for all known constructions of boundary points. 