 In trying to determine whether an ordinary web of cloth has a hole in it, for example, one would naturally rely on the fact that the web exists in space and time. In this case one can point to a hole in the cloth by specifying points of space at a particular moment of time not currently occupied by any of the cloth, but which would complete the cloth were they so occupied. When trying to conceive of a singular spacetime, however, one does not have the luxury of imagining it embedded in a larger space with respect to which one can say there are points missing from it. In any event, the demand that the spacetime be maximal rules out the possibility of embedding the spacetime manifold in any larger spacetime manifold of any ordinary sort. It would seem, then, that making precise the idea that a singularity is a marker of missing points ought to involve some idea of intrinsic structural incompleteness in the spacetime manifold rather than extrinsic incompleteness with respect to an external structure. 