Prolegomenon to an epistemology of orbifolds

The field of the epistemology of spacetime interrogates how, if at all, we can come to know about the various constituent parts of spacetime. Historically in this field, the bulk of attention has rested on the epistemology of the metrical structure of spacetime; the question of the epistemological significance of various sub-metrical components of spacetime, e.g. topological structure, has up to this point been substantially neglected. In this article, we propose to rectify this situation, focussing in particular on exploring the epistemological and empirical upshots of generalising standard manifold topology to that of a orbifold. We demonstrate that there are various possible empirical signatures of orbifold structure, and various tests which could in principle be implemented in order to test whether one inhabits an orbifold. Along the way, we highlight certain other philosophically significant features of orbifolds---for example, the significance of the 'mirror' orbifold for Kantian discussions of incongruent counterparts.