What is mereological harmony?

Say that mereological harmony is the view that there is at least some mirroring between the mereological structure of material objects and the mereological structure of their locations: each, in some way, mirrors the other. As it turns out, there is a confusing array of systems of harmony available to the substantivalist. In this paper, I attempt to bring some order to these systems. I explore some systems found in the literature, as well as some natural systems which haven’t been discussed. Along the way, I explore a number of metaphysical consequences of the different systems of harmony. The paper ends with a roadmap of possible views for the substantivalist. The material world has a certain mereological structure to it. And so does the spatiotemporal world. One very natural thought to have is that it is impossible for something x to be a part of y without x’s location also being a part of y’s location. For instance, it is impossible for my arm to be a part of my body without my arm’s location being a part of my body’s location. And a second very natural thought to have is that it is impossible for x’s location to be a part of y’s location without x also being a part of y. Call cases where these misalignments do in fact occur parthood misalignment cases. The former thought suggests that the mereological structure of spacetime mirrors the mereological structure of the material world with respect to the parthood relation and the latter thought suggests that the mereological structure of material objects mirrors the mereological structure of spacetime with respect to the parthood relation. Very few people, I think, are willing to accept the possibility of the first kind of misalignment. The second type of parthood misalignment is a bit more controversial. However, I can imagine