Cases of coincidence, the paradigmatic example being the statue and the lump of clay, involve purported property differences that motivate the claim that there are numerically distinct coincident objects. These cases are philosophically important insofar as they put pressure on a range of interconnected questions and intuitions about material objects and their individuation, persistence conditions, location, and mereology.
The standard taxonomy of responses to these cases is relatively coarse-grained: one either accepts numerically distinct coincident objects (pluralism) or rejects them (monism), with a handful of further disagreements among variants. I argue that this picture significantly underdescribes the landscape and that disagreement over these cases involves several dimensions.
I will focus on the distinction between different ways that coincident, or merely apparently coincident, objects might be related to one another, differentiating locative coincidence from mereological coincidence. I then offer and defend methodological conceptual pluralism: a particular view about which concept(s) of coincidence we ought to employ, given the goal of clarifying what these cases consist of. This reveals multiple layers of disagreement: metaphysical, conceptual, and higher-order conceptual. The result is a far more fine-grained set of competing views of what these cases involve. It also shows that some arguments for or against the standard coarse-grained positions, in fact, target only subsets of these more fine-grained views.
