 A classic argument for the existence of properties—mind-independent abstract entities, such as those invoked in (1), that can be shared by multiple particulars—is that they are needed in order to metaphysically explain the objective resemblances we find in the world (see the entry on  properties, especially §§3–4).  Both Socrates the philosopher and the bust of him in our seminar room are snub-nosed. However (so the argument goes), it cannot be a brute fact that this is so; there must be something in virtue of which both of these things, separated by space and time, are snub-nosed. Specifically, (so the argument concludes), the fact that these two entities share the same property metaphysically explains why they resemble each other in this respect. Yet even if objective resemblances are, in fact, metaphysically explained by the sharing of properties by things that resemble—a big “if”, although let us suppose so for illustrative purposes—it remains to be said what kind of metaphysical explanation is to be envisaged here. Reflecting on (2)–(4) reveals at least three varieties of metaphysical explanation that have been the focus of recent work on the topic and in terms of which (1) could be understood.