This paper is about a puzzle concerning the metaphysics of material objects: a puzzle generated by cases where material objects appear to coincide, sharing all their matter. As is well known, it can be illustrated by the example of a statue. In front of me now, sitting on my desk, is a statue – a statue of a lion. The statue is made of clay. So in front of me now is a piece of clay. But what is the relation (...) between the statue and the piece of clay? Are they identical, or are they distinct? (shrink)

It seems plausible to say that what changes an entity can or cannot survive depends on its persistence conditions, and that these depend, in turn, on its sortal kind. It might seem to follow that an entity cannot belong to two sortal kinds with potentially conflicting persistence conditions. Notoriously, though, this conclusion is denied by ‘contingent identity’ theorists, who hold, for example, that a permanently coincident statue and piece of clay are identical, although the persistence conditions associated with the kinds (...) statue and piece of clay are potentially conflicting. A clash with Leibniz’s Law is avoided by treating modal predicates as what Harold Noonan has called ‘Abelardian predicates’, as in the version of ‘inconstant’ counterpart theory developed by David Lewis. In addition to other difficulties, however, there is a question whether this ‘Abelardian’ theory does justice to the intuitions expressed in such statements as that the piece of clay could, while the statue could not, have survived a radical reshaping of its matter. I present an argument, which I call ‘the vacuous satisfaction argument’, for the conclusion that the theory does indeed fail to capture the significance of such de re modal statements. (shrink)