<p>This paper provides a response to a wide class of arguments for the existence of either coincident objects or 4-dimensional objects. These arguments proceed by pointing to certain intuitions we have—about things like statues and lumps of clay—and arguing that in order to account for the truth of these intuitions, we need to endorse the existence of either coincident objects or 4-dimensional objects. This paper undermines these arguments by developing a novel (and intuitively pleasing) theory of reference that explains how our intuitions here could be true—or, more precisely, how the sentences that express these intuitions could be true—even if (a) there are no such things as coincident objects or 4-dimensional objects, and (b) ordinary objects like statues and rocks and cats are numerically identical to the hunks of matter that constitute them.</p>