 One solution to the problem posed by the cup case is to reject what Peter van Inwagen calls the Doctrine of Arbitrary Undetached Parts (see van Inwagen 1981). In setting the problem up we assumed that earlier Cup consists of the following parts: a handle together with Tcup. That assumption is justified if the following is. Tcup existed as a part of Cup when Cup still had its handle. Van Inwagen would reject that assumption. According to him it is illegitimate to assume that any old way of notionally dividing up an object yields an existing undetached part.