 This promising idea raises several questions. First, it is conceivable that certain items that are standardly regarded as abstract might nonetheless occupy determinate volumes of space and time. Consider, for example, the various sets composed from Peter and Paul: \(\{\textrm{Peter}, \textrm{Paul}\},\) \(\{\textrm{Peter}, \{\textrm{Peter}, \{\{\textrm{Paul}\}\}\}\},\) etc. We don’t normally ask where such things are, or how much space they occupy. And indeed many philosophers will say that the question makes no sense, or that the answer is a dismissive ‘nowhere, none’. But this answer is not forced upon us by anything in set theory or metaphysics. Even if we grant that pure sets stand in only the most trivial relations to space, it is open to us to hold, as some philosophers have done, that impure sets exist where and when their members do (Lewis 1986a). It is not unnatural to say that a set of books is located on a certain shelf in the library, and indeed, there are some theoretical reasons for wanting to say this (Maddy 1990). On a view of this sort, we face a choice: we can say that since impure sets exist in space, they are not abstract objects after all; or we can say that since impure sets are abstract, it was a mistake to suppose that abstract objects cannot occupy space.