In this paper we consider a puzzle concerning Hume's account of time and what he calls “steadfast unchanging objects”—that is, unchanging objects coexisting with temporal successions. On the one hand, Hume maintains that steadfast unchanging objects are temporally indivisible. On the other, he allows that such unchanging objects are capable of undergoing a determinate number of alterations in a given length of time, which seems to imply that they are at least potentially temporally divisible. After arguing that Donald Baxter's influential (...) interpretation of Hume's theory of time cannot resolve this tension, we propose that Hume offers a skeptical resolution of the difficulty. (shrink)