In this paper I argue that in several passages Plato sympathizes with the following view: sensible particulars undergo continuous, pervasive physical change; as a consequence, where there seems to be one and the same object which is identical through time, there is in fact a succession of impermanent objects numerically distinct from each other but similar to each other. I illustrate the difference between this view—which invites interesting comparisons with modern and contemporary theories—and other, superficially similar views which Plato criticizes. I also suggest that this view might contribute to explaining Plato’s contention that sensible particulars lack being and are confined to coming to be. Finally, I show that my interpretation was well attested in antiquity; and I put forward the hypothesis that part of the aim of certain Aristotelian claims about substance might be to correct Plato in this respect.