Jeff Wisdom has recently defended the proposition that any view of moral supervenience worth its salt must incorporate a diachronic view of base property exemplification. Let us call the proposition defended by Wisdom p. In this paper, I try to show that Wisdom has offered no good reasons for accepting p. My argumentative strategy proceeds along two separate tracks. First, I try to show that the thought experiment Wisdom employs in order to underwrite p does not offer the intended support (...) for the proposition. Secondly, I try to show that even if the problems with the thought experiment in question are ignored, there is at least one other reason for thinking that Wisdom has not offered a convincing argument in favor of p. (shrink)