Abstract
According to a thesis that David Lewis calls Humean supervenience ‘all else supervenes on the spatiotemporal arrangement of local qualities throughout all of history, past and present and future’. Local qualities are understood as ‘perfectly natural intrinsic properties which need no bigger than a point at which to be instantiated’. Humean supervenience aims to express the logically or metaphysically necessary connection between properties at the ‘fundamental level’ and all other properties, including objects’ dispositions, powers and sensible qualities. I shall argue that Humean supervenience so understood is not consistent with Hume’s own metaphysical outlook; and that this inconsistency is not only of historical interest: it reveals an essential tension in contemporary Humean metaphysics.