  A third puzzle relates to vagueness. Aristotle's definition (as well as standard topology) suggests that there is always a sharp demarcation between the inside and the outside of a thing. Yet it may be observed that ordinary objects and events, as well as the extensions of many ordinary concepts, may have boundaries that are in some sense fuzzy or indeterminate. Clouds, deserts, mountains, let alone the figures of an impressionist painting, all seem to elude the idealized notion of a sharply bounded entity. Likewise, the temporal boundaries of many events, let alone their spatial boundaries, seem to be indeterminate.  When exactly did the industrial revolution begin? When did it end?  Where did it take place? And certainly the concepts corresponding to such predicates as ‘bald’ or ‘heap’ do not posses definite boundaries, either. As again Frege famously put it, to such concepts there seems to correspond “an area that ha[s] not a sharp boundary-line all around, but in places just vaguely fade[s] away into the background” (1903: §56).