impredicative definition

Term coined by Poincaré for a kind of definition in which a member of a set is defined in a way that presupposes the set taken as a whole. Poincaré believed that paradoxes like those of Russell and the barber were due to such definitions, and therefore proposed banning them. But it turns out that classical mathematics requires such definitions at too many points for the ban to be easily observed. See also vicious circle principle.