Full Idea
A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set.
Gist of Idea
'Impredicative' definitions refer to the thing being described
Source
Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
Book Reference
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.9
A Reaction
The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise.