more from A.George / D.J.Velleman

Single Idea 10031

[catalogued under 2. Reason / D. Definition / 8. Impredicative Definition]

Full Idea

When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'.

Gist of Idea

Impredicative definitions quantify over the thing being defined


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.35

A Reaction

Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known.