more from Stewart Shapiro

Single Idea 8730

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism]

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


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.