more from Kurt Gdel

Single Idea 8747

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

Full Idea

Gdel defended impredicative definitions on grounds of ontological realism. From that perspective, an impredicative definition is a description of an existing entity with reference to other existing entities.


See Idea 8721 for impredicative definitions

Gist of Idea

Realists are happy with impredicative definitions, which describe entities in terms of other existing entities


report of Kurt Gdel (On Formally Undecidable Propositions [1931]) by Stewart Shapiro - Thinking About Mathematics 5.3

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.128

A Reaction

This is why constructivists must be absolutely precise about definition, where realists only have to do their best. Compare building a car with painting a landscape.

Related Idea

Idea 8721 An 'impredicative' definition seems circular, because it uses the term being defined [Friend]