more from A.George / D.J.Velleman

Single Idea 10124

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism]

Full Idea

For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem.

Gist of Idea

Gödel's First Theorem suggests there are truths which are independent of proof


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.168

A Reaction

Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths.