Insight is essential even if it is fallible
Just because insight is sometimes unreliable, we should not conclude that it plays no essential role in mathematics.
  • Doubts about consistency in mathematics only arise when mathematicians use systems that go beyond ordinary mathematics
  • When we do become assured of the consistency of the mathematical system, it is always because of insight.
Roger Penrose (1990).
Immediately related elementsHow this works
-
Artificial Intelligence Â»Artificial Intelligence
▲
Are thinking computers mathematically possible? [7] Â»Are thinking computers mathematically possible? [7]
▲
No: computers are limited by Gödel's theorems Â»No: computers are limited by Gödel's theorems
▲
Mathematical insight is non-algorithmic Â»Mathematical insight is non-algorithmic
▲
The absurdity of algorithmic insight Â»The absurdity of algorithmic insight
▲
Gödel’s theorem is not decisive Â»Gödel’s theorem is not decisive
■
Insight is essential even if it is fallible
◄
Roger Penrose Â»Roger Penrose
+Commentaires (0)
+Citations (0)
+About