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).
CONTEXT(Help)
-
Artificial Intelligence »Artificial Intelligence
▲
Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
▲
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
▲
Mathematical insight is non-algorithmic »Mathematical insight is non-algorithmic
▲
The absurdity of algorithmic insight »The absurdity of algorithmic insight
▲
Gödel’s theorem is not decisive »Gödel’s theorem is not decisive
■
Insight is essential even if it is fallible
◄
Roger Penrose »Roger Penrose
+Comments (0)
+Citations (0)
+About