Logical paradoxes, Gödel's theorems, and self-confidence

 

You can't always get what you want,
But you can sometimes get what you need.
-- Rolling Stones

Logical discoveries, mainly of the 20th century, impose limitations on the formalisms we can used without paradox. Other discoveries place limitations on what can be computed. In essence, the limitations apply to both people and machines, and intelligence can live within the limitations.

• The paradoxes
• The incompleteness theorems
• Iterated self-confidence
• Relative consistency