Great Ideas in Theoretical Computer Science: Gödel's Incompleteness Theorems (Spring 2013)

CMU 15-251: Great Ideas in Theoretical Computer Science
Spring 2013 Lecture #23: Gödel's Incompleteness Theorems

Taught by Ryan O'Donnell

[ucanihl]

On the way to the proof of stronger incompleteness theorem, I think you also proved that for any strong enough computable and consistent system A, there exists a statement whose truth can be seen by a human mathematician but cannot be proved by A. Isn't that a proof that human mathematical thought cannot be encapsulated in a formal system?
I wonder your stance regarding the Lucas-Penrose argument.

[Suav]

The difference between scientific consensus and science. "Essentially nobody/everybody believes..." We all need our daily bread to survive and this our need for effective entropy transport is at the bottom of the difference.