Questions for GEB Unit XV

Mårten Stenius URL:

Page and figure references are from the English Penguin Books edition, unless otherwise noted.

"Birthday Cantatatata ..." and "Jumping out of the System"

(p. 471) About Lucas: "He says that we humans can always do the Gödel trick on any formal system as powerful as TNT - and hence no matter what the formal system, we know more than int does."

But how do we know that humans actually can do the Gödel trick on any formal system (as powerful as TNT)?

And do we then know more than the system does? After all, we just derive from it - without it we wouldn't be able to do the generalization.

At the end of the chapter, Hofstadter again states that there may be a limit to the human "system" - which maybe would imply a fundamental similarity betwen human brains and computers. But at the same time, he seems to be aiming at showing that (human) intelligence cannot be implemented on computers. Do we get any clues as to what arguments he would use for this - since he (at p. 472) says that he thinks Lucas is wrong (on which I agree)?