At 10:33 PM 12/29/2005, George Levy wrote:
Bruno Marchal wrote:
Godel's result, known as Godel's second incompleteness theorem, is
that no consistent machine can prove its own consistency:
IF M is consistent then M cannot prove its consistency
After I read your email, we had a gathering of family and friends,
and my head being full of the subject of this post. I wanted to test
the idea of Godel's second incompleteness theorem on the average
people just to see how they would respond. I found the right place
in the discussion to insert the paraphrase:
If I am sane, it is impossible to know for sure that I am sane.
This povoked some hilarity, especially with my kids (young adults)
who probably view me as some kind of nutty professor. While this
statement is mathematically true, it was not considered serious by
the people I was talking with. I guess that the average human has no
doubt about his own sanity.(But my kids had some doubts about mine)
One way to prove that you are crazy is to assert that you are sane.
This means that the average human is crazy! :-)
Hm. . .
Godel was discussing sharply defined mathematical constructs,
specifically, proof of N requires knowledge of non-N. As I'm sure you
know, sanity is a *legal*, rather than a mathematical term. While
this sort of logical fuzziness is probably in keeping with these
times, I doubt if it really applies to Godel's theorem.