Re: Lobian Machine

From: rmiller <rmiller.domain.name.hidden>
Date: Fri, 30 Dec 2005 00:08:02 -0600

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
>
>
>Bruno,
>
>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! :-)
>
>George
>
>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.


RMiller
Received on Fri Dec 30 2005 - 01:10:57 PST