George Levy writes:
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
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! :-)
"If I am sane, it is impossible to know for sure that I am sane."
Everybody believes he is sane, whether he is sane or not, and nobody can
prove he is sane. In psychiatry, this is the key problem with delusions. If
it were possible in general to prove one's own sanity, then deluded
patients, who more often than not retain their ability to think logically,
would be able to demonstrate to themselves that they were deluded. But by
definition of a delusion, this is impossible.
If you want to know what it is like for a psychotic patient to have forced
treatment, imagine that people from the local psychiatric facility knock on
your door tonight and, after interviewing you, politely explain that your
belief that you are an engineer, married with adult children, own the house
you are living in and the car in the driveway, and so on, is actually all a
systematised delusion. All the evidence you present to show you are sane is
dismissed as part of the delusion, and all the people you thought you could
trust explain that they agree with the psychiatric team. You are then
invited to start taking an antipsychotic drug which, over time, will rectify
your deranged brain chemistry so that you come to understand that your
current beliefs are delusional. If you refuse the medication, you will be
taken to the psychiatric ward with the help of police, if necessary, where
you will again be offered medication, perhaps in injection form if you
continue to refuse tablets.
Frightening, isn't it?
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