`I mainly agree. I think this is true not only for "sanity", but also`

`for "happiness", "cleverness", and a lot of *positive* predicate.`

A clever person will not say "I am clever" (or will look stupid)

`An happy person will rarely say "I am happy" (or will look or be`

`unhappy)`

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(Unless special context, and nuances). Those adjectives are solution of the equation Bx -> ~x. Communicating x entails the contrary of x.

`So it is interesting that something as sober and crisp as Peano`

`Arithmetic or Zermelo-Fraenkel set theory, or any sound machines,`

`already obey that equation for any x of the shape D#. (Dt, DBf, DDt,`

`DDDt, DDDDDDDBBBBBBf, ...), and can prove it once enough rich.`

`Lobian machine cannot prove any sentence beginning by a diamond. Any`

`possibility (consistency) need some sort of act of faith.`

Very generally, inconsistency, that is Bf, can be used to modelise

`Death (cf Bf can only be true in the cul-de-sac world of the Kripke`

`multiverse)`

Lies (to communicate the false, 1) Error (to communicate the false, 2) Dream (to communicate the false to oneself) Madness (as you say) Dt -> DBf can then be read respectively: (reading the D by "I can"). If I am alive I can die If I am honest I can lie If I am correct I can fail If I am awake I can dream If I am sane I can be mad Bruno Le 30-déc.-05, à 05:33, George Levy a écrit :

Bruno Marchal wrote:Godel's result, known as Godel's second incompleteness theorem, isthat no consistent machine can prove its own consistency:IF M is consistent then M cannot prove its consistencyBruno,After I read your email, we had a gathering of family and friends, andmy head being full of the subject of this post. I wanted to test theidea of Godel's second incompleteness theorem on the average peoplejust to see how they would respond. I found the right place in thediscussion 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) whoprobably view me as some kind of nutty professor. While this statementis mathematically true, it was not considered serious by the people Iwas talking with. I guess that the average human has no doubt abouthis own sanity.(But my kids had some doubts about mine) One way toprove that you are crazy is to assert that you are sane. This meansthat the average human is crazy! :-)George

http://iridia.ulb.ac.be/~marchal/