[FOM] 18 Word Proof of the Godel, Rosser and Smullyan Incompleteness Theorems

[Panu Raatikainen]

"Charlie V" <axiomsandrules at yahoo.com>:

> Godel’s 1931 First Incompleteness Theorem is equivalent to the  
> assertion that truth and provability do not coincide.  Rosser’s 1936  
> extension is equivalent to the assertion that provability and  
> unrefutability do not coincide.

It should be added, though, that this is only a rather weak version of  
Gödel's (Rosser's) theorem. It does not provide a concrete example of  
a true but unprovable statement. More adequately, one could call this  
a version of Tarski's theorem.

Best, Panu



-- 
Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy, History, Culture and Art Studies
P.O. Box 24  (Unioninkatu 38 A)
FIN-00014 University of Helsinki
Finland

E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/