[FOM] Godel Sentence

Torkel Franzen torkel at sm.luth.se
Sat Aug 23 04:08:45 EDT 2003


V. Kanovei says:

 >Those who believe  in the paradigm 
 >*there exist true, but unprovable sentences of PA* 
 >in its straightforward sense 
 >are welcome to kindly present such a remarkable sentence 
 >along with a demonstration of its desired properties. 

  What's to believe? It's a mathematical theorem that there exist
true sentences in the language of PA which are not provable in PA.
You might as well ask why anybody believes that every natural
number has a unique prime decomposition.

  Of course, if you do not mean "unprovable in PA", but "unprovable"
in some absolute sense, there is nothing in Godel's theorem to suggest
that there are such sentences.

---
Torkel Franzen



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