[FOM] Godel Sentence

Kanovei kanovei at wmwap1.math.uni-wuppertal.de
Sat Aug 23 00:13:34 EDT 2003


As I had a chance to note in another occasion, 
the problem with "Goedel sentences" is not that they 
depend on the choice of the coding system in the background, 
but rather that the common interpretation of great Goedel 
results is wrong. 
In particular, the common belief that 
*there exist true, but unprovable sentences of PA* 
(allegedly by Goedel's theorems) 
is plain wrong in its straightforward sense, because the 
25-centuries of development of mathematics under more or less 
current standards of rigor fail to produce anything near 
a mathematical sentence accepted to be TRUE 
(as a mathematical sentence) 
but NOT because its mathematical proof IS GIVEN 
(or at least, as for facts like 2+3=5, it is a common agreement 
that a proof can be maintained by anyone with a minimal 
knowledge of the subject). 

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. 

V.Kanovei



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