X-Message-Number: 23896
Date: Thu, 15 Apr 2004 09:57:08 EDT
Subject: excluded middle

Michael Price writes in part:
>I interpret Godel's result as disproving the law of the excluded 
>middle.  Of course I don't know if Godel saw it that way.
Goedel did liken his result to the "paradox" of The Liar, but that was 

misleading. Excluded middle refers to logic (true or not), not to provability. 
and provability are different things. 

And once more, for those who insist Goedel's result is significant, I remind 
them that a sentence undecidable in one formal system can be made decidable by 
expanding the formal system, which certainly shows that the problem is in the 
particular system.

There is a famous debate about this, with the "systems" being in the heads of 
two different people. Each can out-Goedel the other. This shows conclusively, 
if more proof were needed, that it's just a language mess, nothing more. And 
I repeat that the other weaknesses of formal systems are much more serious 
than Goedelian unprovability.

Robert Ettinger

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