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From: byron on 28 May 2010 01:08
colin leslie dean has shown Godels seconded theorem ends in paradox


http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Proof_sketch_for_the_second_theorem
[quote]The following rephrasing of the second theorem is even more
unsettling to the foundations of mathematics:

If an axiomatic system can be proven to be consistent and complete
from within itself, then it is inconsistent.[/quote]

now this theorem ends in self-contradiction

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
[quote]But here is a contradiction Godel must prove that a system
cannot be proven to be consistent based upon the premise that the
logic he uses must be consistent . If the logic he uses is not
consistent then he cannot make a proof that is consistent. So he must
assume that his logic is consistent so he can make a proof of the
impossibility of proving a system to be consistent. [b] But if his
proof is true then he has proved that the logic he uses to make the
proof must be consistent, but his proof proves that this cannot be
done[/b][/quote]
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