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Godel's 2nd theorem is about

"If an axiomatic system can be proven to be consistent and complete from

within itself, then it is inconsistent.â€

But we have a paradox

GÃ¶del is using a mathematical system

his theorem says a system cant be proven consistent

THUS A PARADOX

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. 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

THUS A PARADOX