I have a question about Godel_ey type stuff: Here goes: (where T is a theory that is sufficiently powerful to express statements about itself ) if a theory is consistent, con(T), then it cannot prove its own consistency. ¬( T_provable(con(T) ). (1) con(T) => ¬( T_provable( con(T) ) But an INconsistent theory can prove ANYTHING, including its own consistency. ¬con(T) => T_provable( con(T) ) Therefore if a theory can NOT prove its own consistency, it definitely ISN'T an INconsistent Theory. ( assuming it is otherwise sufficiently expressive ) ¬( T_provable( con(T) ) =>¬( ¬ con(T) ) (2) ¬( T_provable( con(T) ) => con(T) since: ¬( ¬ con(T) ) => con(T) therefore: by (1) and (2) con(T) < = > ¬( T_provable( con(T) ) ) This is exactly of the form: G < = > ¬( T_provable(G) ) where G is the/a Godel statement for the theory. My question is: How does one show that G is DIFFERENT from merely the statement "con(T)". and that it does not 'contain' con(T) as any sub-part of G ? since the statement "con(T)" fulfills exactly the same criteria. "con(T)" is just such a statement. I probably won't understand your answer, but it might be a good excercise for your logic students!

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