 This would mean that the proof of consistency of the language L could be given within L. A simple analysis shows that this would not improve the situation, since in this case our proof of consistency of L would be of value only if we were sure that L is consistent. In case L were not consistent, we could also deduce the statement of the consistency of L, with the qualification that then the negation of the statement were deducible too. Thus if the consistency of L were deduced within L, this fact would not prove the consistency of L. (p. 409–410)