 To prove the latter statement first, let us inquire into the significance of the theorem stating that the proof of consistency is only to be given in the metalanguage. What then would happen, if the metalanguage should turn out to be inconsistent? This would lead to the consequence, not that our deduction of the statement of consistency is incorrect, but that the contrary of this statement could also be deduced; and this indeed would make our statement valueless. Now let us assume for a moment that Gödel’s second theorem did not hold, or with other words, that Gödel had proved the contrary of his theorem.