1. It is quite straightforward to see that what G says is true. Indeed, as we observed earlier, G says: ‘There is no PM demonstration of G’. (At least this is the meta-mathematical interpretation of G; when read at the number-theoretical level, G merely says that there is no number x that bears a certain relationship—namely, the ‘dem’ relationship—to the number sub (n, 17, n).

2. To convince ourselves that G is true, it suffices to consider only the former interpretation.) But we have just shown that G is undecidable within PM, so in particular G has no proof inside PM. But that, recall, is just what G asserts! So G asserts the truth. The reader should carefully note that we have established a number-theoretical truth not by deducing it formally from the axioms and rules of a formal system, but by a meta-mathematical argument.