 The similarity to Kreisel’s argument is clear: Define \(C(A)\) to mean that \(A\) is a is correct mathematical calculation; then by Hilbert’s thesis, \(C(A)\) implies \(V(A)\) and by completeness \(C(A)\) implies \(D(A)\). Moreover, apart from the appeal to the completeness theorem, Kripke’s argument is essentially the same as the Church-Kleene argument mentioned earlier and discussed in  supplement A.1: