 Let us start with point \((\beta)\). By 1928, the metalogical results can fairly be said to have been inevitable. Hilbert &amp; Ackermann had isolated and described first-order logic; the distinction between mathematics and meta-mathematics was by then well understood; they had shown how to prove the completeness of the propositional calculus; and they explicitly raised the completeness of first-order logic as an important open problem. It was certain that, within the next few years, some enterprising logician would provide an answer: as it happened, Gödel got there first. It would then have been an obvious next step to inquire about the completeness of higher-order systems. So within a few years of Hilbert &amp; Ackermann the basic metalogical theorems would have been established.