 Carnap, in fact, understood the import of Gödel’s theorems (Tennant, 2008); he knew of the results directly from Gödel, who indeed read drafts of the Logical Syntax. Despite this he displayed what looks like remarkable insouciance with respect to its implications for his position. He acknowledged the need, in demonstrating consistency, to move to a stronger language (§60c), and freely helped himself to mathematical techniques which could in no sense be classed as finitary (in §14 he used, for example, rules with infinitely many premisses, notably one which was later to be called the \(\omega\)-rule). In this way he can deny, for arithmetic at least, that there are any non-determinate sentences since every true arithmetic sentence is provable using the \(\omega\)-rule (relative to a fairly weak finitary logic, considerably weaker than classical logic).