 From Foundations of Logic and Mathematics (1939) (and Introduction to Semantics, 1942) Carnap had taken up Tarski’s conception of semantic truth. The principle of tolerance in the Logical Syntax remained intact, but in the following refined form: the syntactic rules of formation can be chosen freely; if the syntactical rules of transformation (derivation, inference) are determined prior to the semantic rules, they may be determined freely as well, but the semantic rules will have to be selected such that the transformation rules are sound with respect to them; vice versa, if the semantic rules are chosen prior to the transformation rules, the former may be determined freely, in which case the latter will need to match the former by being sound with respect to them (see, e.g., section 12 of Carnap 1939). Completely new questions arose, e.g., whether the rules of inference of classical propositional logic would determine the semantics of the standard logical connectives uniquely (given certain constraints): this novel type of categoricity question was answered in the negative by Carnap (1943). (In recent years, this part of Carnap’s work has sparked a lively debate: see, e.g., Raatikainen 2008, Murzi &amp; Hjortland 2009.) Semantics became just as important in Carnap’s work for the construction of formal languages as syntax had been in the Logical Syntax.