 A few properties of the present semantics are noteworthy. First, it accounts for Carnap’s idea that the axioms \(A(\TC)\) have a twofold function, viz., setting forth empirical claims and determining the meaning of theoretical terms (Carnap 1958). For, on the one hand, the truth values of the axioms \(A(\TC)\) depend on empirical, observable facts. These axioms, on the other hand, determine the admissible interpretations of the theoretical terms. These two seemingly contradictory properties are combined by allowing the axioms \(A(\TC)\) to interpret theoretical terms only on condition of there being a structure that both extends the given interpretation of the observation language and that satisfies these axioms. If there is no such structure, the theoretical terms remain uninterpreted. This semantics, therefore, can be seen to formally work out the old contextual theory of meaning for theoretical terms.