 What about the converse of Padoa’s method? Suppose we can show that in each interpretation of the ground language, a theory \(T^*\) fixes a unique semantic value for the defined term. Can we conclude that \(T^*\) is admissible? This question receives a negative answer for some semantical systems, and a positive answer for others. (In contrast, Padoa’s method works so long as the semantic system is not highly contrived.) The converse fails for, e.g., classical second-order languages, but it holds for first-order ones: