 What happens if the axioms A(TC) are inconsistent or fail to be empirically adequate? In other words, what happens if there is no interpretation of the theoretical terms such that this interpretation satisfies all the axioms and agrees with the antecedent interpretation of the observation terms? In this case, the axioms of the respective theory fail to interpret the theoretical terms. The set of admissible structures, as defined by Definition 3, is empty. At the same time, we think we have some understanding of the theoretical terms, even if the respective theory fails to be fully consistent with the empirical data. For example, we think we have some understanding of the theretical terms in classical mechanics, even though classical mechanics is not universally applicable. Moreover, we seem to have inconsistent, yet non-trivial scientific theories, such as classical electrodynamics.