 But model-theoretic validity (or derivability) might be theoretically adequate in some way even if some possible meaning-assignments are not modeled straightforwardly by (actual) set-theoretic structures. For model-theoretic validity to be theoretically adequate, it might be held, it is enough if we have other reasons to think that it is extensionally adequate, i.e. that it coincides in extension with our preferred pretheoretic notion of logical truth. In subsections 2.4.2 and 2.4.3 we will examine some existing arguments for and against the plain extensional adequacy of derivability and model-theoretic validity for Fregean languages.