  This argument—which is usually called the “just more theory” argument—has received a huge amount of attention in the literature. The most common response to the argument involves drawing a distinction between describing the features of a model which make that model intended and simply adding new sentences for that model to satisfy. Put otherwise, it involves distinguishing between changing the semantics under which our axioms get interpreted—e.g., by restricting the class of structures which count as models for our language and/or strengthening the notion of satisfaction which ties sentences to models—and simply adding new axioms to be interpreted using the same old semantics. The response then goes on to argue that proposals like those discussed two paragraphs ago—e.g., that intended models should be transitive or well-founded or satisfy second-order ZFC—should be understood as falling on the description side of this distinction rather than on the “adding sentences” side (although the latter is where Putnam's just more theory argument resolutely insists on putting them).