Models are fictional so non-referring terms within them pose no particular problem, as long as the properties of those fictions refer. Because models are fictional conceptual entities there is no mystery as to how we can manipulate them: m-interventions are the conceptual changes allowed within the rules of the fictional world. The m-interventions are licensed moves in a game of make believe. Which manipulations are possible is not set by experimental standards (or some, potentially vague, generalisation of the physical processes involved in causation in experiments), but is set by the props and rules of generation in the fictional world of the model. The logic of experimental manipulation underpins both notions.
Models are props for fictional thinking. All that matters in an explanatory context is that models capture modal structure. The explanatory role of models in modern science can be primary in some cases, their representational role secondary. Models are epistemic tools, and the
means of representation165 and the limits of misrepresentation are set by a
particular explanatory context. Knowing which parts of reality can be misrepresented to facilitate capturing modal structure is a skilled art. The modal connections between variables depends upon the choice of those variables, hence justificatory steps are built into model construction, demonstrating that the choice of variables will lead to fruitful modal connections. Models may capture modal structure through different means. Which properties a system has is in part a matter of perspective. That is, viewed from certain perspectives of coarse graining and universality/abstraction certain systems appear as if they have a certain set of properties they may not actually possess. This surrealistic take on the properties of systems allows the use of nihil models to be understood. These perspectives are not hopelessly relative, they are not cultural, rather they reflect the epistemic limits of human minds, just as the arrow of time may be an illusion of sorts, an artefact of the way human cognition operates, but that does not mean it cannot be explanatory.
Abstraction can remove unexplanatory irrelevancies and allow dependencies to be perceived from the mass of specific details. They also allow generalities to be discovered and otherwise diverse phenomena to be unified. Nihil models should be viewed in the same terms. The non- removable idealisations of asymptotic explanations allow disparate systems to be viewed as sharing common modal topologies relative to a particular variable set, even though the concrete micro-realisers of those systems, and the short term behaviour, may be very different. In the same way physical fictions, such as those used in semi-classical methods, allow common modal structure to be explicated, as we can say what different systems have in common. Two different quantum billiards may each be described numerically in purely quantum terms but we can see the continuity between them, a continuity based upon modal structure, by modelling them using non-referring classical elements.
This modal theory of models offers a middle ground between semantic and pragmatic intuitions. The notion of models as fictional worlds, constructed as tools for inquiry that contain context dependent props and user defined rules of generation, allows us to include a lot of the desirable aspects of the pragmatic approach. Yet at the same time, we can go beyond some of the potential fuzziness of these accounts and say what is objectively necessary in science that is not required of works of literary fiction, for
instance. That objective, ontic, component is found in requiring explanatory models to capture the modal structure of the world. That modal structure can be explored and investigated by pseudo-manipulating models to discover what depends upon what in them, then demonstrating that we have reason to think the model is modally accurate, either by experimental confirmation, novel prediction, bootstrapping, or top-down justification from wider theoretical considerations.166
Once viewed as fictions, having fictions within fictions shouldn't particularly worry us, just as a play within a play in Hamlet shouldn't worry an audience. How can a work of literature without referring terms say true things about the world? By containing true statements about properties and relations between things in the world. Containing a fictional element within a nihil model should not worry us in and of itself as any advanced model is itself a fiction that recreates modal structure.
SUMMARY
The kernel at the heart of all explanation is capturing modal structure, how this is achieved varies greatly from case to case, but once models themselves are viewed as fictional entities fictional elements within them shouldn't pose any particular difficulty. If we can provide modal information by using fictions then they can be explanatory. The reason why a fictional entity is able to capture certain elements of modal structure will vary from case to case.167 Often it will involve some kind of structure that the world has, or
appears to have when viewed from a certain perspective, that is recreated by the model. So in the case of quantum chaos, an overlap of dynamical structure is important to understanding how these models can be explanatory, but the dynamical structure is a means to an end, that end being modal structure. In that sense the “structure” in Bokulich's structural model explanations should be generally understood as modal structure.168
By understanding structure as modal structure we see there may be many means to capture this, partial-isomorphisms, similarity, analogy etc. Whether fictions are explanatorily tolerable will depend upon the specific explanandum. In one explanatory context a fiction may aid in the capturing of a section of the modal topology of a system, but in a different context, with different explanatory requests, that same fiction may destroy any hope of providing the correct modal information.169
We are still left with an ontological puzzle, do non-referring explanatory terms force us to either adopt an anti-realist view of explanation, or to adopt a purely epistemic definition of explanation? After all the ontic intuition would suggest we may get understanding from nihil models but we do not get explanations, the objective facts about the world that tell us what is responsible for what. In chapter 7 I will defend a circumscribed form of realism and ontic explanation. A type of ontic explanation that is compatible with the canonicalised manipulationist framework presented here, a form of modal surrealism that fits nicely with this picture of models. Ontic yet surreal facts, can be used in explanations if they are capable of reproducing modal structure. It is a sign of a sophisticated advanced scientific community that they can knowingly use explanatory fictions in this way, but it also is an appropriate framework for viewing historical case studies, such as in Carnot's, in which fictions were used unwittingly.