An Example From Biology

The use of multiple conflicting models to study the same phenomenon is widespread in biology, since biological modelers often require vari-ous kinds of idealized models to describe interactions at different spa-tial scales ( Green and Batterman 2017 ; Qu, Garfinkel, Weiss, and Nivala 2011 ). In addition, biological modelers often face the challenge of mod-eling processes that operate on very different timescales: seconds, days, or years ( Davidson, von Dassow, and Zhou 2009 ). For example, cellular phenomena take place across a range of scales and “each scale of cell biol-ogy not only has its characteristic types of data, but also typical model-ing and simulation approaches associated with it” ( Meier-Schellersheim, Fraser, and Klaushcen 2009 , 4). That is, biologists investigating cellular behaviors often require multiple models due to the wide gaps between the spatial and timescales of various aspects of the target system(s), such as between the timescales of intra-molecular dynamics (10 ⁻² seconds) and chemical aspects of the interactions (10 ³ seconds). As a result, multiple inconsistent modeling techniques are used at different scales to investigate the same biological phenomenon. Moreover, because many biological phenomena take place across multiple scales, biologists often construct a variety of conflicting models for the various possible interactions across multiple scales ( Green and Batterman 2017 ; Meier-Schellersheim et al.

2009 ). That is, in addition to multiple conflicting models at different scales, biologists often build multiple conflicting multiscale models as well ( Dallon 2010 ).

These sets of models often make conflicting assumptions about the fundamental ontological components and interactions of the target sys-tem. For example, “while cellular automata models treat the single ‘cells’

in their simulations as entities with fixed shape and size, Potts model simulations aim at reproducing the shape changes cells undergo due to mechanical contact with neighbor cells or extracellular matrices” ( Meier-Schellersheim et al. 2009 , 6). Furthermore, these sets of models represent the interactions of the target system in contradictory ways, for example, modeling the same system dynamics using both individual-based and continuum models, which make contradictory assumptions about which aspects (and scales) of the system are relevant ( Byrne and Drasdo 2009 ).

Moreover, some of these models aim to represent dynamical interactions of the system with well-defined functions, while others investigate the same behaviors by simply assigning (idealized) computational algorithms to the elements of the system and studying the emerging behaviors ( Qu et al. 2011 ). These models not only represent the fundamental nature of the entities in drastically different ways, but they also make very different assumptions about which features of the system are relevant and irrel-evant to the phenomenon. Indeed, when it comes to multiscale modeling approaches in biology, “despite the attractiveness of this method, it faces many challenges, such as the gaps between models of different scales and inconsistencies between different methodologies” ( Qu et al. 2011 , 23).

The challenge is to figure out how to use the insights provided by these conflicting modeling approaches in order to develop explanations and understanding of the same target phenomenon. One approach is to try and construct “master models” that integrate the data from multiple scales into a single multiscale model ( Meier-Schellersheim et al. 2009 ).

However, while integrating input data from multiple scales into a single model might produce additional insights about the phenomenon, build-ing a master model does not resolve the contradictions among the various assumptions of the multiple models used to study the phenomenon, nor does it guarantee that the master model will provide an explanation.

Instead of focusing on the construction of master models, I argue that a more promising response to these challenges is to consider how these various conflicting models can be related to the same target phenomenon by multiple overlapping universality classes. That is, these different mod-els can belong to different (overlapping) universality classes that each contains the target system(s) of interest to the biological modelers. For example, model M ₁ might be in universality class U ₁ that contains the target system, while model M ₂ might be in universality class U ₂ that also contains the target system (see Figure 5.1 again). Some of these ideal-ized models might also be in the same universality class as other models

used to study the phenomenon, but the important point is that they can each be in at least one universality class that also contains the target system(s). ⁷ Because these models are in the same universality classes as the target system(s) in which the phenomenon of interest occurs, they will display some similar patterns of behavior. In addition, since different universality classes will focus on different universal patterns, models in different universality classes can be used to extract different sets of modal information about the biological phenomenon. Importantly, this account does not require that the conflicting models be interpreted as accurately representing the difference-making (or otherwise relevant) features of the target system. Moreover, because the modal information extracted from models within different universality classes need not conflict in the ways that the representations of the models themselves conflict, scientific mod-elers can use this plethora of modal information to construct (consistent) explanations and understanding of the phenomenon without having to build a “master model” intended to accurately represent all of the rel-evant features across a variety of scales.

In sum, every biological system will be a member of many overlapping universality classes. Some of these universality classes will involve univer-sal behaviors that hold only at particular scales, some of them will hold across multiple scales, and many will include the model systems repre-sented by idealized biological models . Consequently, an idealized biologi-cal model can provide modal information about those target system(s) within the same universality class even if the model conflicts with other idealized models used to study the same phenomenon (in other universal-ity classes). Furthermore, since universaluniversal-ity classes do not link their sys-tems through accurate representation or mapping, we need not interpret multiple conflicting models as making conflicting metaphysical claims about the features of real systems. As a result, multiple conflicting ideal-ized models in different universality classes can provide different sets of modal information about the target system that can be used to construct various explanations and understanding of the phenomenon of interest. ⁸ 4.2 An Example From Physics

A second example of using multiple inconsistent models to study the same phenomenon comes from physicists’ modeling of the nucleus ( Morrison 2011 ). There are over 30 different nuclear models, each of which provides some insight into some aspects of nuclear structure and dynamics. How-ever, the set of assumptions made by any one of these models is in con-flict with fundamental claims made by the others ( Morrison 2011 , 347).

For example, “some models assume that nucleons move approximately independently in the nucleus . . . while others characterize the nucleons as strongly coupled due to their strong short range interactions” ( Morrison 2011 , 347). Indeed, widely used models for studying the nucleus, such as

the liquid-drop model and the shell model, make contradictory assump-tions about the fundamental nature of elements and interacassump-tions involved ( Morrison 2011 , 349). In addition, these conflicting assumptions are typically necessary for the models to produce the behaviors of interest to physicists—that is, without these assumptions the models would be unable to provide insights into how the nucleus gives rise to the range of observations physicists want to explain and understand. In particular,

“nuclear spin, size, binding energy, fission and several other properties of stable nuclei are all accounted for using models that describe one and the same entity (the nucleus) in different and contradictory ways” ( Morrison 2011 , 349). As before, the problem of inconsistent models is seeing how we can interpret these sets of conflicting idealized models as providing genuine explanations and understanding of the same phenomenon.

The perspectivalist might try to interpret these inconsistent models as each only representing the nucleus in different ways from the perspective of different theories. That is, the liquid-drop model and the shell model simply represent the nucleus in different ways from within different theo-ries, such as classical physics or quantum mechanics. However, as Mor-rison points out, this really isn’t much of a solution to the problem of inconsistent models, since “none of those ‘perspectives’ can be claimed to

‘represent’ the nucleus in even a quasi-realistic way since they all contra-dict each other on fundamental assumptions about dynamics and struc-ture” ( Morrison 2011 , 350). In other words, it is difficult to see how we could make the realist inference from predictive success of these models to the accuracy of the models, given that their basic assumptions conflict with one another and those assumptions are essential to the limited pre-dictive successes of each model.

As before, I suggest the main reason this use of inconsistent models appears problematic for the realist is the (mistaken) assumption that accurate representation is essential to interpreting the models as provid-ing explanations and understandprovid-ing. It is clear that none of these nuclear models ought to be interpreted as providing an accurate representation of all the relevant (e.g., difference-making) features for nuclear phenom-ena. However, the universality account shows us how explanation and understanding might be achieved without providing accurate representa-tions of the relevant features of the system. Accordingly, I suggest that we should instead interpret these various nuclear models as relating to their target system(s) via different (and sometimes overlapping) universality classes that capture different universal nuclear behaviors across a range of perturbations to the physical features of the system. For example, the liquid-drop model might be within universality class U ₁ that includes real nuclei and displays a certain range of universal behaviors, whereas the shell model might be in universality class U ₂ that also includes real nuclei but displays a different range of universal behaviors, and so on for the other models. Because these models are in the same universality classes as

real systems that display nuclear phenomena, they will display some simi-lar patterns of behavior as those real systems. In addition, since different universality classes will capture different universal patterns across differ-ent classes of systems, models in differdiffer-ent universality classes can be used to extract different sets of modal information about the nucleus without having to interpret any one of the models as an accurate representation of a single set of relevant or difference-making features for the phenomenon of interest. Different models can then provide a plethora of modal infor-mation about nuclear phenomena even if no single model can provide enough information to explain and understand all of those phenomena.

Indeed, while none of the models provides an accurate representation, Morrison does grant that these conflicting nuclear models have “gener-ated information about nuclear phenomena that can be used in practical contexts” ( Morrison 2011 , 350). Moreover, while no single model is able to explain all the various features of nuclear phenomena, some mod-els have provided “an explanatory foundation for understanding certain processes” ( Morrison 2011 , 350). I argue that we can understand how this can be despite the inaccuracy and inconsistency of the models by appealing to different universality classes for the idealized models that allow them to provide different sets of modal information about the tar-get phenomena. Since universality classes do not link systems via accurate representation or mapping, we need not interpret these multiple conflict-ing models as makconflict-ing conflictconflict-ing metaphysical claims about the features of real systems. Instead, multiple conflicting idealized models in different universality classes can provide different sets of modal information about the target system that can be used to construct various explanations and understanding.

5 Multiple Conflicting Models, Modal Information,