2. The standard view of model deidealization and its limitations

Although there is substantial disagreement regarding the need for model deidealization, there is some consensus on what deidealization amounts to, or at least would amount to if it were needed. Commonly, model deidealization is understood as a process in which scientists successively relax assumptions to build increasingly more realistic models.Footnote ¹ Moreover, often, such a process is understood primarily as a process of adding (back) causal factors that have initially been omitted. At the same time, explicit definitions of deidealization are rare. Peruzzi and Cevolani (Reference Peruzzi and Cevolani2022, 28) have recently characterized model deidealization in a way that I think tracks a widespread view that often remains implicit: “Roughly, de-idealizing a theory or model means removing one of its idealized assumptions and replacing it with a new one that it [sic] is less idealized, that is, more realistic in being closer to the actual phenomena.”

While widespread this view of model deidealization has also attracted considerable criticism.Footnote ² For one, philosophers have disputed the feasibility of model deidealization so conceived. For example, some critics argue that because of the way in which models are constructed, their assumptions cannot usually be relaxed one by one (e.g., Alexandrova Reference Alexandrova2008; Carrillo and Knuuttila Reference Carrillo and Knuuttila2022; Reiss Reference Reiss2012; Rice Reference Rice2019). Scientific models are usually intricate constructions that must hold together so that “it is not normally possible to tinker with individual assumptions that are deemed ‘too highly idealized for the purpose at hand’ while leaving others fully intact when building a new, less idealized model” (Reiss Reference Reiss2012, 379). Rice (Reference Rice2019) has indirectly reinforced this criticism. If models are usually “holistically distorted representations” (Reference Rice2019, 196) that cannot be decomposed into accurate and inaccurate parts, then it is not possible, as the standard view requires, to “remove or replace the idealizations within our scientific models while leaving the contributions of the isolated accurate components intact” (Reference Rice2019, 189).

Others have argued that even if deidealizing models in this way were feasible, it might not be desirable. For example, both Michael Weisberg (Reference Weisberg2007) and Robert Batterman (Reference Batterman2009) have argued that often we do not want to deidealize our models (see also Potochnik Reference Potochnik2017). It is simply wrong to assume that the more complex, detailed, and realistic a model is, the better. Idealizations can play productive roles, and therefore, whether idealizations need to be deidealized depends on the kind of idealizations used in model construction. Idealizations can, for example, increase the explanatory power of a model and, therefore, deidealizing a model is counterproductive in such cases.

Moreover, the standard view of model deidealization is also put under pressure by conceptual difficulties that appear within an ambiguity about deidealization’s aim. Critics of model deidealization often seem to assume that model deidealization is a process that is geared toward bringing about a convergence between a model and its target phenomenon so that a “fully realistic” model emerges. For example, Batterman (Reference Batterman2002, Reference Batterman2009) describes what he calls the “traditional view” as one that requires a “convergence between model and reality” (Batterman Reference Batterman2002, 21) and that “aims for the most exact and detailed representation of the phenomenon of interest” (2009, 429). If that were the case, the standard view would run into serious difficulties because, as Cassini (Reference Cassini, Cassini and Redmond2021) has forcefully argued, this requirement is too strong. Most strikingly, this ideal is incompatible with most accounts of scientific models that are widely accepted nowadays. But one might also wonder whether a fully deidealized model, that is, one that is exact and complete, would still be considered a model.Footnote ³

Given these criticisms, model deidealization would appear as an, at best, marginal activity in scientific modeling. However, more recent defenses of model deidealization have contested this conclusion by countering with cases in which model deidealization has, in fact, occurred. Thus, it is argued, deidealization is often both feasible and desirable (e.g., Peruzzi and Cevolani Reference Peruzzi and Cevolani2022; Wajzer Reference Wajzer2024). It has also been noted explicitly that there is no need to assume that model deidealization aims at any sort of “fully realistic” model. For example, Peruzzi and Cevolani (Reference Peruzzi and Cevolani2022) state explicitly that they are primarily interested in model deidealization as a comparative concept only. When scientists deidealize they replace idealized models with less idealized ones without the requirement that models should be deidealized fully. I agree with such proposals to the extent that writing deidealization off as unimportant is a hasty conclusion. But the positive proposal associated with these recent defenses raises its own difficulties. For example, having turned deidealization into a comparative concept only, proposals like Peruzzi and Cevolani’s still seem to envision a uniform process of replacing idealized with less idealized assumptions. This is in line with many others who have discussed model deidealization primarily as a process of relaxing assumptions (e.g., Hindriks Reference Hindriks, Kuorikoski, Lehtinen and Ylikoski2012; Mäki Reference Mäki, Humphreys and Imbert2012), eliminating idealizations (e.g., Batterman Reference Batterman2010; McMullin Reference McMullin1985; Potochnik Reference Potochnik2017), or adding back “details” (e.g., Batterman Reference Batterman2009; McMullin Reference McMullin1985; Weisberg Reference Weisberg2007). However, if we look at concrete scientific practices, we might find that processes of model deidealization are much less uniform than this would suggest. Yet, we might also already suspect that processes of model deidealization are much more diverse for conceptual reasons. For example, given the now prevalent distinction between idealizations as intentional distortions and abstractions as omissions without distortion (e.g., Godfrey-Smith Reference Godfrey-Smith2009; Jones Reference Jones, Jones and Cartwright2005; Levy Reference Levy2021), we might consider not only distinguishing between different kinds of idealization but also similarly between different kinds of deidealization.Footnote ⁴ Such diversity seems to be suppressed both on the original standard view and its recent revisions.

Furthermore, many explicit discussions of model deidealization conceive of model deidealization not simply as any process of relaxing assumptions to make a model more realistic but as a concept that treats relations between a succession of models formally (e.g., Kuipers Reference Kuipers and Brzeziński1985; Niiniluoto Reference Niiniluoto, Kuorikoski, Lehtinen and Ylikoski2012). Peruzzi and Cevolani (Reference Peruzzi and Cevolani2022), for example, seem to retain this approach by offering a definition of model deidealization in terms of formal relations between models that need to hold. For them, one model (model B) is a deidealized version of another model (model A) if i. both models share the same target, ii. model B has relaxed one of the assumptions of model A so that model B does not include an idealized assumption that model A included and iii. model A can be shown to be a special case of model B. The problem with this account is that it turns deidealization into an exceedingly narrow concept. If we accept Peruzzi and Cevolani’s definition, it would seem that examining model deidealization primarily means treating cases in which two models are compared that differ only in a single dimension. This is because if more than one element is changed, “we would quickly find problems of incommensurability” (Cassini Reference Cassini, Cassini and Redmond2021, 99; also Jones Reference Jones, Jones and Cartwright2005). While I do not want to deny that we might find such cases, we should expect them to be rare. In most cases, more than one element is changed as a model is deidealized.

Thus, although a view of model deidealization along the lines of Peruzzi and Cevolani (Reference Peruzzi and Cevolani2022) can avoid the initial conceptual criticism and can counter claims that deidealization is never called for or possible, it effectively focuses on what we should expect to be a small subset of relevant deidealization processes. What it primarily targets are those processes of model deidealization in which assumptions are relaxed in a way that allows for a neat ordering of the models involved. These cases surely exist. But model deidealization is not exhausted by such cases. Moreover, such a revised standard view still does not adequately distinguish between the different processes it implicitly seems to talk about.

3. A practice view of model deidealization and its merits

To the extent that Knuuttila and Morgan (Reference Knuuttila and Morgan2019) argue that deidealization is a prevalent and important element of much scientific modeling, they concur with the recent defenses of model deidealization discussed in the preceding section. Yet, they also share many of the criticisms sketched—they too question the feasibility and desirability of model deidealization as envisioned by the standard view. Thus, their main concern is that despite these worries about feasibility and desirability, deidealization is still commonly understood as a simple “reversal process” (Reference Knuuttila and Morgan2019, 642) that does not warrant much attention.

As an alternative, Knuuttila and Morgan propose to examine processes of model deidealization more explicitly, to consider that they are often complex and to scrutinize how scientists avail themselves of a potentially diverse set of strategies to deal with the multifaceted challenges of model deidealization. Thus, in one way, their proposal is simple: Rather than preempting that deidealization, by definition, requires adding back to make a model more realistic, Knuuttila and Morgan (Reference Knuuttila and Morgan2019) propose to study model deidealization by examining how scientists achieve model deidealization in practice. To this end, Knuuttila and Morgan suggest a guiding framework that differentiates between four distinct processes of deidealization: what they call “deidealizing as recomposing,” “deidealizing as reformulating,” “deidealizing as situating,” and “deidealizing as concretizing” (Reference Knuuttila and Morgan2019, 642; emphases suppressed). Knuuttila and Morgan thus approach “deidealization” as a comprehensive category within which several distinct processes can be differentiated. This is important to recognize because it shows how Knuuttila and Morgan’s treatment of model deidealization does not begin from the increasingly widespread distinction between abstraction and idealization (which would suggest that we reserve the term “deidealization” for those processes that deal with assumptions that distort, while “concretization” would refer to those processes that deal with assumptions that omit without distortion, i.e., abstractions). Instead, they suspect that the processes of model deidealization are much more diverse than even this distinction would suggest and retain “deidealization” as a generic term that can be used to refer to several different processes.Footnote ⁵

A second novelty of Knuuttila and Morgan’s proposal is their framing of model deidealization as a means to diverse ends. Rather than conceiving of model deidealization as a process that primarily aims to make a model more realistic, for them, deidealization is required “for different kinds of attempts to apply models to the world” (Reference Knuuttila and Morgan2019, 642). Thus, a practice view of model deidealization positions the processes of deidealization as a means for different kinds of model “applications”: application designates a goal, deidealization is what a scientist might have to do to achieve this goal. It is important to recognize, however, that this covers a great deal of ground. Specifying the goal as model application that might call for model deidealization encompasses, for example, cases in which a model is used to explain a specific phenomenon but also cases in which a model is transferred across domains to study different kinds of phenomena (Reference Knuuttila and Morgan2019, 653).Footnote ⁶ But on a practice view, we should expect that the processes of model deidealization could look very differently depending on whether a model is used for explanation or whether it is transferred into a new domain. Lastly, it is not only the case that deidealization might look differently depending on the purpose to which a model is put. It is also only required to the extent that it helps to achieve that particular purpose. This, in turn, is in line with Cassini (Reference Cassini, Cassini and Redmond2021) who argues that deidealization is only required to the extent that it helps with achieving the epistemic purpose that the model is meant to serve. As a result, scientists only want to deidealize a mathematical model if it helps them with “obtaining better explanations or predictions, or more generally, improving the expediency of our models to solve the problems that originated their construction” (Reference Cassini, Cassini and Redmond2021, 88).Footnote ⁷

Importantly, then, Knuuttila and Morgan’s practice view has the resources to overcome the weaknesses of the standard view as discussed in the previous section. Above all, their practice view makes visible and tries to conceptually account for the diversity of model deidealization processes which the standard view neglects. Moreover, Knuuttila and Morgan do not only suggest that the processes of model deidealization are diverse. They also emphasize that model deidealization is not only after “more realism” but can serve several different goals thereby reframing standard feasibility and desirability concerns. In sum, a practice view along the lines of Knuuttila and Morgan (Reference Knuuttila and Morgan2019) offers a new perspective and important new resources for better understanding how models are deidealized.

4. Deidealization by narrative

Generally, Knuuttila and Morgan (Reference Knuuttila and Morgan2019) thus redirect attention to the diversity and complexity of processes of model deidealization in scientific practice. More specifically, however, their proposal includes the suggestion that processes of model deidealization might not be exhausted by processes in which one theoretical mathematical model is replaced with another theoretical mathematical model because they suggest that “deidealizing may involve making a choice of different representational modes” (2019, 650). This is especially important to consider given the vacancy that arises on those recent revisions of the standard view that dispense with the requirement of “full” model deidealization: As a comparative concept only, it directs attention to those processes of scientific practice in which idealized mathematical models are replaced with less idealized ones. But beyond such a comparative analysis, processes in which a highly idealized mathematical model that is deemed sufficiently realistic for a purpose at hand is put to such a purpose and the challenges of dealing with the idealized nature of such models remain beyond view. While Knuuttila and Morgan (Reference Knuuttila and Morgan2019) hint at the possibility that representational modes can be changed as models are deidealized, they do not develop this fully. In this section, I develop and extend their suggestion by considering narratives as one important representational mode that scientists might decide to rely on in processes of model deidealization.Footnote ⁸

The general idea that narratives might play an important role in the sciences has increasingly been studied by philosophers and historians of science (e.g., Morgan and Wise Reference Morgan and Wise2017; Morgan Reference Morgan, Morgan, Hajek and Berry2022; Morgan et al. Reference Morgan, Hajek and Berry2022). In this literature, a narrative is commonly understood as a representation of a connected sequence of events. The defining feature of narrative is then often marked by contrasting it with a chronicle: Both chronicles and narratives are representations of a sequence of events, but unlike chronicles that only order events in time, narratives also draw connections between events thus ordered (e.g. Morgan Reference Morgan, Morgan, Hajek and Berry2022).Footnote ⁹ From a narratological perspective, this is a relatively minimal definition of narratives (e.g., Fludernik and Ryan Reference Fludernik and Ryan2020). But it is in line with what Ryan (Reference Ryan and Herman2007) has called “the most universally accepted feature of narrative” (Reference Ryan and Herman2007, 25) namely that narratives are a representation of an “ordered sequence of events” (Reference Ryan and Herman2007, 23). One of the points of contention important for this context is the nature of this ordering. It is often assumed that something more than temporal ordering is characteristic of a narrative—this is what distinguishes narratives from chronicles. On some definitions, these connections of the narrative have to be causal (e.g., Carroll Reference Carroll2001; for a discussion see Abbott Reference Abbott2002, Ryan Reference Ryan and Herman2007). While I do not assume that narratives, by definition, posit causal connections, we will see that the narratives I am concerned with in this article are of the stronger form where the connections are indeed causal.

Now, one important theme in those analyses of the role of narratives in science is the oft-observed complementarity between mathematical models and narratives (e.g., Currie and Sterelny Reference Currie and Sterelny2017; Hartmann Reference Hartmann, Morrison and Morgan1999; Miyake Reference Miyake, Morgan, Hajek and Berry2022; Morgan Reference Morgan2012; Rosales Reference Rosales2017; Wise Reference Wise2011, Reference Wise2017; see also Morgan Reference Morgan2024). More specifically, for several different fields, narratives have been observed to operate on the model-world axis in that they often seem to assist mathematical models in achieving their epistemic aims by “linking” (Morgan Reference Morgan2012) or “relating” (Wise Reference Wise2017) a model and its target system. In the following, I will propose to analyze such a “linking” relation in terms of the activity of deidealizing models. While the epistemic aims that narratives seem to promote in mathematical modeling vary somewhat, often narratives are observed to help models with achieving their explanatory aims. Thus, in the discussion that follows, the focus is on modeling practices that aim at explanation. At this point, such a focus is helpful given that, on a practice view of model deidealization, the kind of purpose to which a model is put determines both the extent to which model deidealization is called for and the kind of processes that might be required. Moreover, a focus on explanation also allows for some continuity with previous analyses which have often linked model deidealization to the issue of explanation in particular (e.g., Hindriks Reference Hindriks, Kuorikoski, Lehtinen and Ylikoski2012; McMullin Reference McMullin1985; Niiniluoto Reference Niiniluoto2018; Nowak Reference Nowak, Nowak and Nowak2000).

4.1. Case study: “The superstar firm model”

To argue that narratives can contribute to deidealizing a mathematical model, in this section, I first discuss a case study to show in concrete terms how a narrative is constructed in the process of modeling and how, in this process, subtle extensions and elisions are introduced. This should provide sufficient concrete resources to then discuss how narratives can deidealize a model—primarily by concretizing and recomposing it.Footnote ¹⁰

The case study comes from economics and centers on what is called the “superstar firm model.” Although the model has this particular name, it is a modified extension of a widely used international trade model (Autor et al. Reference Autor, David Dorn, Patterson and Van Reenen2020; see also Melitz and Redding Reference Melitz, Redding, Gopinath, Helpman and Rogoff2014). It explicitly builds on a model that was developed by two economists (Melitz and Ottaviano Reference Melitz and Ottaviano2008), which in turn extends one of the standard models of modern international trade (Melitz Reference Melitz2003). The economists of the case study introduce this superstar firm model to explain a macroeconomic pattern of changes in the distribution of an economy’s aggregate income, namely that the labor share has fallen in many industrialized economies in recent decades. What this means is that the proportion of the gross domestic product going to labor in the form of wages has fallen vis-à-vis the proportion of national income that goes to capital in the form of profits. This change to the labor share is of interest to economists not only because these shares have long been considered to be relatively stable—the stability of the labor share was one of the “stylized facts” of twentieth century economics—but also because a shifting labor share points to important changes in an economy’s income inequality levels. While the economists of the case study assume that the fact that the labor share has fallen is well supported by the available evidence, they recognize that there is considerable disagreement about the causes behind this phenomenon. Technological innovations, international trade, social norms, and labor market institutions have all been suggested to be responsible for the fall of the labor share. So, while the superstar firm model is a typical theoretical mathematical model as commonly used in contemporary economics, its name already indicates the specific use to which this otherwise standard model is put. This specificity of the model, in turn, is needed to exemplify the processes of deidealization.

The superstar firm model consists of a system of equations, some of which are shown here:

(1) $$q{\rm{\;}}\left( {{p_{\rm{\omega }}}} \right) = {\rm{\;}}{p_{\rm{\omega }}^{ - \sigma }}d\left( {{\rm{A}}{p_{\rm{\omega }}}} \right)$$

(2) $$q\left( {{p_\omega }} \right) + \left( {{p_\omega }{\rm{}} - {c_\omega }} \right)q^\prime\left( {{p_\omega }} \right) = 0$$

(3) $$\varepsilon {\rm{}}\left( {{p_\omega }} \right) = A{p_\omega }d^\prime(A{p_\omega })/d(A{p_\omega }) - {\rm{}}\sigma $$

(4) $${m_\omega } \equiv {{{{p_\omega }}}\over{{{c_\omega }}}}$$

(5) $${S_\omega } \equiv {{wV} \over {{p_\omega }{q_\omega }}}$$

We can interpret these equations by assigning economic meaning to the mathematical variables and parameters: q(p _ω ), for example, refers to the quantity demanded for an individual good ω, p _ω refers to the price of such a good, σ is a preference parameter, ε(p _ω ) is the so-called elasticity of demand, ${m_\omega }\;$ are what economists call firm markups, and c _ω are marginal costs. Thus interpreted, these equations basically tell you about the demand side (equation one), the supply side (equations two and three), the markups (equation 4), and the labor share (equation 5) in the model economy.

In practice, the economists not only interpret the model by assigning meaning in this way. They tell us much more about the model by offering further verbal descriptions that outline other features of the model in economic terms. For example, they tell us that “in the model, entrepreneurs entering an industry are ex ante uncertain of their productivity z _i . They pay a sunk entry cost κ and draw z _i from a known productivity distribution with density function λ(z). Firms that draw a larger value of z will employ more inputs and have a higher market share” (Autor et al. Reference Autor, David Dorn, Patterson and Van Reenen2020, 654). While this verbal description tells us more about the model, importantly, this is not where I want to suggest that we find the narrative.Footnote ¹¹ To appreciate the role that the narrative plays in this case study, we need to pay attention to the fact that the economists not only posit the model or describe the modifications they have made to its predecessor(s). They further engage with it.Footnote ¹²

One thing that the economists of the case study do with the model is that they manipulate it to mathematically derive results. These results are presented in terms of three major “propositions” (Autor et al. Reference Autor, David Dorn, Patterson and Van Reenen2020, Appendix) establishing relationships between key variables considered in the model. The first result establishes a relationship between two variables, the size of a firm and the size of its labor share, and the second and third results establish a relationship between two variables conditional on a third. These latter two results thus discriminate between three cases by specifying how the average and aggregate labor share change depending on the form of the productivity distribution in an industry. But the economists do not leave it at deriving these results. They also engage with the model and its results further and in the process, I suggest, construct a narrative. I reconstruct how the narrative is developed in the economists’ further engagement with the model as two steps because this allows us to see more clearly how the narrative is constructed and how exactly it differs from the model and the mathematically established results.

In the first step, the economists verbally summarize the results that they have derived in the appendix as:

Proposition 1 of the model delivers the intuitive result that markups are higher for more productive firms. Thus, the labor share is lower for larger firms. An increase in market toughness that reallocates more output to these firms which [sic] will tend to reduce the aggregate labor share. However, a change in market toughness will also change the level of each individual firm’s labor share. Greater toughness will tend to … increase the firm-level labor share. … Propositions 2 and 3 show that when the underlying productivity distribution is log convex, the reallocation effect dominates the within firm effect so that the aggregate labor share unambiguously falls even though individual firms’ labor shares rise. (Autor et al. Reference Autor, David Dorn, Patterson and Van Reenen2020, Appendix, 68; emphasis in original)Footnote ¹³

Most importantly, in this first step, we can see how the economists engage with the mathematically derived results further by embedding them in a broader context. “Proposition 1” now specifies a condition at the beginning of a sequence that is initiated by an external change that induces two opposing effects, and “Propositions 2 and 3” help to establish what effect this external change has on the aggregate labor share as the variable of interest. Notably, by relating their results in this way, the economists generate an ordering that neither maps the structure of the model nor follows necessarily from the mathematical results derived in the model manipulations. Yet, importantly, this first step involves not only such ordering but also selection. For example, the economists have eliminated two of the three possible cases that they developed during their model manipulations. Having derived the results mathematically, it is not yet decided whether an increase in market toughness leads to a decrease, an increase, or a neutral effect on the aggregate labor share. Depending on the form of a productivity function, all three effects are possible. But when the economists summarize their results at the end of the appendix, they select one of these cases. They choose the case in which the labor share falls in response to market toughening.Footnote ¹⁴

Next, the economists arrive at the narrative that I want to draw attention to. This narrative tells you what the authors claim to be behind the fall of the labor share. In the main body of the text, the authors write that

globalization, which increases effective market size, or greater competition…will tend to make markets tougher…causing low-productivity firms to shrink and exit. The reallocation of market share toward more productive firms will increase the degree of sales concentration and will be a force decreasing the labor share because a larger fraction of output is produced by more productive (superstar) firms. (Autor et al. Reference Autor, David Dorn, Patterson and Van Reenen2020, 654–55)

Although both quotations put forward a representation of a connected sequence of events, only the connections in the second quotation are put forward as causal claims because only in the second excerpt do the authors use causal language: from describing things that “increase,” “decrease,” and “change” to describing things that “tend to make tougher,” “cause,” “shrink,” and “exit.” But not only do these two quotations differ with respect to causality the components that appear have also changed. For example, the element at the beginning of the sequence of events differs. Whereas the economists speak only of a “change in market toughness” in the first quotation, in the second quotation it is “globalization” that initiates the changes. Notably, “globalization” is not only more ambiguous than “increase in market toughness” as operationalized in the model but also not fully determined. In the article the authors do not commit themselves on whether “globalization” means that the effective market size has increased or whether competition has risen (Autor et al. Reference Autor, David Dorn, Patterson and Van Reenen2020, 654). Similarly, the meaning of “firm” also has subtly changed: from firms in the model that are defined as existing in a world where there is only one factor of production and where their productivity is determined by a draw from a probability distribution to “superstar firms” such as Google, Facebook, Amazon, and Uber, with which we interact in the real economic world (Reference Autor, David Dorn, Patterson and Van Reenen2020, 650–51).Footnote ¹⁵

In sum, this shows how in using the model for this particular epistemic purpose things happen that do not involve replacing the mathematical model with a less idealized one but nonetheless respond to the idealized nature of the model. It is also meant to exemplify how this further engagement can yield a narrative simply because it shows how the economists have constructed a representation of a causally connected sequence of events in the process. Importantly, this representation does not automatically follow from either the model or its mathematically derived results. Instead, in constructing a narrative to explain the fall of the labor share, the economists of the case study have selected elements of the model deemed relevant, changed the meaning of some of these elements, and ordered and related them to yield a representation that is meant to be able to causally account for the phenomenon.

5. Narratives as a strategy on the deidealization “menu”

Knuuttila and Morgan (Reference Knuuttila and Morgan2019, 646) present their framework as proposing a “menu” of deidealizing processes emphasizing that we should expect scientists to combine them in various ways depending on their goals. Thus, on a practice view, we should expect that the processes of deidealization can look differently depending on the purpose to which a model is put. In this article, I have suggested to consider narratives as one important strategy of model deidealization when such models are used for explanation. In those cases, it is narratives that, as additional representational forms, help with achieving the goal of explaining with the model by recomposing and concretizing it.

By proposing to add narratives to the menu, I have thus focused on one particular implication of Knuuttila and Morgan’s proposal that widens the attention from processes of deidealization in which one theoretical mathematical model is replaced by another one to processes of deidealization that involve a change of representational mode. Importantly, however, by recognizing the role that narratives can play in deidealization we do not need to deny the importance of those processes of model deidealization in which mathematical models are replaced by other less idealized mathematical models. Rather, on a practice view, we should expect that these processes are prevalent and warrant close attention, too. Thus, examining how mathematical models can be deidealized by narratives should be thought of as an extension rather than as a replacement of such processes. Nor does recognizing the role that narratives can play in deidealizing models mean that narratives are always called for or that all narratives deidealize.

At the same time, there are reasons to believe that finding narratives as an important means of deidealizing mathematical models when the goal is explanation might be a more widespread phenomenon. On the one hand, there are those analyses that have discussed narratives as a close companion of mathematical models that mediate between model and target when models are used for explanation in several different sciences (e.g., Morgan Reference Morgan2012; Morgan and Wise Reference Morgan and Wise2017; Wise Reference Wise2011).Footnote ¹⁹ On the other hand, one might also think that it is not only economists who build up such narratives when using models for explanation if we believe that often explaining means describing causal mechanisms (e.g., Bechtel and Abrahamsen Reference Bechtel and Abrahamsen2005; Glennan Reference Glennan2002; Machamer et al. Reference Machamer, Darden and Craver2000). While Kaiser and Plenge (Reference Kaiser, Plenge, Kaiser, Scholz, Plenge and Hüttemann2014) sketch some of the affinities between mechanistic accounts of explanation and narrative representation, Glennan (Reference Glennan2010, Reference Glennan, Kaiser, Scholz, Plenge and Hüttemann2014) has explicitly put forward an account of mechanistic explanation that assigns narratives an important representational role. He even claims that a “mechanistic explanation characteriz[ing] entities and activities, describing how their organization in space and time gives rise to some phenomenon … is in essence a narrative” (Reference Glennan, Kaiser, Scholz, Plenge and Hüttemann2014, 279). More work is required to spell out when and how narrative representation is involved in mechanistic explanation, especially in mechanistic explanations using mathematical models.Footnote ²⁰ At the least, this would require close attention to the ways in which mechanisms are often viewed as both systems/structures and as processes (Glennan Reference Glennan2002, Reference Glennan, Kaiser, Scholz, Plenge and Hüttemann2014) and to the complexity of mechanisms—because mechanisms not only have parts that are organized but all mechanisms have “an active element that is seen through the inter-relationship of the parts” (Crasnow Reference Crasnow2017, 8). But at this point those affinities already observed indicate why we might expect narratives to be an especially important strategy of model deidealization when models are put to explanatory uses.