Modelling Nature

Roman Frigg and James Nguyen

Reviewed by José Díez

Modelling Nature: An Opinionated Introduction to Scientific Representation
Roman Frigg and James Nguyen
Cham: Springer, 2020, £79.99 / £59.99
ISBN 9783030451523 / 9783030451554

Roman Frigg and James Nguyen’s Modelling Nature is a comprehensive, critical review of the latest developments in the modelling literature. The book offers the most complete and exhaustive monograph on representation to date. With an encyclopaedic scope, only idealization and approximation are—explicitly—left without a detailed treatment, a sensible decision given that they would require a book of their own. This is not only an opinionated survey of the ongoing debate, Frigg and Nguyen also make their own substantive contribution to the topic. For both its critical survey and their original contribution, Modelling Nature is bound to become the classic reference in the field, a must-read book for every philosopher and scientist interested in modelling and representation in scientific practice.

The book has nine chapters that can naturally be grouped into five blocks. The first two chapters play an introductory role. Chapters 3 and 4 focus on similarity and structural accounts of representation, which share an emphasis on similarity relations between traits of models and targets. Chapter 5 analyses inferential accounts, in which the transfer of information lies at the heart of representation. Chapters 6 and 7, respectively, focus on fictional and representation-as approaches that are at the origin of authors’ own account, which is presented in detail in Chapters 8 and 9.

The explicandum notion is representation. The project faces an immediate obstacle, since the current literature on models does not always focus on the same set of problems nor does it use the same evaluative standards for assessing answers to these problems. Chapter 1 aims to remedy this situation by first introducing five problems that an account of scientific representation needs to address, and then presenting five conditions that acceptable answers to these problems have to meet. The problems are the representational demarcation problem (do scientific representations have to be distinguished from other kinds of representations?), the representation problem (what turns something into a representation of something else?), the problem of style (what representational styles are there and how can they be characterized?), the problem of accuracy (under what conditions is a representation accurate?), and the problem of carriers (what objects are used as carriers of representations and how do scientists engage with them in practice?). The conditions are the directionality condition (identify the root of representation’s directionality), the surrogative reasoning condition (explain how a representation can provide information about its target), the misrepresentation condition (an account of representation must make room for misrepresentation), the targetless representations condition (account for how targetless models work), and the applicability of mathematics condition (explain how mathematics is used in representing a target). There are complex interrelations between these problems and conditions, and this chapter details what these are. These problems and conditions provide the analytic lens through which the different accounts of representation are discussed.

This is a helpful analytic apparatus that also has an important consequence, which the authors do not, perhaps, highlight sufficiently. Among the problems mentioned, the representation problem and the problem of accuracy are arguably the most fundamental and, importantly, they imply that there is a distinction between the conditions for the existence or performance of a representation and the (additional) conditions for an existing representation to be accurate or correct or adequate (as Frigg and Nguyen specify later, to a degree relevant in the context). Yet, these two problems of existence and adequacy have not always been clearly distinguished in the literature, which has unfortunate consequences. For instance, similarity and structuralist proposals are plausible only if they are read as answers to the problem of accuracy, but are non-starters as answers to the problem of performance. If, for instance, the existence of the relevant morphism between model and target were a condition for the existence of the representation, then (leaving aside the issue of approximation) every existing representation would be correct or adequate, and there would be no room for misrepresentation. But misinterpretation is a well-known phenomenon: just think of Ptolemy’s misrepresentation of the heavens, phlogiston’s misrepresentation of combustion, or of the triple helix’s misrepresentation of DNA. In these and other cases, the existence conditions for representation are met, but the representation is inadequate. This would seem to be immediately obvious, and yet it is true that the extant literature is not always clear in this regard. For example, some authors claim simply that isomorphism is the condition for representation, without making it explicit whether they are talking about existence or adequacy conditions. Accordingly, several critics of these accounts read the condition as a condition for existence and not for correctness. It is thus crucial to neatly distinguish the two problems and their corresponding conditions, and to make explicit to which of these a proposal is intended to respond (Frigg and Nguyen themselves opt for a cautious interpretation and discuss similarity and structuralist proposals on both readings).

All this, of course, presupposes that there is a problem of (scientific) representation to begin with, and Frigg and Nguyen devote Chapter 2 to answering those who deny the existence of any such problem. In particular, they respond to Callender and Cohen’s ([2006]) ‘stipulation by fiat’ approach, according to which anything can represent anything else so long as a subject stipulates that it do so. The moral of the chapter is that the intentions of an agent play an important role in scientific representation, as many accounts already acknowledge, but that this does not mean that mere intentional stipulation suffices for modelling. This seems the correct conclusion, although it might have been convenient to qualify the reply further. For instance, we can distinguish between, on the one hand, the representational function of the (taken as) simple parts of a model that are aimed at standing-for parts of the target and, on the other hand, the representational function of the model as a whole to inform us about an (alleged) complex state of affairs. Then we could accept that stipulation works only for models-parts and that for the model as a whole to represent an intended target more than mere intention is needed. To use Cohen and Callender’s example, a saltshaker (taken as a simple entity) may stipulatively represent (in the sense of standing-for) Madagascar, but it is far from clear that it can represent, even wrongly, the battle of Trafalgar as a complex state of affairs. If one insists that it is still a representation, even though extremely inadequate, one should at least distinguish the failure of the (simple) saltshaker in representing the (complex) battle of Trafalgar, from say, the failure of Ptolemy’s (complex) model in representing the (complex) state of affairs of the motion of planets; terminological preferences aside, it seems uncontroversial that these are different kind of failures.

Chapters 3 and 4 present the main similarity and structuralist accounts on offer in the literature, and assess the ability of these accounts to solve the problems introduced in Chapter 1. Frigg and Nguyen’s exhaustive analysis distinguishes several versions of the accounts in both similarity and structuralist families, starting with the simplest that are read as claiming that the existence of either similarity or a relevant structural morphism suffices for the existence of a representation. These versions are obvious non-starters for several reasons already discussed in the literature and summarized by Frigg and Nguyen, the main one being their inability to account for misrepresentations. Frigg and Nguyen discuss possible modifications and conclude that the problem may be fixed in amended versions in which what is required for (a correct or incorrect) representation is not the existence of the appropriate relation between model and target, but the formulation by an agent of a theoretical hypothesis to the effect that there is such a relation. Frigg and Nguyen conclude that, thus interpreted, this would be a Pyrrhic victory, for what now does the heavy lifting is not similarity or structural morphism, but the agent’s formulation of a hypothesis. This reinforces the idea, suggested above, that similarity and structuralist accounts are better understood as answers to the problem of correctness, not to the problem of existence.

Chapter 5 assesses inferentialist accounts, according to which X represents T if X’s representational force points from X to T and if X allows competent and informed agents to draw inferences about T. This makes room for misrepresentations, for inferences drawn about T can be wrong. Yet, this deflationary version does not explicate the notion of representation but merely restates some platitudes about it. This is not a problem for deflationists, but it is a problem for those who, like Frigg and Nguyen, believe that an analysis must provide a substantive elucidation. This is why the different non-deflationary inferentialisms add substantive conditions specifying that the transfer of information is due to the way that the agent connects the components of the model with components of the target. Frigg and Nguyen consider this a promising family of approaches, but note that they have difficulties accounting for representations without targets and for alleged cases of representations in which no valid inference from X to T is sound.

Chapters 6 and 7 focus on fictionalism and representation-as accounts, respectively. In the last decade, a large literature on models and fiction has emerged. The most prominent idea in this literature is that modelling is akin to a game of make-believe in which the model is like a prop used by the agent to help the audience imagine things being a certain way. According to its proponents, this approach is able to tackle some of the problems of representation, including the nature of carriers, the intended falsehood of (parts of) some models, and representations without targets. There are a variety of fictionalist accounts, including some by Frigg and Nguyen themselves, and in this chapter they summarize and defend fictionalism against several criticisms. The conclusion is that a correct formulation of fictionalism is immune to such criticisms. The main problem with fictionalist accounts is not their incorrectness but their incompleteness, and Frigg and Nguyen’s recent DEKI (denotation, exemplification, keying-up, and imputation) account is designed to provide the required completion. According to Frigg and Nguyen, part of what is needed for this is related to representation-as accounts and their distinction between ‘representation of Z’ and ‘representation as Z’, which allows representation X to impute to target T some Z-features. There is a question, however, whether this account, which originally derived from an analysis of caricatures, helps in scientific cases. It is true that, for example, the triple helix model represents DNA as formed by three helicoidal structures, but this simply means that representations often attribute to the target additional features, that is, features that are imputed in addition to those used in the pre-modelling individuation of the target, and it is not totally clear why the representation-as account is needed to explicate this attribution.

In the last two chapters, Frigg and Nguyen present and defend their DEKI account, introducing it with a detailed analysis of their favourite example, the Phillips–Newlyn hydraulic machine that models an economy. I cannot enter into the details of the account here but the idea is, roughly, that X represents T when X denotes T (and possibly parts of X denote parts of T); X represents T as Z, exemplifying properties P₁,…, P_n;  X comes with a key, K, specifying how P₁,…, P_n are translated into a set of features Q₁,…, Q_m; and finally the model imputes at least one of properties Q₁,…, Q_m to T. Frigg and Nguyen argue that DEKI gives satisfactory answers to the all problems introduced in Chapter 1 and that, overall, it fares better than its rivals.

DEKI is no doubt a promising account, but it also gives rise to some concerns. It does not distinguish between model-as-a-whole denotation and model-component denotation as being of an essentially different kind. It allows for a large-scale non-imputation of features because it suffices that only one be imputed. It does not require any logical congruency between model and target for the existence of a representation (which implies, for example, that a red dot may—incorrectly—represent the structure of DNA). It does not explicitly ground the correctness, where it occurs, of surrogative reasoning in (structural) resemblance between model and target, as it intuitively seems it should. These and other features are controversial, although Frigg and Nguyen probably think that they are more virtuous than problematic. In any event, Frigg and Nguyen’s own proposal in the last chapters makes this book not only the most complete analysis of the ongoing debate on scientific representation, but also a substantive and promising new contribution to it.

José Díez
University of Barcelona
jose.diez@ub.edu

References

Callender, C. and Cohen, J. [2006]: ‘There Is No Special Problem about Scientific Representation’, Theoria, 55, pp. 67–85.