Completing the landscape on models and scientific representation 

Roman Frigg: Models and theories: a philosophical inquiry. London:Routledge, 2022, 495 pp, 

Open access at: https://www.taylorfrancis.com/books/9781844654918

“What are theories? What are models? And how do models and theories relate to each other? These are the core questions that this book is concerned with” (1). These expansive questions predictably give rise to a monumental 500-page monograph that Roman Frigg presents as, at once, an introduction, a literature review, and a critical assessment (1). On all these tasks, the book works very well. Unlike standard textbooks, Frigg does not indulge in didactic simplification: he smoothly walks the reader from the elementary concepts to the upper echelons of the question under analysis.  Having been an active participant or direct witness of two decades of debates on the title topics, Frigg’s scholarship and insight are often extraordinary. And so is the organization of the material presented. In a time where books are often collected papers in disguise, here discussions are systematically developed through the book’s four parts until each of the running threads is exhausted. Yet, the number of cross-references and signposts makes it almost impossible for the reader to get lost.

Reviewing this book requires hard choices. I will mainly focus on the first two parts in which Frigg presents his original view of the old masters’ views in our discipline, from Carnap to Suppe, hoping it will be less known to the average reader than the content of parts three and four. In them, Frigg discusses the last forty years of work on models and scientific representation, completing the landscape that he had already presented in his previous volumes. 

The first part of the book introduces the Linguistic View of Theories: “a scientific theory is a description of its subject matter in a formal language” (5). Frigg’s first move is to separate the Linguistic from the traditional Received View (RV) to make his initial claim: the latter may have fallen, but the former lives on.  Both are based on three principles, and the first two are reasonably similar between the two views: 1) “The language in which the theory is formulated has a logical structure that allows scientists to derive propositions from other propositions and to formulate proofs of theorems,” and 2) “A theory contains general principles, or axioms, which are the theory’s laws” (18). The difference lies in the third principle: 3) whereas for the linguistic view, in the language of the theory there are pre-theoretical terms and technical terms that arise within the theory, in the Received View, the terms are either logical or extra-logical and the latter are further divided into theoretical and observational.

Frigg rehearses, in Chapter 1, some standard objections against the RV, showing that most of them are based “either on misattributions, misunderstandings, or on hasty conclusions” (25). The real problems for the linguistic view appear in the following three chapters, and they are addressed in an equally constructive way. In Chapter 2, Frigg presents the role of models in the RV as alternative interpretations of a theory’s formalism, i.e., as logical models without any representational role. A consequence of the denial that models play a representation role is that according to RV a theory is connected to the world only by the observation terms and correspondence rules. A persistent strand of argumentation is that the limiting results in first-order logic, notably Gödel’s first incompleteness theorem and the Löwenheim-Skolem theorem, show such an analysis to be untenable. But, Frigg observes, these arguments are not conclusive, and they would only be a problem if the RV was inextricably tied to first-order logic, a claim for which he finds no evidence.

The challenge discussed in Chapter 3 is whether the distinction between theoretical and observation terms is tenable, to what extent observations are theory-laden, and how the relation between observation and data should be understood. Frigg concludes that the distinction between observation terms and theoretical terms should be given up and replaced by a dichotomy between antecedently understood and new terms, where the latter might be analysed in terms of Balzer, Moulines and Sneed’s notion of the T-theoreticity. This leaves the question of how data models fit into a linguistic view of theories. According to Frigg, the linguistic view is not reductive in this regard: scientific data should not be reduced to sentences to understand their epistemic input on a theory, data models can also do the job. 

Chapter 4 is about the semantics of theoretical terms, and how to define them. Although the review of the alternatives under discussion is significantly longer than in any other chapter—starting with verificationism ending with the causal theory of reference—Frigg takes no sides here. “This is still an active field of research” (140) is the chapter’s bottom line. Probably he does not need to take sides: of the three principles defining the RV, he just needs the first two, pertaining to the logical structure of theories and the presence of axioms, to assert the viability of the Linguistic View.  

The next step is to show the compatibility of the Linguistic View with the Model-Theoretical View (MTV), in which a scientific theory is mainly a family of models. Frigg had already warned his readers, in the first part of the book, that his “liberal” version of the RV is “in fact indistinguishable from a liberal” MTV: for both, the analysis of theories should be formal; in the liberal RV a theory would be “a language with a family of models”; in the liberal MTV a theory would be a family of models with a language. Here is another foundational claim of the book: “The consensus then is that any reasonable analysis of a theory must be a dual view” (167). 

The second part shows how far this consensus goes. Chapters 5 to 7 deal with the mainstream version of the MTV, in which models are mathematical structures.  Chapter 5 presents Suppe’s foundational ideas, lists the main developments of this view, and considers how the MTV solves the problems discussed in Part 1. New problems, of course, appear—-e.g., do models constitute or represent a theory? Crucially, Frigg presents here his case for having language as a key ingredient of the MTV. 

In Chapter 6, he hammers this point in a thorough discussion of the representational role of models in the MTV, in which Frigg draws on his previous work on scientific representation to map the territory with several adequacy conditions and reference problems. Two contending approaches are considered: the Data Matching Account and the Morphism Account. In the former, “a model M is a scientific representation of target T iff a measurement performed on T yields data model D and D is isomorphic to M’s empirical substructure” (212).  Siding with Bogen and Woodward, Frigg quickly discards it, arguing that the theories represent phenomena, not data models. In the Morphism account, “M is a scientific representation of T iff M is isomorphic to T” (201). The first problem here is in specifying in what sense the objects in the target system are a structure isomorphic to a set-theoretic M. And then Frigg proceeds to show in detail how morphism accounts are ill-equipped to deal with some desiderata that any view of scientific representation should meet. 

Chapter 7 explores the links between models belonging to the same theory in the light of the Munich structuralist school, Balzer, Moulines, and Sneed. The distinctions introduced in this account to deal with the different models within a theory successfully illuminate problems like theory-ladeness. But the Munich school does not have a solution for the problems so far detected in other structuralist accounts.
Chapter 8 completes this second part examining Giere’s and Suppe’s non-structuralist accounts of the MTV. Although the key ingredients are now models conceived as abstract entities representing the world through similarities, these accounts equally fail to meet Frigg’s desiderata for scientific representation, for the same underlying reason: language also plays an essential, but unexamined role in these alternative versions of the MTV.  

We are now halfway through the book. The lesson that emerges clearly from the discussion is that “purist” versions of either the linguistic or the model theoretical view are untenable. As Frigg puts it in the Envoi: “Any tenable account will have to see theories as consisting of both linguistic and non-linguistic elements” (490). This means that a defensible analysis of theories must be a dual view. Frigg’s discussion at this point remains programmatic. He sketches the main outlines of a dual view, but he leaves the task of working out the details of such a view to future research.  

In the third and the fourth part, we are treated to an in-depth exploration of twenty-five more years of controversies on scientific representation. Unlike the previous two parts, there will be no unifying threads like the RV or the MTV: the focus is now on models in scientific practice, without any overarching program of rational reconstruction. 

Each chapter in Part 3 deals with open questions about how models represent. In Chapter 9, we find several contenders for the very notion of scientific representation: namely, direct representation, inferentialism, and representation-as approaches. The next three chapters present critical discussions of specific kinds of representation via models: analogy in Chapter 10, abstraction and approximation in Chapter 11, and idealisation in Chapter 12. Whereas Chapter 9 closes with an overview of Frigg’s own DEKI account (where the acronym stands for denotation, exemplification, keying up, and imputation), on which he has extensively published elsewhere, the other chapters in this third part are critical assessments of the state of the art in the respective subject areas.

In Part 4, the author really struggles not to be carried away by casuistry and find philosophical threads connecting an immense and disperse literature. The opening thirteenth chapter engages in a mostly case-based debate on the autonomy of models from theories. Frigg provides a reasonably representative sample of how this autonomy has been analysed in the models in scientific practice literature. We also find a very nice overview of the debate between some leading authors in this approach and their counterparts in the MTV on whether the latter’s account of models captures the diversity of scientific practice—Frigg doubts it. The three final chapters are also opinionated. In Chapter 14, discussing the ontology of models, Frigg sets some desiderata and defends his own Waltonian fictional account, in line with DEKI. Chapter 15 deals with some philosophical dilemmas arising from the proliferation of models, exploring, for example, how robustness analysis exploits it for good or how perspectivism makes sense of the variety. These are ongoing debates, and the challenges Frigg proposes for the latter view are, in my view, worth considering. The last chapter, Chapter 16, contains an original classification of model types that I will just quote, for the sake of brevity: “1) Model types pertaining to model-target relations; 2) Model types pertaining to carriers; 3) Model types pertaining to the process of model construction and to models’ relation to theory; 4) Model types pertaining to the uses and functions of models in the scientific process” (467–468).  

What is the moral that the reader should draw from this second half of the book? In the final “Envoi”, Frigg is at once short and ambitious: “The next step in a discussion of representation will be to get to a better understanding of particular representation relations and the styles to which they belong, as well as to integrate an account of how models represent into a broader understanding of the structure of theories” (490). In other words, merge the main threads of this book into a unified view. Frigg has masterfully laid out the foundations of this project for any newcomer in the discipline, like Suppe did with his own volume in the 1970s. We can only hope it will orient future debates with similar success.

{January, 2024} {Metascience}