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}

The rule in the knowledge machine

Michael Strevens, The Knowledge Machine: How Irrationality Created Modern Science, Liveright, New York, 2020, 350 pp. hard-back, 30$

The Knowledge machine is a book about the Iron rule of explanation (IRE). According to Michael Strevens, science has worked because scientific communities have strictly played by this rule ever since Newton. In the author’s own words, this is:

The rule demanding that all scientific arguments be settled by empirical testing, along with the elaborations that give the demand its distinctive content: a definition of empirical testing in terms of shallow causal explanation, a definition of official scientific argument as opposed to informal or private reasoning, and the exclusion of all subjective considerations and nonempirical considerations (philosophical, religious, aesthetic) from official scientific argument. [293]

With the IRE Strevens wants to settle the Great Method debate, initiated by methodists like Popper and Kuhn and then dominated by radical subjectivism (now prevalent among historians and sociologists of science). According to Strevens, the former focused on the wrong rule, be it falsificationism or the organization of scientific paradigms. The latter deny that there is any correct rule,  scientific outcomes are just like any social agreement, a matter of taste, interests, power etc. Strevens accepts the role of all these factors in the dynamics of science, but condensed into plausibility rankings, “a scientist’s level of confidence that a hypothesis or other assumption is true” [293]. But subjectivity is then constrained by the IRE: the game of science is about scientists organizing empirical tournaments in which a winner emerges, independently of the conflicting interests or values of the participants. According to Strevens, the accumulation of evidence, in the long run, brings about consensus on the true theory, the one that explains all relevant observations.

The gist of the iron rule is to minimize scientific debate about things scientists may not easily agree on and motivate scientists to “squeeze every last drop of predictive power” from a scientific paradigm. For Strevens, playing by the IRE and only the IRE is irrational: the IRE “imposes a wholesale prohibition on all forms of nonempirical thinking, no matter their track record, no matter how well they synergize with empirical observations” [237]. A chapter on the fruitfulness of beauty as a guiding principle of science exemplifies this point. But the alternative (using some other guiding principles in addition to the IRE) is worse: scientists may never reach an agreement.

Strevens discusses the Thirty Years’ War to illustrate how making religion a private matter is the best strategy to avoid civil unrest, and modern science would have its foundation in this separation. The recipe is still valid today: Keep empirical tests separate from any other consideration and let these tests proceed until a consensus is reached, keepscience working like a well-oiled automaton (a knowledge machine), do not meddle with the IRE.

Although Strevens is famous for his dense prose and subtle conceptual analyses, The Knowledge Machine was conceived as a popular philosophy book, an a quite successful one at that –already with reviews in major international newspapers and magazines such The New Yorker. A reason for this lies in the long collection of snapshots in the History of science that illustrate the concepts presented above and make for a fun reading. Radical –and a few moderate- subjectivists will probably challenge the details of these abridged case studies, but this is a scholarly debate, for which Strevens will probably be ready –although the footnotes and references are rather sketchy so that it is often difficult to determine the depth of his knowledge of each particular case.

What was less clear to me though was the message this book is sending to the public. As Strevens acknowledges in the first half of the book, his predecessors in the Great Method Debate were all conveying an image of scientists that became hugely influential among the educated Westerners: the Popperian dissenter, the Kuhnian Cold warrior, the Latourian black-boxer. These images made plain sense against the background of the political dilemmas of their time, partly reconstructed by Strevens for his readers. However, about our own dilemmas, Strevens remains mostly silent and his final advice sounds almost like an oracle: “Do not tamper with the workings of the knowledge machine. Set its agenda, and then step back: let it run its course” [285]. Strevens does not explicitly says  who is meddling with the IRE and who would oppose it after grasping Streven’s consequentialist argument. Perhaps a few ongoing agendas in philosophy of science (and on Science and Technology Studies) could be seen as targeting the IRE. Feminist standpoint theories, for instance, defend a reassessment of what counts as evidence to illuminate potential sexist biases. Similarly, advocates for the embedment of philosophers in scientific laboratories claim that conceptual analyses can have a real impact on the advancement of science. Would any of these approaches count as threats to the IRE?

Perhaps  more serious meddlers  are the many forms of populism proliferating around the world. After all, the IRE has a technocratic taste: once their goals are set by democratic parliaments, science, like hospitals, courts, or central banks, work better as independent institutions where experts make relevant decisions according to their own rules. Challenging the autonomy of science in the name of “subjective or nonempirical considerations” would be a typical populist move. For instance, I would count as populist the call to accommodate  patients’ preferences in the design of clinical trial at the expenses of traditional debiasing methods (such as blinding). But I cannot tell whether this is the sort of challenge with which  Strevens is concerned because almost of all of the examples discussed in the book are success stories from the natural sciences before 1950.

It is always nice to be reminded of how well some scientific disciplines have worked in the past and, at least to me, the IRE seems a plausible account for this success. But I am not sure about the effectiveness of such a reminder in persuading contemporary audiences about the benefits of the autonomy of science. My first concern is that such reminders have been tried before with not much success. Reading The Knowledge Machine, I could not but think of Max Weber’s arguments about the scientific vocation. Like Strevens, Weber was inspired by how the Protestant reformation and brought about a world in which the private faith of individual agents had unintended beneficial consequences for everyone (i.e., economic growth), provided that the Church and the State were kept apart. Like Strevens, Weber praised scientific specialization and called for leaving aside all value judgments so as to prioritize consequentialist considerations. And yet the Great Method debate started because, after World War II, only Merton was persuaded that a general code of conduct was enough to account for the success of science. WillStrevens’ arguments be more persuasive today?

I agree that having clearly articulated (iron) rules will  increase the public trust in any institution. Nonetheless, my second concern is that the problem we are now facing is the increasing mistrust regarding the enforcement of any such rule. Think again of randomized clinical trials in medicine: despite the conflicting interests at stake, the systematic implementation of the IRE allows the truth about whether medical treatments work to emerge with the accumulation of evidence (thanks, e.g., to the Cochrane collaboration). And yet more and more patients are persuaded that the whole testing system is bankrupt because some particular trials are rigged by their corporate sponsors. A Weberian reminder that scientists have successfully played by the IRE in the past to everyone’s satisfaction and that we should keep their effort going will do little, in my view, to appease an audience sceptical about whether the IRE is being enforced today

But maybe I am overinterpreting Strevens’ argument. After all, defending science from the meddlers is just the topic of 7 pages out of 300. Perhaps this is just a public reminder that science works for a very simple reason that the examples in the book easily convey. It is an entertaining read and it will help to comfort any Weberian soul struggling to keep alive her faith in science in our increasingly challenging world. At least, it has helped me. 

{August, 2021}

{Metascience}

 

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Adolfo García de la Sienra.  A Structuralist Theory of Economics. London/New York: Routledge (INEM Advances in Economic Methodology), 2019. XII+222 pp.  

Adolfo García de la Sienra is one of the most prominent philosophers of economics in the Spanish-speaking world. He has held a meeting of the International Network for Economic Method in Xalapa and actively participates in the Sociedad Iberoamericana de Metodología Económica. Thanks to García de la Sienra, the structuralist approach to economics is now mature, with a full-fledged analysis of some of the most significant varieties of economic theorizing in the 20th century. This analysis is now thoroughly presented in A Structuralist Theory of Economics, where we also find García de la Sienra’s own take on the structuralist programme, connecting it with its Suppesian roots.

 

The first half of the book is an introduction to the pillars of the structuralist approach. In Chapter 1 we find the Suppes informal structural view, articulated on set-theoretical predicates and data structures, in which the key epistemic notion is the observational adequation between the two. Chapter 2 presents the concept of structure, drawing on the seminal work of Sneed and his school, on the one hand, and Da Costa and Chuaqui, on the other. Structures are informally defined as “a list of sets together with relations built over such sets” (p. 30). García de la Sienra then formalizes this intuition using types, to classify power sets, and a modified version of the Ackermann-Müller theory of classes. He is then ready to define set-theoretical predicates rich enough to capture the complexity of actual scientific theories. This is illustrated, in Chapter 3, with an analysis of classical particle mechanics, followed by a short but effective introduction to the key elements in the Sneedian structuralist view of theories (theory core, theory element, and theory nets).

 

García de la Sienra closes the first half of the book with two additional chapters on idealization and concretization (ch. 4) and measurement (ch. 5). In the former, García de la Sienra answers some regular objections against the ability of the structuralist view to grasp empirical phenomena. For García de la Sienra, scientific theories reach this grasp through the interplay of four items: there are, on the one hand, set-theoretical structures (intended applications, models of data) representing reality, but there are also, on the other hand, model systems (conjunctions of predicates expressing idealizations, in the sense of Mäki and Portides) and the real concrete systems that the former represent. This same dialectic between set-theoretical structures and its empirical targets reappears in chapter 5 with the distinction between metrization and measurement. For García de la Sienra, metrization occurs when an empirical property is proven mensurable, according to a given unit of measurement. The representational theory of measurement establishes the set-theoretical conditions under which such property is metrizable, independently of how it is actually measured.

 

This fifth chapter starts the transition from general philosophy of science to the philosophy of economics. In order to illustrate how metrization is achieved independently of the representational theory of measurement, García de la Sienra briefly discusses two classical 20th century controversies: the measurement of demand functions and the measurement theory debate. Chapter 6 establishes the target of any economic theory, the general concept of an economy, a structure covering four basic activities: production, distribution, exchange and consumption.

 

Chapter 7 covers preferences and utility where we find one of the author’s main conceptual achievements. For a structuralist, a preference relation may be idealized, but it is nonetheless empirical, and its content should be represented by a (theoretical) utility function. The problem is that in standard microeconomic theory, utility functions are continuously differentiable, a pre-requirement for the topological analysis of economic equilibrium. But what would be the empirical counterpart of differentiability in a preference relation? García de la Sienra suggests that differentiability captures a way in which the agent’s tastes are stable in the vicinity of any consumption menu. Capturing this apparently simple intuition requires a long mathematical digression showing the correspondence between algebraic and geometric difference structures, and then between the latter and preference structures. Against instrumentalist or positivist interpretations of utility theory, where its mathematical apparatus would not require any empirical justification provided it delivered empirically successful predictions, García de la Sienra vindicates a realist account in which every empirically meaningful element of a preference relation would be represented by the corresponding utility function.

 

No less original is the analysis of game theory in chapter 8. Focusing on dynamic games, García de la Sienra provides an axiomatic formulation from which the theory-element of neoclassical economics will emerge as a specialization. Its empirical content is captured as follows. On the one hand, García de la Sienra shows that behavioural strategies “determine a probability measure over the space of all possible histories of the game”, making some trajectories more probable than others -those that maximize the expected utility of the agent.  The empirical behaviour of economic agents generates a histogram over the same space. According to the author, the fundamental law of game theory states that such empirical distribution must approximate the probability measure -i.e., agents behave strategically and the empirical distribution approximates an equilibrium of the game.

 

In chapter 9 García de la Sienra solves the main conceptual problems that have ravaged the labor theory of value. He provides a general definition of abstract labor and a representational measurement of the same. He then shows that a uniform profit induces abstract labor, and finally he proves that a given determination of abstract labor induces a system of prices which is unique up to similarity transformations. In chapter 10, the author recasts classical economics fusing the labor theory of value with “neoclassical” economics, proving the existence of an equilibrium in which the prices are induced by labor value, they clear the markets, and all the agents maximize utility.

 

In chapter 11, he reconstructs, in the same vein, with Sraffa’s Production of Commodities by Means of Commodities. And to close the book, and his sweeping survey of economics, García de la Sienra tackles econometrics building up on Aris Spanos’ analysis of the connection between probability theory and data generation processes via model specification. And then the book ends up abruptly, without a conclusions chapter.  

 

As the reader may have already guessed, this is quite an impressive monograph for many different reasons. First, breadth and scope: A structuralist theory of economics is both a primer in some central themes in philosophy of science plus a broad introduction to economic theories, covering on equal grounds neoclassical and Marxist approaches. Although this is an exercise in formal philosophy of science, García de la Sienra makes the philosophical message clear at every step and, as conveyed -I hope- in the summary above, there are plenty of insightful intuitions. There are also some perplexities, let me just comment on a salient one.

 

Like many others, I have the impression that structuralist approach is perhaps too powerful, since it can reconstruct formally almost every articulated doctrine with a minimal amount of empirical content. Treating neoclassical and Marxist approaches on equal grounds shows, in my view, this sheer excess of power. Most practitioners and methodologists of economics would see these two approaches in open contradiction: García de la Sienra shows, with his reconstruction, that this is clearly not the case. Except that his reconstruction becomes something more than meta-theory: García del Sienra is actively picking up those threads in economics that will fit better with the structuralist template. This may be a legitimate strategy. After all, Suppes and his school tried to capture the distinguishing traits of the most successful scientific theories. If economics wants to achieve the same success, we should better focus on the structures it shares with other scientific disciplines.

 

Here comes the second perplexity: García de la Sienra’s analysis stops every time at the same point: the identification of the empirical claim of the theories reconstructed. He says very little about the truth of these empirical claims, despite decades of debate on whether economics succeeds at grasping the truth about the phenomena under analysis. But the reason for this, as he told me personally, is that whether a theory is successful in some applications is an entirely empirical matter. I hope the discussion of this empirical matter will provide a good enough reason for García de la Sienra to keep writing on economics.

{April, 2020}

{Theoria}