Mauricio Suárez’s inferential conception is one of the leading philosophical accounts of representation in science. His recent monograph Inference and Representation demonstrates the inferential conception’s coherence and applicability to a range of topics within and beyond the philosophy of science. As such, the book should serve as an essential reference for scholars of scientific representation, illuminating both Suárez’s decades-long contributions and the state of the field.

The inferential conception emphasizes models’ role as surrogates for reasoning about phenomena. Suárez characterizes this capacity for surrogative reasoning so as to accommodate the diversity of representational resources in science while avoiding a “reductive metaphysical analysis” of the relation between representational vehicles and their targets. Inference and Representation succeeds in meeting these aims, although Suárez’s minimalist strategy may leave some readers unsatisfied.

The book consists of three parts: a historical and philosophical introduction to the “modeling attitude,” a theoretical exposition of this attitude’s core features, and an extension of this account to art and the epistemology of science. As the preface notes, the first and last parts comprise the book’s most novel contributions. They provide a valuable backward- and forward-looking context to the theoretical core, imbuing Suárez’s view with greater comprehensiveness and cohesion than his earlier work.

The book’s centerpiece is Suárez’s refinement of a position he has been developing since the early 2000s. At its core stand two conditions for one thing A (a source, in Suárez’s parlance) to be a scientific representation of something else B (its target). First, the source must have representational force, by which “consideration of A leads an informed and competent inquirer to consider B” (118). Second, the source must have the capacity to license inferences about its target that are “specific,” meaning they go beyond the simple claim that A represents B. Together, these “provide the set of necessary conditions for any object, system, artifact, conceptual schema, mathematical entity, or item of any sort to represent any other such item” (160).

Suárez’s “minimalism” or “deflationism” consists of his claims that (i) these conditions exhaust what can be said regarding what it means for A to represent B as a general matter, and (ii) no general explanation can be provided regarding what it is that enables A to represent B—for example, what substantive relation must obtain between A and B for the one to be informative of the other. The argument for deflationism primarily consists of showing that attempts to reduce representation to a specific relation, such as isomorphism or similarity, fail to capture important features of representation, including its asymmetry, nonreflexivity, and nontransitivity and its embodiment in diverse forms, each bringing a potential for inaccuracies, mischaracterizations, or idealizations. Suárez argues that this diversity is better captured by adopting his minimal analysis of scientific representation, while holding that any actual instance of representation will employ some specific means for evaluating source–target fit tailored to the particularities of that case. Similarities or morphisms are best viewed as candidate means, among other relations that may be employed in specific contexts of inquiry.

The earlier and later sections of the book provide additional justification and elaboration of the view. Chapter 2’s discussion of Maxwell, Hertz, and Boltzmann is especially notable, highlighting how 19th-century philosophy of science contains untapped resources that anticipate aspects of Suárez’s philosophy of modeling. Chapter 8’s detour into the philosophy of art is similarly illuminating. There, Suárez identifies a basic yet neglected feature of the modeling experience: Treating something as a model requires a simultaneous awareness of the “surface” features of a model and those features of the target it represents insofar as they are “seen in” the features of the model. Suárez shows how phenomenological theories of the “twofold-ness” of artistic representation clarify this dimension of model-based reasoning.

Overall, Suárez’s most interesting contribution may be his pairing of particularism about representational means with deflationism about the concept of representation. This grants other accounts of representation their due while undermining their claims to generality or metaphysical substantiality beyond specific use cases. As he states, “The bulk of this book is in essence a sustained attempt to argue for pluralism regarding the means of representation and minimalism regarding its constituent” (8). It largely succeeds; his schematic criteria for being a representation render the account extremely pliable in the face of diverse inferential. But some readers may find this argumentative strategy to sit uneasily with the underlying objective of the book. According to Suárez, “The aim of any account of scientific representation is to understand modeling practice” (4). The inferential conception is claimed to be the best framework for this task, yet the account’s intended minimalism translates to an equally minimal account of modeling practice. This is seen in chapter 3, which is framed as an inductive argument from three cases to show that models are constructed with the aim of using them representationally, that is, to inform users about some target. It’s an uncontroversial conclusion, but surely there are further general features of modeling practice to be drawn from the rich number of details that Suárez presents with each case! Philosophical and science, technology, and society (STS)-based studies of modeling since the 1980s have sought to characterize the recurring features of modeling practice, spawning an ever-growing menagerie of related topics: abstraction, idealization, de-idealization, analogy, partiality, complementarity, robustness analysis, asymptotic reasoning, model assessment, calibration, confirmation, and adequacy, just to name a few. Suárez has been a noteworthy contributor to this subfield. His book is littered with insights on modeling techniques, and it provides an excellent guide to elucidating how models are used on a case-by-case basis. And yet, he offers few conclusions that might inform a generalized account of modeling practice of the kind proposed in, say, Weisberg’s (Reference Weisberg2013) Simulation and Similarity.

I suspect this suits Suárez just fine, as he harbors healthy skepticism toward highly abstract theorizing about scientific representations. But this complicates judgments of the work’s success in achieving its professed goal of understanding modeling practice. What, exactly, is modeling practice, and what makes one philosophical work more adequate to it than others? It has become a shibboleth among philosophers of science of a broadly antimetaphysical stripe to claim that we are basing our views on scientific practice, rather than the detached apriorism of the bad old days. Bueno and French’s (2018) Applying Mathematics, which presents an opposing account of representation, is similarly framed as faithful to scientific practice. What does it mean to say Inference and Representation is more faithful? As long as the operative notion of “practice” remains relatively undertheorized or based on a small handful of cases, its capacity to adjudicate between competing accounts remains unclear. Furthermore, one might worry that some of the principal disputants are now talking past each other. Suárez does not engage very extensively with amended versions of the views he targeted in his 2003 critique; Bueno and French do not cite Suárez’s work after 2009.

This issue is further complicated by the fact that appeals to practice undergird important parts of Suárez’s view of representation. Take representational force, the first necessary condition for representation. That some source points to some target is “determined in part by correct intended uses … maintained by socially enforced conventions and practices” (119). Similarly for Suárez’s second condition: How can model users infer specific claims about a target phenomenon from some models but not others? Such informative uses of models are ultimately explained by features of practice: “Mapping between claims [about model and target] is the product of the inference rules licensed within the modeling practice.… The propriety of the mapping depends on the inference rules that are operative within the practice. No further assessment is available independently or from anywhere beyond that practice” (151). Thus, he states, “There are objective matters of fact about both inferential capacities and representational force. It just so happens that these are objective matters of fact regarding the features of a practice rather than any self-standing relation between objects” (171).

This perspective is compelling, but it raises a foundational concern. Insofar as these features of practice remain unspecified and undertheorized at a general level, it is unclear how they secure the informative use of representations. Which features of practice should we look for to understand how a model informs its users? Does this vary from one practice to the next? What about these features renders certain inferential uses of models authoritative, rather than others? And if there is no assessing the propriety of these inference rules outside of a given modeling practice, then what does it mean to say there are objective matters of fact about this practice that establish the model’s informativeness? If the justification for these uses bottoms out in a scientific community’s say-so, undergirded by no further standard, then its norms might be little more than arbitrary conventions. An account of scientific representation along these lines would arguably fail, in the final analysis, to account for what makes these representations scientific. To avoid this conventionalism, we should resist conflating representational modeling with the “world-involving” activities underlying scientific experimentation (as Suárez sometimes appears to do in his final chapter). On the contrary, we ought to get a better understanding of how these two realms of activity interact. We might start by asking: How do scientists arrive at a target for modeling? Philosophers working on scientific representation have tended to pay far more attention to one side of the model–target relation than the other, but both are equally essential for understanding how model-based representation works.

That these remain open areas of inquiry does not imply that Suárez simply ignores them out of hand. In fact, his book lays the groundwork for exploring the interactions between modeling and other empirical practices more deeply. A novel theme in this work concerns the dynamics of model construction that arise at the “fork” where practices establishing the representational force of a model meet with those that explore its inferential capabilities. Interactions between these practices result in mutual adjustments: Novel inferences shift scientists’ conceptions of what models “point to”; redescription of targets or changes in models’ intended uses license different inferences. Thus, the “model source can affect how we see and conceive of its target phenomenon … conversely too, as we explore … the features of the system modeled, we often come to see certain aspects of the model source in a different light” (216). These are tantalizing ideas. To be more fully realized, they call for the integration of the inferential conception with a more thoroughgoing account of “practice,” further analysis of the way experimentation and modeling interact, and perhaps some corresponding reinflation of what being a scientific representation entails.