‘Scientific representation’ is now a firmly established topic in the philosophy of science. It appears on undergraduate syllabi, it’s the topic of plenary sessions at international conferences, and it has its own dedicated page in the Stanford Encyclopedia of Philosophy. As Mauricio Suárez documents in his new book Inference and Representation: A Study in Modeling Science, we can trace its roots at least as far back as the philosophical-methodological reflections of nineteenth-century physicists, and in the modern philosophical literature it is a topic deeply entwined with debates on the structure of scientific theories. Yet it is only in the last twenty or so years that it has emerged as a self-standing research topic in its own right.

Central to the current debate are ideas originally developed in (Suárez [2003], [2004]). The former provides a salvo of arguments against the idea that the representational relationship that holds between scientific models and their targets reduces to similarity or isomorphism. The latter develops an ‘inferential conception’, according to which, and in a deflationary spirit, we can’t say much about scientific representation (at least from an analytic perspective), other than that it involves the pair of individually necessary conditions. The first of these conditions is that the ‘representational force’ of the model ‘points’ towards the target and the second is that the model allows competent and well-informed agents to draw specific inferences about the target.

In Inference and Representation: A Study in Modeling Science, Suárez develops a book-length treatment of this inferential conception and why we should prefer it to some of its more substantive competitors. What results is a discussion that situates the conception in the aforementioned historical context; enriches our understanding of the conception itself; and explores how it relates to and informs adjacent issues such as the structure of scientific theories, the nature of pictorial representation, and scientific epistemology in general. In doing so, it serves to coherently tie together a career’s worth of work on the nature of scientific modelling and expand that project in several intriguing ways. This is no mean feat.

Here I present a broad overview of the book, along the way indicating what I take to be some of its highlights but also some open questions. The latter lead to a more critical discussion, suggesting a worry that cuts to the heart of the inferential conception. This worry deserves further scrutiny if we are to understand how future engagement with the inferential conception might proceed and, I hope, helps to illuminate the central idea that stands behind the book.

Inference and Representation has a neat logical structure, consisting of three parts that build on one another. After an introductory chapter that sets out the book’s roadmap and introduces some terminology, we arrive at part 1, consisting of two chapters. In the first, we find a genealogy of what Suárez calls the ‘modeling attitude’, which is traced to two scientific traditions emerging in the nineteenth century: the English-speaking school exemplified by Maxwell and Kelvin, and then the German-speaking school exemplified by Hertz and Boltzmann. In the former, Suárez identifies the idea of ‘analogies’ (broadly understood) acting as ‘conductors of reasoning’, supporting inferences from models towards their targets. In the latter, he explicates ideas from Helmholtz-inspired Bildtheorie, according to which Bilder are systems of signs with their own inferential structure, whose role is to track dynamic processes in nature and, in virtue of which, one can draw inferences from Bilder to their targets.

Both discussions are fascinating and inject a much-appreciated historical perspective into the contemporary discussion on scientific representation. Moreover, Suárez makes a convincing case for the centrality of the idea of model-to-target inference within both traditions. But a question (returned to below) remains as to whether the deflationary, or minimal, aspect of the inferential conception—the idea that its two conditions are all that can be said about scientific representation in general—find their origins in these historical schools. This question arises again towards the end of the second chapter in this part, which provides a useful discussion of several case studies that then act as tests for the accounts of scientific representation discussed later in the book. The discussions of these cases are of independent interest, and Suárez is surely correct to infer from the diversity of things we call scientific representations that we are unlikely to find a single concrete model–target relation in common to all model–target pairs. But he is a little quick to infer from this that the inferential conception is the only viable alternative.

This brings us to part 2, which forms the book’s analytic core. Here we are first introduced to a pair of distinctions that are key to the book’s overall dialectic. Suárez argues that when framing scientific modelling as representational, we may ask: what is the relation that constitutes the representational relationship, in common to all models and their targets? Alternatively, we may ask: for a given model–target pair, in a given context, what is the means by which an agent draws inferences from the model about the target in that context? Suárez calls the investigations into the first question the ‘analytic inquiry’, and into the second the ‘practical inquiry’. Engaging in the analytic inquiry (and drawing on an analogy with debates about the nature of truth), Suárez suggests that we can offer a substantive (typically reductionist) account of the constituent of representation, or we can offer a deflationary (typically primitivist) account. With this framework in place, Suárez goes on to explore and ultimately reject two substantive accounts, namely, views according to which models represent their targets in virtue of being similar or structurally related to them (positions he refers to as ‘sim’ and ‘iso’, respectively). In the second half of this part of the book, he develops his own deflationary inferential conception, stated above, initially via a discussion of the semantic view of theories, then through a comparison with (Hughes [1997]), before finally, in the last chapter in part 2, drawing everything together by arguing for the inferential conception itself. This is understood as the minimal, deflationary claim that both conditions stated above are necessary conditions on the constituent of scientific representation (and on cognitive representation more generally). And, moreover, this is all that can be said from an analytic perspective.

Readers of Suárez’s previous work on scientific modelling will find some of this familiar, but it should be emphasized that the discussion expands and refines both the critical discussions of sim and iso, and the inferential conception itself. One intriguing claim, which stands in stark contrast to the likes of Bueno and Colyvan ([2011]) is that even where the models in question are mathematical, structural mappings are rarely even the means through which scientists reason representationally. For those not so familiar with his work, this part of the book is a useful stand-alone presentation of Suárez’s view.

Part 3 acts to broaden the discussion in two different ways. First, as is now common in the literature, Suárez addresses the analogy between artistic, particularly pictorial, representations, on the one hand, and scientific representation, on the other. He provides an easily digestible overview of the aesthetics literature on pictorial representation, particularly discussions of why and how we might attempt to distinguish between representational and non-representational art. Again, we are cautioned against thinking about the former as depending on a substantive relationship of similarity (let alone a structural relationship; although see French [2003]). Then, he turns to ‘conventionalist’ and ‘phenomenological’ accounts. According to the former, associated with Goodman ([1976]), pictorial representation is akin to linguistic representation and so should be analysed in the same manner. According to the latter, associated with the likes of Wollheim ([1987]), it should rather be understood as distinctively involving a ‘seeing-in’, which Suárez describes as that which ‘allows the experience of the surface [of the painting] and the experience of the content of the painting simultaneously’ (p. 211). For example, when we view Velázquez’s Portrait of Pope Innocent X the experience is two-folded: we see the distribution of pigmented oil on canvas and we see the Pope at the very same time. Finally, in one of the most innovative discussions, Suárez suggests that, despite the obvious phenomenological differences between using a model and viewing a painting, the inferential conception’s ‘representational force’ condition can be seen as a generalized version of ‘seeing-in’. I am very sympathetic to this idea, and I think it captures something central to modelling practice: in certain contexts, modellers do ‘see’ (not typically visually) their targets ‘in’ their models. Modelling has a two-foldedness, and such a two-foldedness does seem analysable in the same spirit as Wollheim’s seeing-in. This discussion is one of the book’s real highlights and I hope it will be taken up in more detail.

In the final chapter of the book, Suárez turns to questions of scientific epistemology more generally. Here he attempts to demonstrate how adopting the inferential conception casts a variety of debates in the contemporary epistemology of science in new light. We are treated to insightful, albeit individually brief, discussions about how Hacking and Cartwright’s experimental realism and van Fraassen’s constructive empiricism avoid certain objections, and take on a new flavour when combined with a deflationary account of representation. Another intervention into a contemporary debate begins from the second condition of the inferential conception, which relies on ‘inferential rules’ governing what a scientist should infer about her target from her model’s behaviour, rules that are embedded in social and normative representational practices rather than relying on substantive ‘metaphysical’ model–target relations. This allows Suárez to argue that Fine’s metaphysically quietist natural ontological attitude, Kitcher’s real realism, and Longino’s emphasis on the role of social values in science can all be developed in novel and interesting ways once they are combined with a deflationary account of representation. The book is then rounded out with a discussion of how the inferential conception allows us to appreciate the distinction between scientific understanding (at least ‘minimal understanding’) and scientific explanation, where only the latter requires embedding the inference-generating model responsible for the explanation within a well-confirmed theory.

As is perhaps obvious from my summary, this chapter is a little whistle-stop. But this doesn’t undermine it. Suárez is right to point out that many debates in the epistemology of science proceed, often somewhat unreflectively, on the basis of certain assumptions about the nature of scientific representation. And once those assumptions are interrogated, and alternative accounts of representation offered, the tenor of, and pivot points in, those debates can change, sometimes substantially. One way of demonstrating this is precisely to canvas a variety of such debates and explicitly indicate how they may be suitably recast, which this chapter deftly does. Obviously this does not settle these debates once and for all, but philosophical progress often proceeds in this way.

Having said this, the final chapter, and indeed much of the rest of the book, rests on a dialectical strategy that I do not find fully satisfying. While I think Suárez is right to claim that abandoning either sim or iso can deliver new philosophical perspectives on familiar debates, I do not think that these new perspectives are gained only in so far as one adopts his inferential conception, particularly with respect to its specific deflationary flavour—namely, that the two conditions outlined above are necessary and all that can be said about scientific representation in general. This brings me to my primary critical discussion, to which I now briefly turn.

There is nothing objectionable in the idea that the inferential conception’s two conditions are necessary conditions on scientific representation. What is less clear is whether this is all can be said, even in the context of the analytic inquiry. If it were, the view faces a worry: For any individual inferential practice, the drawing of inferences from a specific model’s behaviour to claims about its specific target, we can ask why that particular inference is licensed rather than any other. And, at least as stated, the inferential conception provides us with no resources to answer this question.

There are two ways to approach this why-question: either deny that it is meaningful or attempt to answer it by pointing to some features particular to the inferential context to answer it. My impression is that the first response is most in line with the deflationary spirit permeating the book. But it faces the objection (first posed against the inferential conception almost twenty years ago) that without an answer to that why-question, the practice of drawing model-to-target inferences is ‘an activity as mysterious and unfathomable as soothsaying or divination’ (Contessa [2007], p. 61).^[1] Perhaps this is a mystery to be embraced, but this is not explicitly defended in the book.^[2]

Or, one might attempt to answer the why-question. Here I think that there are two general strategies, depending on the sort of features one invokes. One might point to some particular model–target relation (either proposed or actual). This seems to be what Suárez has in mind when he discusses the ‘means’ of representation; whatever it is that a scientist exploits when she performs such an inference. But one of the book’s central claims is that since such means vary from context to context, they cannot be constituents of representation and are therefore outside of the purview of analytic inquiry. But why? Even if there is no single, fully concrete relation that underpins all such inferences, it does not follow that we cannot analyse them together as having a certain form in common (we might say, for example, that the constituent is multiply realized by its means and, as a result, has a certain functional structure, amenable to philosophical analysis).^[3] Moreover, there is some hope that identifying such a structure will thereby illuminate actual modelling practices in a way that the deliberately uninformative conditions of the inferential conception don’t.

Alternatively, rather that appealing to model–target relations, one might appeal to socio-normative factors present in the modelling context itself. This has philosophical precedence; it is associated with Brandom’s ([1994]) ‘inferentialism’ (which, for obvious etymological reasons, is occasionally associated with Suárez’s inferential conception). According to that project, the traditional way that inference is explained by reference is reversed: rather than explaining why some sentence (‘the cat is in the house’) is inferred from some other (‘the cat is on the mat’) by appeal to referential facts (‘house’ refers to house; ‘mat’ refers to mat; the mat is in the house), we instead explain reference in terms of inference, where facts about the latter are features of our socio-normative practices (the giving and asking for reasons). Despite the intriguing possibly of applying this analytic programme to scientific representation (something recently explored by Khalifa et al. [2022]), and despite Suárez’s emphasis on the importance of understanding modelling as practices embedded in socio-normative contexts (see, in particular, chapter 9), we are told early on that ‘the inferential conception of scientific representation is not committed to any of the core elements of Brandom’s inferentialism’ (p. 15), and that it is in fact compatible with either an inferential or referential approach (refreshingly liberal, but one might worry that this opens the possibility of further developing the conditions, contra the conception’s spirit).

Here is not the place to resolve how we should answer such why-questions. But if either of the latter two responses is correct, then there is, in fact, more to say about the constituent(s) of scientific representation within the analytic inquiry. Moreover, neither requires a commitment to sim or iso, and so it is at least plausible that the fruits that arise from their rejection are also available to those who prefer to take one of these routes. That the book fails to engage with this issue is a little disappointing. On the other hand, this suggests that there is further philosophical work to do on scientific representation. And in light of my introductory remarks about the topic being a self-standing part of the contemporary discussion, it would be a shame if the inferential conception’s cautioning against saying anything beyond its two conditions were correct. Fortunately, I don’t think this is the case.

Such critical discussion is not intended as an attempt to refute the inferential conception, nor to undermine the value of Inference and Representation. The view is certainly influential and, as I hope is obvious from this review, the book is important reading for philosophers working on the topic. As is well demonstrated in chapter 9, it is also of clear value to those exploring adjacent issues, in aesthetics and the epistemology of science, and indeed practising scientists who themselves engage in the sorts of methodological reflections that preoccupied the nineteen-century physicists we encounter in chapter 2. Overall, the book is excellent.

James Nguyen
Stockholm University
james.nguyen@philosophy.su.se

Note

^[1] This objection can be posed descriptively (why do model users draw the inferences they do?) or normatively (how should models be interpreted? what establishes the ‘inferential rules’ associated with them?). As presented, the inferential conception doesn’t provide the resources to answer either.

^[2] Note that the analogy with philosophical discussions about truth will not immediately block this concern; deflationists about truth are not automatically precluded from invoking referential semantics.

^[3] At times I read Suárez as endorsing such a view. For example, in chapter 7 where the earlier historical discussion of Bildtheorie is invoked in defence of the inferential conception, he discusses ‘horizontal’ (model-to-target), rather than ‘vertical’ (internal to the model) rules of inference, according to which the ‘overarching requirement of conformity [required of all Bilder] then merely entails that the state descriptions in the source [model] must always be applicable back to the system [target]—that is, that they can always be rendered as descriptions of the state of the system described in the target’ (p. 162). Presumably, explaining the conditions under which this can be the case is a worthwhile analytic project.

References

Brandom, R. B. [1994]: Making It Explicit: Reasoning, Representing, and Discursive Commitment, Cambridge, MA: Harvard University Press.

Bueno, O. and Colyvan, M. [2011]: ‘An Inferential Conception of the Application of Mathematics’, Noûs, 45, pp. 345–74.

Contessa, G. [2007]: ‘Scientific Representation, Interpretation, and Surrogative Reasoning’, Philosophy of Science, 74, pp. 48–68.

French, S. [2003]: ‘A Model-Theoretic Account of Representation (or, I Don’t Know Much about Art… But I Know It Involves Isomorphism)’, Philosophy of Science, 70, pp. 1472–83.

Goodman, N. [1976]: Languages of Art, Indianapolis, IN: Hackett.

Hughes, R. I. G. [1997]: ‘Models and Representation’, Philosophy of Science, 64, pp. S325–36.

Khalifa, K., Millson, J. and Risjord, M. [2022]: ‘Scientific Representation: An Inferentialist- Expressivist Manifesto’, Philosophical Topics, 50, pp. 263–92.

Suárez, M. [2003]: ‘Scientific Representation: Against Similarity and Isomorphism’, International Studies in the Philosophy of Science, 17, pp. 225–44.

Suárez, M. [2004]: ‘An Inferential Conception of Scientific Representation’, Philosophy of Science, 71, pp. 767–79.

Wollheim, R. [1987]: Painting as an Art, London: Thames and Hudson.