(non-)Review of Models as Mediators

Models as Mediators, edited by Mary Morgan and Margaret Morrison (so many Ms!), is a collective book from 1999 that has now become kind of a classic for whoever is interested in modelling activities in science. It played an important role in impulsing a trend in philosophy of science that consists in focusing more on modelling activities, considered scientifically important for their own sake, and less on the content of abstract theories (a trend that arguably started earlier, in particular with Nancy Cartwright’s work, who contributed to the book, and also perhaps even earlier with Mary Hesse, cited in the introduction).

This book is somehow relevant for my project of discussing how a pragmatic conception of theories could fare better than a semantic conception, because, as we will see, it opposes, or at least attempts to supersede the semantic conception of theories in some respects. However, it is also partly irrelevant to my project, because my main focus is still on abstract scientific theories! This is why I won't review the book in depth here, but still provide a few comments.

Short summary

The introduction of the book provides a helpful presentation of the semantic conception in its various versions. The second chapter, also written by Morgan and Morrison, then presents an overview of the content of the book and main theses. We can see how its project departs from the semantic view: by endowing models with autonomy with regards to theories. Models are not just the kind of structure that satisfy theoretical laws and serve to apply them to particular cases. Often, they don’t even satisfy these laws, but rather approximation to these laws (which is not the same, Morrison will insist, as approximately satisfying these laws!). The laws can be “distorted”, and models can incorporate, on top of these laws, ad-hoc postulates that don’t derive from theories, and not from empirical data either (such models are often called “phenomenological” by scientists). Constructing a model is not just following a recipe, it is more of an ability and an art. This autonomy allows models to fulfil a variety of functions: not only explaining and predicting, but also participating in the elaboration of future theories, exploring existing theories, allowing for the measurement of theoretical constants (as examined in more detail by Morrison in ch. 3: a pendulum together with its model can be used to measure the gravitational force), designing or planning (interventions in economy for example). In sum, the idea is to conceive of models as autonomous agents that mediate between theories and the world. Boumans (ch. 4) offers an interesting metaphor with baking: models incorporate many ingredients (theories, data, past models, mathematical formalism, assumptions, aims…) that become unrecognisable in the end product, as they are “baked into” it.

Most chapters are case studies (4 in economy, 6 in physics and chemistry) that focus on particular models to make a specific point. I hadn’t read all of them so far, and decided to do so for this review. However, I must say that I was a bit dissatisfied, because, as I’ve just said, few are actually relevant for my project. What I had hoped is to find some illumination on the relation between theories and models, but most chapters discuss how particular models were constructed, say, in economy or in chemistry, without theories playing a particular role, precisely, because there is no well-formed, mature theory on which to rely in these domains, at least not at the time where the studied case takes place. There are a few exceptions though:

• Mauricio Suárez (ch. 7) explicitly discusses the model–theory relationship in the context of early superconduction models. The main point being made concerns the confirmation of theories: in so far as, in general, models make ad-hoc assumptions, i.e. they integrate postulates that are not justified by the theory, the empirical success of models cannot work as direct empirical confirmation of the theory. It confirms something weaker: that the theory is generally applicable to a wide range of phenomena.
• Nancy Cartwright (ch. 9), also in the context of superconduction, restates her famous view that uncorrected theories have very limited scope (they are only about imaginary worlds or highly controlled systems). She also defends an interesting account of theoretical terms (such as “force”, “acceleration” and “distance” in Newtonian mechanics) as abstract: as far as I understand, they are only meaningful in so far as they are placeholders for more concrete description in specific contexts, without strictly supervening on these concrete descriptions (in the same way as writing an article is abstract for either typing words on a computer, writing sentences on paper, etc).
• Stephen Hartmann, taking the case of Hadron physics, argues that models, on top of their formal features (including the way they satisfy theoretical laws), also come with an informal narrative. The narrative justifies idealisations and participates in the explanatory function of models, notably by explaining why something rather than something else needs to be predicted by the model.

Brief comment on Cartwright

Although I found Cartwright’s idea that theoretical terms are abstract interesting for my project of understanding the theories--model relationship (and possibly related to Giere’s view on how models are organised hierarchically?), her account wasn’t crystal clear to me, and I wasn’t very convinced by the way of fleshing it out. In particular, it seems that for her, domain-specific theoretical laws play the role of “filling in” abstract terms. For example, she says:

being located a distance r from another charge q is what it consists in for a particle of charge q to be subject to the force [math expression of Coulomb’s force] in the usual cases when that force function applies. (p. 259).

I understand that distance is a term of Newtonian mechanics in general, of which classical electromagnetism is a specification, but intuitively speaking, I’d say that being located at a distance of another charge is more concrete than the other expression! It seems that distance can be measured independently of said law for instance. And it doesn’t seem to me that the two have semantic relationship at all. The law doesn't merely describe the distance relation. It is about more than this. So, I don’t understand how the law is supposed to be a way of making concrete the notion of distance. But maybe I misunderstood something.

What implications for conceptions of theories?

As for the rest of the book, the main lesson, it seems, is that the way the semantic conception of theories thinks of models isn’t exactly right. It tends to view them as fully dependent on theories: the set of models of the theory is just the set of structures that satisfy some laws. Here, the main claim against this view is that most models, in so far as they are scientifically relevant, do not actually satisfy the laws, or at any rate, much more is involved in their construction, so it's not clear that any law-satisfying structure should count as a (relevant) model.

We’ve already seen in a previous post how Van Fraassen responds: he thinks that satisfying theoretical laws is still very important, and that the difference between the semantic conception and those pragmatically motivated criticisms is mainly a question of focus. And it’s true that a defender of the semantic view can be unmoved by all the aspects of the book. We are talking about phenomenological models and idealised models here, about models that come before full-fledged theories, or that are still poorly integrated in existing theories. These are theories or theoretical models in the making, not the final product of science. What the semantic view of theories is interested in would be the final stage: when these models finally “made it” to become well integrated in the theoretical framework (see this article from Potters responding to Suárez and Cartwright’s accounts of the superconduction episode with a similar (but perhaps subtler) take: from what I take, in the end, phenomenological models with adhoc assumptions are not viewed as entirely satisfactory by scientists until fully integrated in the theory, which requires some work). So, this focus on “messy” modelling activities is interesting in its own right, because it’s a focus on an important process involved in theory building, but a focus on the final product, on the ultimate aim of theorising, is also interesting in its own right, and this is what a conception of scientific theories attempts to provide.

I’m quite convinced (until changing my mind later maybe) by this response. Does it undermine my own project and ultimately justify the semantic conception as an account of the ultimate aim of theorising that abstracts away from the messiness of practice? Does it become irrelevant to devise a pragmatic conception of theories? I don’t think so. I think that one point remains relevant, and potentially devastating for the semantic conception of theories. The point is that in so far as models are scientifically relevant for themselves and involved in practice, they are relatively independent from theories, and cannot be identified (as a collective) with these theories. They constitute a separate level of representation in between theories and the world. And perhaps the response above is roughly correct: in so far as models are so independent from theories, they do not really constitute the end-product of science, but are mere side-products (specific applications) or intermediary products. On this view (which I’m ready to hear criticisms of, but that I temporarily accept), abstract, unified theories still constitute the paradigmatic ultimate aim of “pure” theoretical science. But then, the problem for the semanticist is that such theories are not families of models at all, nor collection of models, but something else that is more loosely related to scientifically relevant models than what they claim. Even if such models are imporantly involved in the relation between theory and experience, the theory is not a set of models.

It looks, in retrospective, that the semantic view wants to have its cake and eat it too: at the same time, it wants to stay close to scientific practice, where modelling activities play a central role, but also wants to be an account of theories taken to be the ultimate aim of theorising beyond the messiness of this practice. However, the notion of a model as a structure strictly satisfying the laws of a theory is some kind of hybrid that is not necessarily relevant for either of these two tasks. It isn’t particularly illuminating when it comes to examining actual scientific practice, because of its “messiness” and plurality of intermediate aims (satisfying theories isn’t always that important here), and it doesn’t constitute the ultimate aim of theorising either (models aren’t that important there).

This is what I’m willing to conclude at this point. I’d be happy to hear some objections.

In any case, since the content of the Models as Mediators wasn’t as relevant as I thought to my project, I won’t comment it any further. I’m currently reading Steven French’s “There are no such things as theories”, and might publish a review here very soon.