Review of Giere's account of scientific theories

After Suppe and van Fraassen, we’re now reaching the last defender of the semantic conception of theories that I will comment on: Ronald Giere. I’m particularly interested in his work, because he takes a much more pragmatic stance that the others, who remain generally more structuralist, and I think I can find much in common with my own stance. I will comment on chapter 3 of his “Explaining science” (1988), chapters 5 and 6 of “Science without Laws” (1999) and chapter 4 of “Scientific Perspectivism” (2006).

Summary of Explaining Science

In “Explaining Science”, Giere tells us: in order to know what a theory is, instead of looking at abstract theoretical reconstructions of their content by philosophers, we can simply have a look at science textbooks. It would be presomptuous to claim that their authors and users do not know what a theory is. And if we do so (he takes a few textbooks of classical mechanics as illustration), what we observe is that indeed, a system of laws is presented, but that’s only the begining of the story. What happens in a typical textbook is that after presenting the laws, canonical applications are presented: a model of free fall, of a spring, of a pendulum, a damped oscillator, collisions, rigid body systems, gravitational systems, etc. Then, depending on the textbook, either other more specific and complex applications are presented as well (fluid dynamic, statistical physics…) or different mathematical techniques are developed (Lagrangian and Hamiltonian).

All this shows, according to Giere, that a theory is not an axiomatic system of laws. It is more like a population of related models. It’s like playing chess: of course, the rules of the game must be presented first, but playing is not just applying the rules. It is mostly about remembering relevant patterns. And so it is in physics too.

If the laws of Newton were taken to be an axiomatic system, it would be a very uninteresting one. The three laws of Newton do not say much before we specify specific laws, for example the gravitational law. They look more like analytic definitions of force and mass (and are sometimes interpreted in this way by physicists). But contrarily to what happens in mathematics, it’s not true that there is one particular structure that is intended by the laws (just like it's not true that only one game is described by the rules of chess ; compare with the axiom of arithmetic, where only one structure, the natural numbers, is intended). On the contrary, they can be applied to a various range of situations. This is what really goes wrong in attempts to identify theories with axiomatic systems.

Giere notes that every application/model presented in a textbook looks like a Kuhnian paradigm, in the sense of a typical exemplar that can be copied in order to devise new, more complex applications. They involve idealisations and approximations of the laws. What building the model means is, roughly, solving equations: the laws and the equations that characterises the specific situation that the model is about.

So far so good. But how does a theory connect to reality and experience? Here is what Giere says (p. 75):

Postpositivist philosophers of science have, of course, been unanimous in rejecting correspondence rules in all their manifestations. Yet any theory of science needs some way of accounting for the phenomenon that motivated their introduction, the fact that scientists do use mathematical symbols to represent things in the real world. Introducing correspondence rules as explicit parts of a theory may be a poor way of accounting for this phenomenon, but one cannot ignore the phenomenon itself.

In sum, a theory must be connected to reality. But how? According to Giere, the answer lies in cognitive science. Just as we associated words like “bird” with prototypes, the exemplars given in textbooks function like prototypes of applications that help us connect the theory and real systems. This is not a purely formal matter: it’s more a matter of seeing similarities between the models and the real systems, in some respects and with some degrees. This assessment of similarity can rest on practical abilities, like the ability to identify birds, learned by training when acquiring a language.

Giere doesn’t think that truth plays an important role in science. Models make the laws true by construction, in a Tarskian sense, but the model-world relation is not captured by truth. This is a sense in which his semantic conception moves away from linguistic approaches, just like other semanticists.

But now come the difficulties. First, a theory is not a set of disparate models, and it does not change everytime a new model is proposed. So, the laws must matter somehow, because they unify all the models together. Then a theory has empirical content. It can be true or false in virtue of the world, believed or not believed. But we cannot identify the theory with its laws if, as Giere claims, they are only true of the models, not of real systems. And a “population of related models” cannot be true or false, since it is no more a linguistic entity. Therefore, we must supplement the theory with a hypothesis: the hypothesis of a relation between its models and real systems. A theory is thus a rather complex entity, composed of laws, models and similarity claims, and it isn’t perfectly defined. Does Giere’s grandfather’s clock count as a pendulum? In some respects and degrees. There is no clear answer, there are borderline cases. The same problem of vagueness also occurs when deciding if a model pertains to a theory: here too similarity judgments play a role. Are there limits to wich force functions are admissible in classical mechanics? The boundaries of the theory are vague, even when only its formal structure is considered. But we have to live with it.

This is Giere’s account of scientific theories, as originally stated in "Explaining Science": a set of laws that describe a family of related abstract structures, some canonical exemplars of them, and various claims of similarity between models and real systems. Now here are a few developments in his subsequent work.

Summary of Subsequent Work

In “Science without Laws”, there’s an interesting move: the full account is explained entirely in linguistic terms! A model is construed as some kind of complex predicate with an internal structure, defining a kind of abstract structure. Giere acknowledges that it’s a mistake to use Tarski's model theory in logic in order to understand the relation between scientific models and theories. Models are linguistic after all (they are predicates, or claims that a predicate applies to a system). He also acknowledges that the distinction between this semantic view and the view that theories are statements is only superficial. The advantage of model-based views is one of presentation that offers a heuristic for applying cognitive science for understanding how science works. Nothing else. Quite a radical departure from traditional presentations of the semantic view! But then he backtracks a bit.

The rest is mostly a development of the previous view, with particular emphasis on the hierarchical structure of models (abstract models can be made more specific in various ways: the damped pendulum, the double pendulum, etc.) and on the way this would match conceptual structures in general (Birds, sub families of birds, etc.). Here is an excerpt that summarises well his view:

On my understanding of a model-based approach to scientific theories, the predicate “pendulum,” as it appears in classical mechanics, does not apply directly to real-world objects like the swinging weight in the grandfather clock that stands in my living room. It applies, rather, to a family of idealized models, the central example of which is the so-called “simple pendulum”. […] The main point for present concerns is that, on this view of scientific theories, the primary representational relationship is not the truth of a statement relative to the facts, or even the applicability of a predicate to an object, but the similarity of a prototype to putative instances. This is not a relationship between a linguistic and a nonlinguistic entity, but between two nonlinguistic entities. Once this step has been taken, the way is clear to invoke other, less abstract, nonlinguistic entities to play a similar role.

Finally, Giere examines the role of pictures in science, taking plaque tectonics as an illustration, thus putting forth the idea that representation in science is generally non-linguistic.

As for “Scientific Perspectivism”, what it brings is mainly that the advantage of thinking in terms of models instead of statements allows for more pragmatic considerations. Giere thinks that linguistic analyses force us somehow to think of theory or model / world relationships as binary relations, whereas users and their aims are crucially involved. See on p. 60:

The assumption that scientific representation is to be understood as a two- place relationship between statements and the world goes along with the view that scientific theories are sets of statements. A focus on the activity of representing fits more comfortably within a model-based understanding of scientific theories.

He mentions a bit later usage base theories of language as a better approach, but this is not developed.

There’s also (p. 60–61) a more complete picture of the model–experience relationship, that corresponds more or less to Suppe and van Fraassen’s accounts.

The attempt to apply models to the world generates hypotheses about the fit of specific models to particular things in the world. Judgments of fit are mediated by models of data generated by applying techniques of data analysis to actual observations. Specific hypotheses may then be generalized across previously designated classes of objects.

He claims again that theoretical laws are not really empirical claims. They are vacuously true of the models constructed from them (here taken again to be abstract objects), and false of real systems (this is perfectly in line with Cartwright’s “How the laws of physics lie”. Teller is also cited). Fundamental theoretical laws are more like principles acting as templates for generating more specific models. But the real empirical claim involved is one of similarity between models and real systems, and this is a matter that is much more practical than linguistic. As for phenomenological laws, which are better candidates for having empirical content, well, they are ceteris paribus anyway. If universal, they are false. If domain-specific, they threatened to be trivially true (true whenever they are true), but it’s not really possible to specify strictly their domain of application. Giere’s solution here is, again, to take models as some kind of mediator, and to make similarity claims. There are no natural kinds, no strict divisions in nature: all divisions are aim-dependent and based on similarity judgments. Scientific kinds are kinds of models, not of real systems.

I think that Giere’s presentation of the semantic view makes it very clear where it becomes problematic: it attempts to do better than correspondence rules for understanding how theories relate to reality, but it ends up somehow vacuous, putting everything under the carpet of the informal, non-linguistic or practical. My point here is not that it is wrong to claim that the coordination of theories and experience is mostly informal, contextual and mediated by experimental practice. I think it’s a perfectly valid point to make. My point is: this has nothing to do with the opposition between linguistic statements and non-linguistic structures that defenders of the semantic view put forth. The semantic view doesn’t really help. Or if it does, it is by emphasising the particular role of models in science. But models could well be linguistic entities (such as equations), with images playing a more psychological supporting role in presenting their content.

Furthermore there is a dilemma in this emphasis on models when it takes the form of an identification of theories with families of models, which is the main claim of the semantic view. The dilemma is the following. Either the theory is constituted of all models that strictly satisfy its laws (this is van Fraassen’s approach). Then this is exactly like saying that the theory is an axiomatic system after all (see previous review). But this runs afoul of Giere’s remarks, that it is an uninteresting one. Recall the important difference that there is not one intended structure in the case of physics, but several potential applications.

Here, the semanticist could retort that the intended structure is actually that of the full universe, in an extensional sense. There are many passages in van Fraassen’s writing hinting at this idea. Or someone leaning to structural realism could say that it is the structure of reality, in the sense of a nomological structure. If there is one intended structure, then scientific theories are very much like axiomatic systems in the end. But Giere is right to object: this doesn’t look like it. Textbooks do not present cosmological models straight ahead, but rather interesting applications. We have something that looks more like a hierarchy of potential applications. And claiming that the theory is constituted by all structures satisfying its laws does not do justice to this aspect, because only some structures are interesting applications.

The second horn of the dilemma is to deny that the theory is constituted of all structures satisfying the laws: only some structures / models are relevant, and they are organised hierarchically. But then, it seems that the models can evolve without the theory evolving, which is problematic. So law statements must play a role too, as acknowledge by Giere.

The solution to the dilemma seems obvious: take the theory as a set of statements, the laws, and consider that models are applications of theories to particular cases. Maybe theories are not axiomatic systems strictly speaking, but the statement view was not entirely wrong. At least, theories are linguistic entities. What was wrong is understanding the interpretation of these statements (and of theoretical terms) in terms of correspondence rules, whereas it is something much more pragmatic and context-dependent. And yes, models can play a mediation role in the interpretation of a theory. But the theory is not just a set of models for this reason.

There is still an important difficulty. But this is ont that affects all kinds of view. The difficulty is this: how shall we understand what it means for a theory to be true or false, since apparently, a theory can be said to be true or false, or believed or denied (we can say that the theory of evolution is true for instance), but correspondence rules won’t do?

It seems that no one wants to be an instrumentalist about theories (they are neither true or false, only useful) or a conventionalist (they are vacuously true). And Giere struggles quite a bit, ending up with a vague account in terms of similarity. It’s never clear to me why vagueness looks like a fatal problem for the claim that laws can be approximately true or false in a statement view, but suddenly, it would become unproblematic for the claim that models are similar to some systems. If the claim is perfectly generic, isn't it vacuous or false, too? And if it's not generic, but a case-by-case kind of claim, then how can we say that a theory is true in full generality? I don’t see a strict account of the sense in which a theory can be said to be true or false that is neither vacuous not false in the final picture that Giere provides. This shows that the fundamental problem of replacing correspondence rules with a better account is not easily solved by just focusing on models instead of statements.