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Reflections (2): Is the semantic view about there being two stages in scientific representation?

Marzipan layered cake

In the previous article, I explained that there seem to be no superficial difference between the syntactic and the semantic views when it comes to presenting theories. Both can individuate theories using the same level of grain, and they will use the same statements to do so. But an important difference remains of course: the syntactic view characterises the theory with the statements that are presented, while the semantic view characterises it with what these statements supposedly describe, namely a family of models satisfying these statements. What shall we make of this? And don't wave your hands and tell me that it's a difference of "stance" of "focus" or whatever: I want something concrete. Tell me exactly why I should subscribe to one or the other conception of theories.

Let's first discard an understanding of it. Obviously, theories and models represent nature. When semanticists say that statements describe the theory, they aren't claiming that theories are some part of nature that we represent using statements. A theory makes claims and can be true or false, believed or denied, accepted or rejected. So the theory is on the side of representations, not of the world. But at the same time, according to the semantic view, it is linguistically represented (described) by textbook statements, and not to be identified with them (the theory is what its formulation refers to, says Suppe)... Isn't it puzzling?

The two-stage picture

The implication is that according to the semantic view, we have at least three levels involved in representation, and two representation relations: the statements describe some collection of structures, that, in turn, represent part of the world.

Statements → Models → Phenomena

This idea of having three levels / two stages is expressed by Suppe (1989) here (assuming a correspondence between what he calls physical systems and, later in the book, model systems, see my review for more detail):

What we have here, then, is a two-stage move from raw phenomena to statements of the theory (p. 69)
[I]n place of the correspondence rules providing a bridge between theory and phenomena, we now have a two-stage transition: (a) the transition from phenomena to physical systems (which reduces to problems of measurement, experimental design, counterfactuals, and the like) and (b) the connection between the theory and physical systems, which are deductively determined by the (often mathematical) apparatus of the theory without requiring additional correspondence rules or postulates other than boundary conditions and data about the initial state of the physical system. (p. 71)

Physical systems constitute an intermediate level between theoretical statements and phenomena. The aim of theorising is to have the "causally possible" physical systems correspond exactly to the models of the theory, in the sense of law-satisfying structures, so it's fair to say that models are the intermediate level of representation.

This two-stage idea is expressed even more explicitly by van Fraassen (2024/2012) (section 6.1), in reference to the two opposite meanings of models (mentioned here on this blog):

Models look in two directions at once: a model is a model of a phenomenon (it represents the phenomenon) and a model is a model of a theory (it satisfies the equations the theory gives us). Both aspects of modeling need to be studied to arrive at a balanced view. If we neglect the first, we will be restricted to pure meta-mathematics, and lose touch with the specific character of the empirical sciences. If we neglect the second, we’ll land in puzzlement with Margaret Morrison’s apt question: where have all the theories gone?

Here we go. The main claim of the semanticist, with their particular focus on models, would be that there are three levels and two stages in representation or in theoretical interpretation, from statements to phenomena, with models in between. One stage (statement to model) is linguistic, and the other (model to phenomena) is something different. The syntactic view sees only one direct linguistic stage between theory and phenomena: that's its main problem, and the main difference with the semantic view. Good...

But wait, there is something fishy going on here. What is the point of these three levels exactly? Is it something we really need to account for scientific practice? Is it that simple? And Is it the right way of doing it? What does it mean to represent using models as opposed to describe using statements? And finally, are theories at the first level, or at the second level, if, per the slogan, theories are collections of models instead of statements? It should be the second level then. But read the quotes again...

Is the staged picture specifically semantic?

Let's start with the first set of questions. These levels could be understood as capturing two different kinds of scientific activities, which seems to be what Suppe has in mind. The first one is model building: description of abstract structures using mathematical statements. Textbooks provide the statements, the descriptions of the kind of structures that can be used, and scientist pick the ones they need for some purpose, presumably using more statements that describe a particular kind of situation associated with specific "initial states and boundary conditions". But it's pure mathematical calculus at this stage. The second stage is model application: representation of a real phenomenon using this abstract structure, including comparison between various structures representing the same phenomenon or counterfactual versions of it (data models, phenomenological models, etc). This is where a particular representation relation (isomorphism or what have you) or more informal aspects enter the picture.

One problem with this understanding is that the idea that there are different stages in theoretical interpretation isn’t specific to the semantic view. Pragmatist philosophers of science have argued as well that models play a mediation role between theories and the world (see the review of “models as mediators” on this blog), so they seem to accept it or something similar. Here, one might say: good, then they implicitly subscribe to some version of the semantic view... Except that they criticise it precisely on the ground that models and theories are two distinct levels! Weird, isn't it?

But there is another problem: it's not only the pragmatists. Contrarily to what Suppe claims, this two-stage picture isn’t so much at odds with logical empiricist’s syntactic view, for the distinction between theoretical statements and correspondence rules on which it is based seems to capture precisely these two stages (see my discussion here). Assuming logical empiricist’s syntactic view, one can reason on the basis of theoretical statements alone, staying inside the axiomatic system of the theory so to speak, and think about specific circumstances or some kind of situation theoretically described and apply the laws of the theory. This is like building a model. This is the first stage, and both semanticists and syntacticists agree that this process of model building is somehow systematic and formal (which is precisely where pragmatists disagree, but this is for another day). Syntacticists can even agree on using model-theory to capture this stage, with the situation described being the model of the theoretical statements.

Then correspondence rules come in to relate these theoretical descriptions to experience: this is Suppe's second stage. Scientists enrich their descriptions, putting in more stuff, adding more statements, perhaps about instruments and so on, also using auxiliary theories, bridge laws and the like, which were typically invoked by authors working in the syntactic tradition, until something directly observable is described and they can compare these descriptions to direct observation reports. Or this could go in the other direction, which is probably more in line with actual practice: enrich observation reports using correspondence rules, auxiliary theories, bridge laws, assumptions about the instruments, and so on, until a description that can be compared to the theoretical one is achieved. In this case, we have something strikingly similar to what Suppe describes, but couched in a syntactic view.

Of course, for the syntacticist, it’s linguistic representation all the way through (they would use model theory equally to account for both stages): comparing predictions and experimental results is checking if two kinds of linguistic descriptions of the same situation that come from different sources, either theoretical or experimental, are consistent together, or how much they say the same things or something similar. And you might disagree with this account for various reasons. But the main point is that they agree with semanticists that there are (at least) two different stages in this process of interpreting a theory, one purely theoretical and the other applicative, since they make a difference between theoretical laws and correspondence rules.

Is it compatible at all with the semantic view?

So, this idea that there are stages or levels involved in representation cannot be the main claim of the semantic view, since it's largely shared by other views.

It’s even worse if you think about it: if really there are exactly three levels of representation in science, then it seems natural to refer to the first one (the statements) as the theory, the second one as the models, and the third one as the phenomena. But this is at odds with the claim that a theory would be mainly characterised in terms of models or structures instead of statements ("what their formulations refer to"), and both Suppe's and van Fraassen's quotes above clearly seem to contradict the semantic view in this respect!

All this sounds confused. Not only is this level picture largely shared by syntactic and pragmatic views, but they seem to make better sense of it, by distinguishing more clearly models and theories. These views can also easily accommodate more than two stages in a way that the semantic view cannot. Many authors (notably Giere) think that there are actually many levels of abstraction in scientific representation, with models being organised hierarchically. But the distinction between statements, structures and phenomena is not obviously hierarchical, and more importantly, it is clearcut. It implies that there are exactly three levels and two representation relations, no less and no more. This doesn't look like a very flexible account of scientific practice.

Even assuming that there are levels of abstraction in scientific representation associated with different stages in practice, there’s something deeply wrong with the idea that the three levels implied by the semantic view (statement–model–phenomena) would correspond to them. This is because levels of abstraction do not necessarily imply layers of representation: in Giere's account, for example, abstract models or theories do not represent more concrete ones, they make them more specific, which is different. But all levels represent in the same way (Giere doesn't actually refrain from claiming that models are linguistic entities, and he doesn't subscribe to these three-layers view: see previous review). Generally speaking, subscribing or not to Giere's account, linguistic statements are needed at any stage: we need them in order to describe theoretical laws and theoretical models, but also data models, models of experiment, phenomenological models, or anything, really. It’s not as if at some point we would only need the structures and put the statements aside. And you could argue that the fact that models or statements aim at representing specific situations of the world or kinds of phenomena is also implicitly present at any stage, even when formulating theoretical laws or presenting a theoretical structure using textbook statements: there’s at least some vague sense of intended application to the world already (vectors of Hilbert space represent states); it’s not pure mathematical calculus. In sum, representation relations, whether linguistic or not, seem orthogonal to these levels of abstraction and associated stages of scientific activity.

So in my view, this idea that there are levels of abstraction from abstract theories to concrete phenomena with models in between is a red herring: an interesting idea for sure, perhaps even true, but completely unrelated to the three levels/two stages of representation that constitute the core of the semantic view. If these three levels are involved, it must be for a different reason.

What makes more sense is to understand the semantic view as claiming that representation is non-linguistic all the way through, whatever the stage we consider (that language doesn’t matter that much in the end), where the syntactic view claims that it is linguistic all the way through. The only reason why the semanticist needs the three levels is, I think, to accommodate a secondary role for language while putting non-linguistic representation in the foreground.

Conclusion

As soon as we accept, as we did in the previous article, that the statements involved in the syntactic or semantic view when presenting a theory are exactly the same, the difference between the two conceptions seems to vanish almost entirely.

A difference could lie in the idea is that there are stages in scientific practice, from abstract theorising to concrete experiment, represented by the three-fold distinction between statements, models and phenomena. This is what I've examined here. However, the conclusion is that this is a red herring, since this kind of view of science is as much compatible, if not more, with alternative conceptions of theories, and speaks in favour of identifying theories with statements, not with models. We don’t need the three levels invoked by the semantic conception to account for this; two are enough: the vehicles and the objects of representation, with different levels from theories to experience to be found on the representational side, in the form of a hierarchy of more or less abstract representations, from fundamental theories to concrete descriptions of experimental results, or even perceptual representations maybe. But most of these representations might well be linguistic in format, and the move from statements to structures isn’t needed at all to account for this.

The only remaining way to maintain a substantial difference between the semantic view and the syntactic view is to assume that there is something specific about representation in science by means of models that is entirely unlike describing physical systems in a language. I think that this is the correct understanding of the semantic view. However, I will argue in the next article that it is also implausible.

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