Reflections (3): Is scientific representation non-linguistic?

We have now settled, in conclusion of the previous article, on the most sensible interpretation of the semantic view: not a difference of grain in theory identification, not the idea that there are different levels of abstraction with models lying in between abstract theories and experience, but simply the idea that scientific representation isn’t linguistic at all.

My understanding of this is the following: for the semantic view, a theory provides us not with literal descriptions of nature, but with a certain way of representing the world, or a certain kind or family of representational vehicles, its models, which are non-linguistic in nature, and which play a central role in science, a role that was neglected by syntacticists. Of course, the theory itself (as well as its models) are expressed by means of linguistic/mathematical formula, but these formula shouldn’t be taken to describe nature directly. There’s an intermediate level, constituted by the models. And the way models represent nature isn’t appropriately captured by correspondence rules or by any linguistic theory for that matter. Notions such as isomorphism or similarity should be used instead, or perhaps something more messy associated with experimental practice: this is non-linguistic representation.

This looks like the most sensible and faithful interpretation of the semantic view and of its difference with the syntactic view. But why this move?

Why non-linguistic?

What does it mean exactly to use an abstract structure, as opposed to linguistic descriptions, to represent part of the world? In the end, theoretical models themselves are expressed using mathematical statements, or formulas in a given language. In concrete applications, aren’t these formulas (the ones that describe the position of the bob of a pendulum for instance) taken to describe real systems, at least approximately? Why not use model-theory to capture this as well, where the model is the situation described? Data models too are often expressed using formulas stating correlations between quantities and the like, for instance. Aren’t they direct descriptions of experimental results? Or is there also an abstract structure doing the mediation in this case? It seems not. And what is the difference between comparing different models of a system (a theoretical model and a data model or phenomenological model when reducing a theory) and comparing two different descriptions of the same system, one deduced from an experiment and the other from a theory for example? Isn’t it more or less the same thing, once we’ve accepted that the statements involved are always the same?

This, to me, is the most puzzling part. I don’t understand how all this is supposed to work and why we should assume that there are important differences between linguistic and non-linguistic representation, adding an intermediary stage everywhere as if at some point, somehow mysteriously, some abstract structures were directly seized and used by our intellect to represent reality in a way that is entirely different from describing it using statements. As if scientists were almost never doing the latter, or only in very particular occasions (in experimental situations when locating systems in state spaces perhaps) but routinely doing the former. To me, this doesn’t make any sense (see Arnon Levy 2015 pleading as well for a more direct account of representation).

Or maybe I can feel that there’s something to it somehow. Maybe there’s one way of making sense of this idea that theories are families of models, but it’s not exactly what semanticists have in mind.

Let’s try anyway. Here are some non-exclusive possibilities to respond to my worry on behalf of the semanticist. Perhaps the representation relation is non-linguistic because:

1. Representation of real systems with models is largely informal; mapping a model with a concrete situation involves non-linguistic input, notably experimental abilities, so using correspondence rules, or thinking of it linguistically in general, is unfit.
2. Model descriptions are not strictly true of the real system that models represent, because of idealisations and the like, so representation is not a matter of linguistic truth; it has more to do with structural comparison.
3. This is a difference of format: representation by means of models is more “pictorial” than linguistic description. This is why syntactic analyses of theories is unfit.
4. Model descriptions, unlike ordinary statements about the world, are schematic rather than truly descriptive or demonstrative; models are vehicles that can be used in various ways in various contexts; they are more like epistemic tools than like sentences.

Non-linguistic because informal?

I think that (1) about the informal aspects of experimentation misses the point entirely. The mappings (isomorphism etc.) that are invoked by semanticists in their theories of representation are typically mappings between different models of the same object: theoretical and data models, one being embedded in the other. This is not very different from correspondence rules linking observation reports to theoretical statements. There's nothing informal here. Surely, building data models requires informal and contextual input that isn’t linguistic, but all these aspects aren’t captured by isomorphism, similarity and the like, and producing the observation reports to which correspondence rules are applied in the syntactic view also requires contextual input that isn’t linguistic, but rather perceptual, and that can rest on informal abilities: the two are on the same boat. All this is quite irrelevant: we don’t need the notion of a model to address the informal aspects of experimentation, since models are just as formal entities as statements.

To be precise, I agree that the fact that messy, contextual and informal aspects are involved is problematic for the syntacticist if understood as logical empiricism did in terms of correspondence rules (this isn’t big news). But if this is the criticism that motivates the semantic view, it is misplaced: it’s not an issue with theories being structural instead of linguistic, but an issue with the particular theory of meaning that was entertained by logical empiricists which would not be flexible enough. Think of it this way: the same problems of "informalities" arise in ordinary languages. Putting everything under the rug of “informal representation” is no solution to these problems of interpretation, and invoking models as opposed to statements is of no help.

By the way, it’s interesting that both van Fraassen and Giere mention pragmatics/used-based semantic theories as potentially relevant for their purpose (see previous reviews on this blog here and here): this would confirm that the true criticism of the syntactic view lies not in reliance on language per se, but rather on regimentation by non-contextual correspondence rules, and that the true remedy is something like a pragmatic theory of language, not a semantic view of theories.

Because representation is idealised?

Let’s move on to point (2) about idealisations. It’s true that model descriptions aren’t strictly true of real systems (imagine that a gas is infinite to simplify the calculus), but I think we do similar things in daily life using language (imagine Italy is a boot, etc.). In any case, modellers must specify what to take seriously or not in their models for these models to be scientifically useful. At any rate, making everything explicit can do no harm. So, a syntacticist could claim that there are implicit correspondence rules qualifying the empirical interpretation of models so as to account for these idealisations, perhaps taking into account the concrete situation as well, the degree of precision of instruments, etc. If the point is that models shouldn't be interpreted literally, this is good news: the logical empiricists are the specialists of non-literal interpretation!

This will seem implausible to many of course. Correspondence rules are rightly viewed with suspicion. For example, one might suspect that the way to handle idealisations is contextual (it would depend on the disciplinary context where the model is proposed, or even on the application context maybe) and this cannot be addressed by universal rules of interpretation. But again, the question is whether this is fundamentally a problem with viewing theories as linguistic entities, or rather an issue with logical empiricist's particular semantic theories, and I see no particular reason to assume the former just because model descriptions are not literally true of real systems, or because their interpretation is contextual. As if this kind of feature was unknown to any use of language (and again, this point to pragmatics as a solution). So, maybe a better strategy is to ask a philosopher of language what to make of scientific discourse, and if really it is unlike anything to be found in ordinary language. As an illustration of this strategy, there are accounts of partial truth initially developed in philosophy of language that have been used to analyse idealisations (Pincock 2021).

Finally, note that in general, idealisations and falsehoods are introduced by specific model descriptions, not at the level of theoretical laws, or less obviously so. Sometimes models even contradict theoretical laws (assuming that the Sun is not subject to the gravitational pull of other planets, despite pulling them, in order to simplify calculus) and generally, when this is so, correcting them improves accuracy. This doesn't really play in favour of the view that theoretical models are mere law-satisfying structures. So, we have a tension with the semantic view here, and a natural way of resolving the tension would be to assume that everywhere an idealised model is used, there is a true, non-idealised model of the theory that could have been used instead, and with better results (if the theory is true).

If this is so, then invoking idealisations as the main reason why representation is non-linguistic is ultimately undermining for the semantic view: either idealisations are eliminable, or they are not (many deny that they are: see my article on idealisations). If they are, then they do not constitute the reason why representation is non-linguistic. We must look elsewhere. If they aren't, then models aren't mere law-satisfying structures as the semantic view claims.

So informalities and idealisations are no good reasons to think that scientific representation is non-linguistic. What else do we have?

Because representation is pictoral or schematic?

Regarding (3): is the best argument for the semantic view that representation by means of theoretical models is more pictorial than linguistic? Is it fundamentally a matter of format?

Surely, diagrams, graphs and pictures are sometimes used in science. But does it make that big a difference? In the end, diagrams are quite similar to sentences: a circle on paper doesn't make true the mathematical formula associated with circles, it is never a true mathematical circle; it only denotes one in a format that is easier to process visually than normal text. So, graphs and diagrams cannot be identified with the notion of models as truth-makers for statements invoked by semanticists. But even if this was what semanticists were after, I think it would be wrong, because when it comes to theories and theoretical models, diagrams, graphs and pictures (even mental pictures) are primarily illustrative or heuristic, with the true content of the model lying in precise mathematical formulas or descriptions of the represented system. They don’t play this intermediary role between statements and real systems that semanticists see models play.

This leaves us with point (4), the idea that models are more like adaptable epistemic tools than like sentences, which I take to be the only good reason to move away from a syntactic view and towards a model-based conception of theories. It’s something I’ve actually defended elsewhere (Ruyant 2025), that I expressed as the idea that models are indexicals. However, I think that the opposition shouldn’t be cast in terms of linguistic versus structural: I don’t think it’s very helpful, and more importantly, I believe that this feature of representation ultimately undermines the semantic view and plays in favour of a pragmatic view that would distinguish more sharply between theories and models and give a role to agents and communities that is not permitted by a semantic conception stictly construed.

However, this article is already too long, so I’ll keep all this for another day.

Summary

Why should we think that representation in science is non-linguistic, but somehow structural?

Informal aspects are present as much in science and in ordinary linguistic uses. Idealisations do not really play in favour of the semantic view, unless they are eliminable. We can handle various representational formats: linguistic, pictorial, etc, but it’s always representation, the same kind of phenomena, and emphasising these differences of format is not as illuminating as the semantic conception pretends to be when it comes to criticising the syntactic view. Furthermore, mathematical or linguistic statements are used extensively in science, at any stage, whereas other formats play more of a heuristic role.

This doesn't mean that a focus on model and modelling isn't an important contribution to a good understanding of science, and there is some truth in the idea that models are unlike direct descriptions of specific parts of the world. However, as I hope to explain in a future post, this aspect is better addressed by moving to a pragmatic conception of theories that distinguishes more sharply between theories and models.