Are Scientific Models Make-Believe?
Comments on Roman Frigg's "Models and fiction"
Roman Frigg, “Models and fiction,” Synthese, Vol. 172, No. 2 (January 2010) pp. 251-268.
In using a scientific model, scientists do two distinct things: “they present a hypothetical system as object of study, and they claim that this system is a representation of the particular part or aspect of the world that we are interested in, the so-called the target system” (p. 252). Frigg calls the hypothetical system the model system, and what he particularly wishes to investigate is the nature of such model systems. What he will argue is that (1) these model systems are essentially the same general kind of thing as fictions in a literary sense and (2) a version of Waltonian theory of make-believe (which Frigg calls ‘pretence theory’) makes sense of how they are used.
A common view of model systems treats them as structures involving objects and purely formal relations, but Frigg notes that this leaves entirely unclear what they would then have to do with any physical system. He wants instead to build in the relation with physical systems; in particular, a model is an “imagined physical system” (p. 253), one which, while not real, would be physical if it were real:
If the Newtonian model system of sun and earth were real, it would consist of two spherical bodies with mass and other concrete properties such as hardness and colour, properties that structures do not have; likewise, the populations in the Lotka-Volterra model would consist of flesh-and-blood animals if they were real, and the agents in Edgeworth’s economic model would be rational human beings. (p. 253)
Scientists, of course, regularly do talk about these models as if they were physical systems; but more than this, Frigg suggests that this explains the function of the model system as related to physical target systems. Bare structure, considered on its own, does not represent anything particular and concrete; it’s a purely abstract thing on its own, and requires an interpretation if it is have a connection to anything that is not purely structure itself. The problem is made more acute when one recognizes that the model systems do not actually describe the target systems. The ideal pendulum is not a description of the non-ideal pendulum; the Newtonian model system of planetary bodies gives an ideal that planetary bodies don’t actually fit well. In reality, the structural descriptions don’t describe any real physical system, but the hypothetical systems themselves. Structures aren’t models of real physical systems; they are descriptions of model systems.1
That these model systems are in some sense fictional is not very controversial, but given that they are, understanding them and their function requires an account of fiction, at least of a sort that could fruitfully be applied to them. Frigg identifies six major points we need to consider if we are to have an adequate explanation of model systems:
(I1) Model systems have identity conditions, because different people use the same model systems in different ways.
(I2) Model systems have physical properties (and must, to serve their function) but do not exist as real physical systems.
(I3) Model systems have to be able to be compared to the physical systems they are used to model.
(I4) Claims about model systems can be true or false, and therefore there must be something about which they can be true or false, and indeed, explains why they are true or false.
(I5) Model systems are things we can investigate in their own right, and therefore there must be a way to discover things, new things, about them.
(I6) Any account of model systems will need to justify or at least explain any metaphysical commitments or assumptions that they involve.
On all of these points, it quickly becomes clear that an account of model systems will be similar in many ways, even if not in every way, to accounts of fictional characters.
We have elsewhere discussed the basic components of Waltonian theory of make-believe, so we will not here go through Frigg’s own summary of the same, although it’s worth mentioning one particularly important one, namely, that in the Waltonian theory, ‘make-believe’ does not indicate something private and subjective but something public consisting of objective props and and shared conventions. Frigg thinks that model systems have all of the features that make the Waltonian theory applicable:
Model systems usually are presented to us by way of descriptions, and these descriptions should be understood as props in games of make-believe. Characteristically, model system descriptions begin with ‘consider’ or ‘assume’ and thereby make it clear that they are not descriptions of fact, but an invitation to ponder—in the present idiom: imagine—a particular situation. (p. 260)
We take it that Frigg sees the model system descriptions as something like the descriptions of a diagrammatic situation in geometry: they give the instructions for imagined constructions that can be used as devices for drawing conclusions. In any case, the Waltonian theory has an account for (I2) above: Model systems have physical properties in the specific sense that it is, in Walton’s sense, fictional that they have the physical properties. The attribution of physical properties is justified by combining the prop (the model system description) with the rules of generation (linguistic conventions and scientific principles) within a game of make-believe.This is a weak sense of ‘attributing physical properties’, but perhaps it is strong enough to let the model serve its function, which is all that is required.
Giving an account of (I4) is necessarily somewhat more complicated, because fictional entities occur in radically different kinds of statements. Intrafictional statements about fictions concern those that are part of the make-believe itself. Frigg accepts the Waltonian idea (which we have elsewhere questioned) that truth in fiction, understood in this intrafictional way, is not a kind of truth; rather it is a species of being to-be-imagined.2 Given this, we can use the Waltonian conception of ‘truth in a fiction’, or ‘being fictional’ (since Waltonians don’t regard this as a kind of truth) to make sense of ‘truth in a model’: A claim p is ‘true in a model m’ if and only if the model system description for m, together with the laws and principles taken to be operative in the model system, prescribes that p is to be imagined.
Metafictional statements, on the other hand, are statements about the fiction itself. The analogue for models would be if our claim were not p but rather ‘in the model, p’. This obviously can be made sense of by taking ‘in the model, p’ to be another way of saying ‘p is true in the model’, thus building on the account for intrafictional statements.
Transfictional statements, statements that compare fictional and nonfictional matters, tend to be much more difficult for pretense theories, but Frigg thinks that in the case of scientific models this difficulty is partly alleviated by the fact that scientific models have a specific use. Thus the only transfictional statements for which one must account are those which compare the model system with the target system in some specifically definable way. We can therefore take this to be a comparison not of two systems but of two properties, which Frigg takes to make the comparison unproblematic. We are not convinced, for a number of reasons, that this works at all; as the Cartesians used to say, nothing has no properties, so if there are two compared properties, and we are not talking purely hypothetically (which we cannot be in a transfictional statement of this sort), there must be two somethings to anchor the compared properties. This seems to us to be tied to the common Waltonian attempt to have their cake and eat it, too, by treating things pretended as officially not objects but attributing object-like characteristics to them. A more plausible way to solve this problem, we think, is to focus on prescriptions. In the Waltonian account, the model system description generates (with the help of assumed scientific principles) prescriptions to imagine something (the model system); we can then take the scientific inquiry to generate prescriptions to take reality as being a certain way for the purposes of inquiry, and compare the prescriptions.
In any case, Frigg moves on to accounting for (I5) and (I6), which he takes to follow straightforwardly from what has been said so far. We investigate model systems themselves by pursuing the logical implications of their explicit descriptions when we combine them with scientific laws and principles; as he rightly notes, this is a good sign, because this is precisely what scientists do in practice. As for metaphysical commitments, there are none; Waltonian theories of make-believe do not posit fictional entities. We think this is probably too quick. Waltonian theories of make-believe attempt not to posit fictional entities, but it’s unclear that they succeed; in particular, it’s difficult to make sense of make-believe in ways that do not slide into thinking of the make-believe in terms of intentional objects. Even if we assume that they do succeed when considering model systems simply in themselves, however, we think that model systems do clearly have metaphysical commitments when taken as representations applying to target systems.
The ideal pendulum commits us to a physical pendulum having a bob that can follow a path while being connected to something reasonably straight (the string); it does not commit us to a lot of other properties that a physical pendulum (or its bob, or its string) will inevitably have, but it has to commit us at least to that. Scientific models are supposed to give us some insight not into the model alone but into reality by way of the model. For exactly the reason that Frigg claims that there are no metaphysical commitments, there can be no straightforward way to ground such a metaphysical commitment in Waltonian make-believe itself (most make-believe clearly doesn’t generate such commitments), so we would seem to have to take this commitment to arise from either the representative function itself or from how the representation works in the practical scientific context; the former seems ruled out because such commitments simply don’t arise in other representative contexts (like paintings of unicorns, which don’t require that there be anything real corresponding to what is painted). The Waltonian theory of scientific models, however, would have to borrow this account from some broader account of scientific practice and how it is using the relevant props (model system descriptions) for scientific purposes; it does not provide it itself.3
Frigg thinks the above arguments show that the ‘pretence theory’ of scientific models is a strong contender, one that can solve problems that the more common structuralist theories apparently cannot. Nonetheless, he does recognize two potential problems that will have to be considered more fully. (We think both are inherited from problems faced by Waltonian theories in general.) The first is that the sense of imagination used in the theory may need to be made much more precise; there are obviously uses of the term that are not appropriate for scientific modelling, but because scientific models often require a considerable degree of precision, an account of such models requires that we be quite precise about the sense in which the model system is something we imagine. The second problem is pinning down the rules of generation. What the rules of generation would be for literary fictions is hotly disputed, and scientific fictions seem only to add to the puzzles and problems that cause such disputes.
Frigg has given us the basics of how you would use Waltonian theory of make-believe to discuss scientific models; we will be looking at other discussions of this. In particular, we hope soon to discuss Adam Toon’s somewhat different attempt to apply the theory to scientific modelling.
We saw this with Contessa’s description of fictional models. Scientists often use mathematical descriptions, but these mathematical descriptions are often more properly descriptions of models than of the things being modeled.
Our own view, of course, is that when we recognize the analogy, recognized by Walton himself, between fictional truth as to-be-imagined and truth in non-fictional contexts as to-be believed, and recognize just how generally we have to take ‘imagination’ for it to apply to the sheer range of fictions, there is just no sharp distinction left. The two will obviously overlap extensionally; we can apply traditional accounts of truth, like William of Auvergne’s adaequatio rei et intellectus, to both; we can apply ‘theories of truth’, like the correspondence theory, the coherence theory, and the pragmatic theory, to both, even if doing so requires a bit more generosity in application to fictional truths. Truth in non-fictional contexts can obviously be thought of as to-be-imagined; sometimes we explicitly invite people to imagine physical and historical facts, for instance. The only squeamishness here seems to have to do not with truth but with belief: there is a hesitation when it comes to saying that truth in fiction is to-be-believed. But we can make perfect sense of saying that we are invited by Sir Arthur Conan Doyle to believe that Sherlock Holmes is a consulting detective; the only question is whether this is a loose, colloquial figure of speech or is talking about some sort of ‘real’ belief. But we don’t seem to have a generally agreed-upon account of belief, whether as a propositional attitude or as a cognitive act, that requires the former.
If you really wanted the make-believe itself explain the metaphysical commitments, probably the most promising option would be to take the props in the make-believe not to be the model system descriptions but the target systems themselves. That is, take it to be the case that when we model we are imagining the target system as if it had the features of the model system. The metaphysical commitments then would come from the target system itself as prop. This is even a plausible description of what scientists sometimes do; they just treat the real thing as if there were no difference between it and the model system. Nonetheless, we think even this approach would fail, because we don’t see any way that it could apply across the board. Despite scientists sometimes treating the target system as if it were the model system, there are many situations in which it seems obvious that they are not doing this.