Fictional Models in Scientific Inquiry
Comments on Gabriele Contessa's "Scientific Models and Fictional Objects"
Gabriele Contessa, “Scientific Models and Fictional Objects,” Synthese, Vol. 172, No. 2 (January 2010), pp. 215-229.
What kind of object is a scientific model? Contessa gives a rough-and-ready classification:
(1) Material models are concrete physical objects. Ball-and-rod models of molecules are an obvious example.
(2) Other things that are considered model are sets of equations; these are mathematical models, and of course they are mathematical objects.
(3) A third kind of model, perhaps the most common kind, is more difficult to pin down. The ideal pendulum, for instance, is said among other things to be a point mass suspended from a massless string. This is obviously not material. No physical pendulum has all of the features of the ideal pendulum. It is also not a set of equations; the set of equations associated with the ideal pendulum is not the pendulum but a mathematical model of how it moves, which requires that it have features independent of the equations themselves. Contessa will argue that this kind of model is a fictional object, and therefore that they are fictional models.
Many of the things that are said of the third kind of model are also said of fictional characters, and vice versa, although there are inevitably some differences. In order to develop this, however, we have to make certain assumptions. Thus Contessa proposes that fictional models and fictional characters are both species in the genus of imaginary objects, and that we should not be ‘fictionalists’ about them – that is, we should take them really to exist, albeit specifically as imaginary objects. There are then a few ways you could develop an account of fictional models under these assumptions.
The first way you might try to understand these models is by taking them to be actual concrete objects that are pretended to be a certain way. With the ideal pendulum, we take a real pendulum and pretend that its string is massless and its bob is a point. The problem with this is that there is no particular, actual, concrete pendulum that the ideal pendulum could be. Precisely what we seem to be doing in talking about the ideal pendulum is ignoring any particular concrete pendular object. So perhaps we should instead take it to be actual concrete pendulums indifferently – sometimes it’s one, sometimes it’s another. The difficulty here is that, while we clearly could do something like this, we often discuss and reason with the ideal pendulum in contexts in which there is no available particular concrete pendular object.
If fictional models are not actual concrete objects, they could be possible concrete objects. One of the tricky things here is that the ideal pendulum has features that may make it impossible. Can we, in any real world, have a particular object that is a point mass attached to a massless string in a completely uniform gravitational field? Contessa, however, is willing to allow this as a possibility. The more serious problem, as he sees it, is that the ideal pendulum has mass m and string of length L, and this means that m and L can take different values. There is no single pendulum with definite measurements that is the ideal pendulum. If we take the ideal pendulum to be any of these indifferently – again, sometimes as one, sometimes as another – we run into the same problem we saw with actual concrete objects. That is, we are often reasoning with the ideal pendulum in contexts in which we are not taking it to have any definite measurements at all. Yet our usual practice with it is to take it to be a definite pendulum.
Beyond this, Contessa thinks that the analogy to fictional characters shows a more serious difficulty with taking fictional models to be possible concrete objects. If we take another fictional model, the Rutherford model of the atom, “fitting the description of the Rutherford model of the atom is neither a necessary nor a sufficient condition for something to be the Rutherford model of the atom” (p. 222). It is not sufficient: Even if something fit the description of the Rutherford model, it is not the Rutherford model, which was proposed as a model of atoms, not as being an atom itself. The model is not that of which it is the model, and therefore, even if there were possible atoms described by the model, none of them could possibly be the model itself. It is not necessary: It is true that the electron in the Rutherford model orbits the nucleus, but there are no literal orbiting electrons in the Rutherford model; but there would inevitably be if the Rutherford model were a possible atom.
Thus we move to the third option. Perhaps fictional models are actual abstract objects. Thus, while the Rutherford model does not actually exist as a concrete physical system, it actually exists as an abstract object. This accommodates the idea that it is neither necessary nor sufficient for something to fit the description of the Rutherford model in order to be the Rutherford model. The tricky thing at this point is that we still seem inclined to attribute to fictional models things that seem odd if they are abstract objects – for instance, the ideal pendulum swings back and forth. Indeed, we seem to need it to do so in order to use it the way we do. But what sense does it make to say that an abstract object swings back and forth?
What Contessa wants is to give an account that has the attractions of both the possible concrete account and the actual abstract account. How do we put them together? He suggests that we return again to the analogy to fictional characters. It’s generally recognized that any adequate account of fictional characters requires us to make sense of what Contessa calls internal sentences and external sentences.1
An external sentence would be something like, ‘Sherlock Holmes is a fictional character.’ For fictional models, external sentences describe them specifically as models, e.g., ‘The Rutherford model of the atom was created by Ernest Rutherford.’ When we say that this is true or false, we do so by going to the actual world and getting evidence. An intellectual historian discussing the matter might look at the question of whether the Rutherford model of the atom was actually created by Hantaro Nagaoka.2
Internal sentences are things like, ‘Sherlock Holmes is a detective who lives in London.’ In fictional models an example would be, ‘In the Rutherford model of the atom, electrons orbit the nucleus.’ We recognize, Contessa says, that these things are not literally true, but we treat them as true in some sense. Our own view is that Contessa is going wrong here, or, at least, that there is no obvious sense of ‘literally’, however we abuse the term (which we have to do to be talking about ‘literal truth’) in which we can make this claim work, unless it just ends up meaning that this sentence is not an external sentence. The reason he is saying this is that he thinks it shows a way in which the actual abstract accounts and the possible concrete accounts are not accommodating intuitions. Taking fictional models to be actual abstract objects seems to leave no sense in which we can say that the internal sentences are true. On the other side, the possible concrete account can accommodate this, but not, apparently, their being true only in a sense. We don’t think either of these is strictly true (abstract objects can have internal content and the possibility of concrete possibilia lets us attenuate truth attributions), but it pushes Contessa to his own view, which he calls the dualist account, which is interesting in its own right.
On the dualist account, “a fictional model is an abstract object that stands for one or other of a set of possible concrete systems” (p. 224). External sentences describe the actual abstract object. This actual abstract object can then stand for possible concrete systems, which are described by the internal sentences. Note that this is strictly dualistic: the internal sentences do not describe the actual abstract object at all, and the external sentences do not describe the possible concrete systems at all. But, Contessa suggests, we can take the internal sentences to be true of the abstract objects “by proxy” (p. 224), in the way that we might take sentences about movie characters to be true in a sense of the actors.3
There are potential questions about the standing-for relation used, here, but Contessa wants us to take it fairly broadly, as being just another example of the common sort of relation of ‘standing for’ something, as when a name stands for a person, or blue on a map stands for a body of water, or a finger stands for a counted object. We are not convinced that this is adequate; in particular, we think that all of these are rather different relations. One of the reasons they are all different relations is that the standing-for relation can only exist within a broader system, and the systems are all different here. Presumably there is a system that could make the standing-for relation work in the case of fictional models, but we really do need to know what it is, if we are to understand the dualist account properly. Fortunately, Contessa does, in discussing another point, give us part of what this would be:
On the dualist account, a scientist creates a scientific model by publicly describing a possible system in an appropriate context and manner and proposing it as a model of a certain (kind of) actual system. For example, if Rutherford is the author of the Rutherford model of the atom, he created it by describing a certain system in his 1911 paper and by proposing it as a model for the atom. (However, it is important to note that, according to the dualist account I defend here, the model is not the possible system described by Rutherford but the abstract object that stands for it and that was actually generated by Rutherford’s speech act. (p. 225)
The original description by which the model is created, Contessa calls the generative description of the model. It is necessarily correct (it is the standard that makes the model), but it is not necessarily complete (there may be further aspects of the model in need of exploration and investigation). The fact that a fictional model can have aspects that are not yet known (because they have not yet been investigated) is interesting and important, but Contessa admits that how this works still needs further study.
If later scientists need to modify the model, it is the generative description they modify; for instance, they might provide specific values where the model itself does not specify them, or they may change some element of the model in order to fit better whatever they are doing with it. Of course, this means that over time models may change into other models; Contessa suggests that the way in which this happens means that there is no particular line to be drawn for ‘when’ the changeover happens; such lines, we take it, are largely drawn conventionally in light of broader concerns about inquiry.
Contessa largely argues for the dualist account by a sort of elimination: not actual concrete, not merely possible concrete, not merely actual abstract, therefore actual abstract standing for possible concretes. There are other possible views, however; for instance, Contessa takes it to be the case that the model is in reality the actual abstract, although only insofar as it has the standing-for relation with possible concretes, but one could presumably reverse this – for instance, we could take the model to be the possible concretes, with the actual abstract formed as a sort of shorthand or summary of them. (We think Contessa’s proposal is much more plausible than this would be, but his argument does not rule it out, and in the combinatorial wheel of academia, someone is bound to propose it as an alternative sooner or later.) No doubt the account could also be varied by changing the standing-for relation into something else – while ‘standing-for’ has a plausibility to it, Contessa never really argues for why it would need to be a standing-for relation in particular. Fictional models are often idealized, so one could propose an idealization or abstraction relation instead.
More intriguing, perhaps, if we follow the fiction analogy, is that one of the things that is clear in the case of fictional characters is that there is not a single abstract/concrete distinction in play. There are several different ones (cf. Thomasson’s theory of dependence). For many of these distinctions, it’s also not clear that the distinction is really exhaustive and exclusive — some of them seem to allow gaps (neither abstract nor concrete) and gluts (both abstract and concrete). All of these are points in need of further consideration. Nonetheless, Contessa’s argument is a great contribution, and a good example of an argument that contributes simultaneously to philosophy of science and philosophy of fiction.
These are most often called intrafictional and extrafictional today, in part because the distinction is recognized not to be exhaustive of the kinds of fictional context that have to be accommodated, but the terminology of internal and external is still sometimes used.
Nagaoka’s model has some features in common with Rutherford’s, and Rutherford certainly knew of Nagaoka’s model, but it’s generally agreed that the two are distinct, and that their similarities are probably a matter of discovered convergence (separate lines of research that began to be recognized as similar) rather than direct influence. The point, of course, is that we can actually discuss this matter, and everything we look at is actual.
We don’t want to get distracted by it, but this analogy puzzles us, because the actors are, of course, actual concrete objects, not abstract, and the situations in which we would say that it’s true that Mark Hamill fought a Sith Lord in a galaxy far, far away seem mostly to be in fun. Perhaps it would be better to reverse the analogy – we can take sentences about possible actors to be true of acting roles “by proxy,” and presumably directors often do when casting and actors often do when working out how to play their roles. But Contessa, of course, just needs the analogy to say that we can transfer truth attributions from one thing to an associated thing.